Table of Content

25 March 2023, Volume 32 Issue 3

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Theory Analysis and Methodology Study

Parallel Machine Scheduling with Order Splitting and Matching Type

ZHENG Feifeng, JIN Kaiyuan, XU Yinfeng, LIU Ming

2023, 32(3):  1-7.  DOI: 10.12005/orms.2023.0072

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In recent decades, the applications of shared manufacturing resources have caught much interest. Manufacturing resource sharing provides a new service mode for various production industries, and efficientlyimproves the utilization of idle resources and customer satisfaction. Therefore, there has arisen a series of manufacturing sharing platforms in China. As a third-party service platform connecting customers and manufacturers, one sharing platform matches scattered and idle manufacturing resources with customized needs of customers. A satisfying manufacturing resources sharing plan, i.e., an efficient scheduling scheme, can not only reduce the production cost of enterprises, but also shorten the delivery times of customer orders. Thus, it is an interesting and important issue to provide sharing platforms with efficient scheduling schemes for completing any given customer orders. Motivated by the above observations, this work aims to depict the operation of a shared manufacturing platform,and produce an optimal or near optimal solution including resource utilization and order processing schedule. Taking 1688 Tao platform as an example, the sharing platform is described as one parallel machine scheduling problem with machine-order type matching and order splitting. Customers demand various types of products in their orders, in the sharing platform. The platform needs to select a subset of available machines (i.e., representing manufacturers) among idle machines, which have registered in the platform, to complete the given orders.Each machine can only process a few types of customized orders, and thus the selected machines must cover all types of the customer orders, ensuring that all the orders can be processed by the machines. For a given set of customer orders, the greater the number of orders a machine can process, the larger the processing capacity of the machine. It is also assumed that all the machines are of the same processing speed. There occurs a fixed processing or rental cost once any machine is used, and the cost is usually in accordance to the length of the planning time horizon, i.e., the time length of rental. Orders can also be split into sub-orders with integer lengths and processed on valid machines simultaneously.Therefore, the corresponding order can be completed and delivered sooner, resulting in a higher level of customer satisfaction.
This work focuses on the objective of minimizing the sum of total processing cost of machines used and total completion time of orders.We first establish an integer linear programming model for the considered problem, and give two fundamental properties of the problem. Furthermore, a theoretical lower bound is derived by relaxing the processing capabilities of the machines. With the relaxation, all the machines are able to process all types of orders. In this case the selection of machines reduces to the decision on the number of machines used. The commercial solver CPLEX is employed to generate optimal solutions for small-scale problem instances. For medium and large-scale instances, CPLEX cannot output even feasible solutions within a limited time. Therefore, a Capability-Based Greedy(abbr. CBG)heuristic and an improved Genetic Algorithm(abbr. GA)are proposed to solve the considered problem. The main idea of algorithm CBG is to select a subset of available machines one by one in an intuitively greedy mode until all the orders can be satisfied by the selected machines. The orders are then processed in the Shortest Processing Time(abbr. SPT)sequence. After the assignment of each order, it requires that the difference of workloads between the machines which are able to process the order is as small as possible, i.e., the difference is at most one. In the improved GA, the solution of CBG serves as one of the initial solutions so as to accelerate the iteration process. We also test various instances to determine the best parameter settings of GA. We carry out extensive numerical experiments. Numerical results show by comparing CBG and GA with the lower bound in small, medium and large scales that the performances of CBG and GA are very close to the exact method of CPLEX. With regard to running time, CPLEX consumes a lot of time, while both of CBG and GA run much faster than CPLEX does. Considering both solution quality and time consuming, CBG may be an efficient and effective method in producing a complete solution of machine selection and order processing schedule in practice, while GA provides slightly better solutions with more running time. In addition, the larger processing capabilities of machines indicate the smaller gap between the solutions of heuristic algorithms and the lower bound. It indicates that the sharing platform shall give priority to lease machines with largest processing capacities. On the other hand, it needs to balance the machine rental cost and the total work of orders to decide how many machines are to be used. If the rental cost of a machine is high, a smaller number of machines shall be selected for processing, and vice versa. One of future research issues is to develop more efficient algorithms, and considering the scenario with setup time is also an interesting variation.

Product Quality and Quantity Decision of Bike-sharing Supply Chain Based on Smart Contract

TAN Chunqiao, LI Jinzhan, DENG Zhicheng

2023, 32(3):  8-14.  DOI: 10.12005/orms.2023.0073

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With the popularity of mobile Internet devices and the continuous development of platform economy, some new online industrieshas been spawned. Shared bicycles are growing continuously with the maturity of Internet of Things and Internet technology, and have become an effective way to solve people's “last kilometer travel problem”. Bike providers can get returns from sharing their idle goods. However, with the deep involvement of Internet companies, the business has changed from the transection that everyone can provide and use, to the business of renting from Internet platforms to consumers. It is urgent to come up with a more effective business model that can return to the nature of sharing economy and promote the sustainable development of bike-sharing business. Blockchain network is regarded as a new decentralized and reliable technology. Blockchain can strengthen trust between entities and provide conditions for transactions through encryption technology. In order to promote the sustainable development of shared bicycles, in this paper we design a new bike-sharing supply chain based on blockchain technology.
We propose a design of the supply chain of shared bikes based on smart contract. The complete service process of shared bikes is an Internet of Things-based consumption system, which mainly includes three sections: mobile, bicycle and remote sever. The smart contract module is embedded into the communication module of the original chip. The embedded chip can process the GPS information obtained from the positioning module and form the consumption bill. We make a comparative analysis of two supply chains in the bike-sharing industry, one of which is the existing supply chain centered on large Internet trading platforms and the other is our decentralized supply chain based on blockchain technology. The game theory of oligopoly market and the method of differential calculation are adopted to solve the Nash equilibrium of two supply chains. We focus on the smart contract-based bike-sharing supply chain. We analyze the operation strategies changes of the supply chain enterprises. Finally, we adopt the method of data simulation to imitate the competition of oligopoly market, and verify the model conclusions.
In the shared bicycle supply chain centered on the Internet platform, there is a unique Nash equilibrium decision between platform providers and suppliers. Therefore, it is beneficial for bike-sharing supply chain to use smart contracts, which will make the supply chain more transparent and reduce invalid competition. Blockchain transaction costs have a significant impact on enterprise decisions on the smart contract supply chain. When enterprises use smart contract technology to build a shared bicycle supply chain, they should choose a blockchain network with lower transaction costs. The pricing of shared bicycle service has a significant impact on profitability of the supply chains. Shared bike supply chain based on smart contract performs better efficiency.
With the increasing popularity of shared bicycles, operation, maintenance and recycling are becoming more and more important. These are also important issues worth studying.

Market Competition, Government Innovation Incentives and Pharmaceutical Enterprises' Innovation Decisions

ZHANG Xinxin, SHEN Chenglin

2023, 32(3):  15-21.  DOI: 10.12005/orms.2023.0074

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Pharmaceutical industry is a typical innovation-driven industry. R&D innovation is not only a basis of production and development of this industry, but also an important source of long-term stable profits and continuous competition for pharmaceutical enterprises. However, the high risk, high cost and high technical complexity of new drug creation have induced many pharmaceutical companies to small innovation and intensive marketing rather than blockbuster innovation. On the other hand, due to the strong spillover effect of pharmaceutical innovation, it is hard to achieve social optimal by market mechanism alone. In this regard, it is necessary for governments in various countries to put forward innovation incentive policies from the national strategic level to enhance pharmaceutical enterprises' innovation incentives and solve the market failure in the research and development of new drugs. However, most previous literature took innovation incentive policy as a whole, and lacked the analysis of the differences within the policy. In particular, little attention has been paid to examine potential differences in incentive effects of various policy instruments. In view of the quasi-public nature of drugs, pharmaceutical market performance is constrained by various factors such as medical insurance policy and therapeutic competition. Thus, it is necessary to further clarify the choice of innovation incentive policy tools as well as their application conditions.
To address the above problems, this paper subdivides innovation incentive policy into cost compensation mechanism (characterized by government innovation cost sharing) and innovation output incentive mechanism (characterized by government strategic innovation subsidy). More specifically, we develop a stylized model comprising two representative pharmaceutical enterprises who produce and sell partially substitutable drugs such as different drugs for the same disease. The two enterprises have two options. One is to conduct R&D innovation and produce innovative drugs, and the other is not to conduct R&D innovation and produce general drugs. We investigate optimal decisions of pharmaceutical enterprises in a competitive market across three different incentive schemes, namely, pure market mechanism (i.e., without government intervention), government innovation cost sharing, and government strategic innovation subsidy. We further compare equilibrium outcomes across the above three incentive policies and examine the influence mechanisms of different incentive policies on drug prices, pharmaceutical enterprises' profits and pharmaceutical market allocation. The main results are as follows.
First, three incentive mechanisms, i.e., pure market mechanism, government innovation cost sharing, and government strategic innovation subsidy can induce pharmaceutical enterprises to conduct R&D innovation. Notably, only the government strategic innovation subsidy can allow pharmaceutical enterprises to achieve social optimality in innovation investment, while the pure market mechanism and the government innovation cost sharing will lead to distortion of pharmaceutical innovation investment in the majority of situations. Second, the government innovation cost sharing always enhances the pharmaceutical enterprises' innovation rewards, while the government strategic innovation subsidy can either enhance or reduce their innovation rewards, which depends the medical copayment level. In particular, when the copayment level is sufficiently high, the government strategic innovation subsidy will lower pharmaceutical enterprises' innovation profits. Finally, the government innovation cost sharing and the government strategic innovation subsidy can both enhance social welfare of the innovation pharmaceutical market, but have opposite different effects on prices of innovative drugs. The government innovation cost sharing will push up the innovative drugs' prices while the government strategic innovation subsidy will lower their prices.
Several managerial insights and policy implications are derived from our main research results. First of all, there is no absolute optimal policy to promote pharmaceutical innovation. Thus, the government should select desirable innovation incentive policies based on different policy objectives. Specifically, if the government aims to control drug prices and improve social welfare, it should select the strategic innovation subsidy policy. It is noteworthy that the government strategic innovation subsidy will lead to decreased innovation rewards for pharmaceutical enterprises when the copayment level is relatively high. In this regard, the government strategic innovation subsidy will lower R&D innovation incentives for pharmaceutical enterprises and increase risk of supply shortages of innovative drugs in the long run. On the other hand, if the government aims to promote the development of the pharmaceutical industry, it should select the innovation cost sharing policy to raise pharmaceutical enterprises' profitability, but such policy is not so effective to control prices of drugs. Moreover, given that the medical insurance plan has significant impact on market expansion effect of innovative drugs, which can either enhance or reduce pharmaceutical enterprises' willingness for pharmaceutical innovation, the government should reasonably match innovation incentive policies and medical insurance reimbursement scheme according to social and economic development goals, so as to improve the sustainability of innovation drug supply and achieve a “multi-win” situation for pharmaceutical enterprises, patients, medical insurance organization and the government.

Facing Up or Waiting for Opportunity: Analysis of Economic Policy Uncertainty Influences Investment Decision of Energy Enterprises

WEI Wei, HU Haiqing, GANG Cuicui

2023, 32(3):  22-27.  DOI: 10.12005/orms.2023.0075

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We discuss the influence of economic policy uncertainty on the physical investment and virtual investment of energy enterprises, with Chinese energy enterprises sample from 2007 to 2019, and further tests the intermediary effect of physical investment cost and virtual investment income. We find that economic policy uncertainty has a negative effect on physical investment, while uncertainty plays a role in promoting virtual investment. Furthermore, we verify the intermediary effect of physical investment cost and virtual investment income. Moreover, robust analysis provides more evidence for our research. Our research enriches the theory of economic policy uncertainty and energy enterprise investment, and also provides a reference for energy enterprises to deal with external high uncertainty.

Clustering Algorithm of Executor Based on Hesitant Fuzzy Linguistic Decision Information

WU Shuangsheng, LIN Jie, ZHANG Zhenyu

2023, 32(3):  28-35.  DOI: 10.12005/orms.2023.0076

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With the rapid development of the economy and society and the continuous deepening of reform and opening up, many lawsuits have increased significantly. Some effective legal documents have not been enforced, which is called “difficult to execute”. For a long time, “difficult to execute” has not only been a pain point that plagued the judicial enforcement of the people's courts but also a hot spot that has been strongly reflected by the people and has attracted widespread attention from all walks of life. In judicial execution, it is difficult for the judge to retrieve and extract high-value information timely and accurately due to a large number of historical property concealment cases, few judges, and complex property concealment clues. In addition, under the influence of such factors as case handling experience, life experience, knowledge accumulation, information asymmetry, and personal bias, judges have systematic reasoning biases in judicial decision-making, which to some extent reduces the accuracy of judgment. If the traditional off-line execution mode is still adopted for one-by-one screening and judgment, it will not only lead to low execution efficiency but also be difficult to ensure the trial quality of each case. When multiple execution cases are received, the judge needs to further determine the priority of the execution cases, and accordingly allocate judicial resources reasonably.
　To address the “difficult to execute” problem of the court, this paper applies the fuzzy clustering analysis method to the judicial execution field. The data type of clustering is extended to hesitant fuzzy linguistic information, and a complete evaluation system of the hidden property behavior of the person subjected to execution is constructed. By estimating the quantified probability of hidden behavior of the person subjected to execution and ranking the execution cases, it provides decision support and judgment basis for the judge to determine the focus of investigation and control. At the same time, it avoids the disadvantages of experiential judicature and improves the objectivity and reasonability of judicature decisions. This paper analyzes the limitations of the existing hesitant fuzzy linguistic distance measures, defines the hesitance degree of hesitant fuzzy linguistic information, and develops a new method for distance calculation of hesitant fuzzy linguistic information. Using the idea of maximizing deviation to determine the optimal attribute weight, a hesitant fuzzy linguistic agglomerative hierarchical clustering algorithm based on maximizing deviation is proposed. The effectiveness of the evaluation system and the clustering algorithm is verified by the cluster analysis process of the executor in the context of hesitant fuzzy linguistic decision information.
Solving the difficult execution problem is a complex systematic project. In future work, it is necessary to refine the research questions and application scenarios, such that execution cases will be divided into enterprise execution cases and people's livelihood execution cases, and decision-making situations will be divided into individual decision-making and group decision-making. The applicability and pertinence of the model will be improved.

An Improved Differential Evolution Algorithm for Solving Nash Equilibrium Problem and Generalized Nash Equilibrium Problem

ZHANG Guoqiang, ZHAO Guodang

2023, 32(3):  36-42.  DOI: 10.12005/orms.2023.0077

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The purpose of game analysis is to predict the equilibrium result of the game according to the game rules, that is, Nash equilibrium.Nash equilibrium is the most basic and important equilibrium concept in the non-cooperative game model.Although some theorems have explained the existence of Nash equilibrium (including mixed strategy Nash equilibrium), the solution of Nash equilibrium is an NP-hard problem. The existing methods have strict restrictions on constraint conditions and objective functions. When the payoff function of the game player is non-concave, multimodal, or highly nonlinear, it is difficult to solve Nash equilibrium, which limits the general application of game theory. Therefore, it has become an urgent problem to develop a general and efficient algorithm for solving Nash equilibrium.
Based on the mining of the concept of relatively dominant strategy, this paper improves a differential evolution algorithm for solving the traditional Nash equilibrium problem(NEP)and the generalized Nash equilibrium problem (GNEP) of nonlinear continuous games.The algorithm has three advantages: (1)simple operation and easy implementation. Only three parameters need to be assigned (population size, crossover probability and variation factor), and there is no need to set multiple parameters. (2)Wide spectrum. As we all know, it is much easier to solve a classical NEP than to solve a GNEP. The algorithm in this paper has no strict restrictions on the payment function, and can be solved without any changes to the algorithm. (3)The algorithm has low complexity and high accuracy. In the process of evolution, there is no need to traverse the entire population to find the best individual. The excellent individual can be retained by comparing two pairs, which not only maintains the diversity of the population, but also enhances the global optimization ability of the algorithm.
In this paper, four NEP and GNEP in the existing literature are selected, no matter simple or complex objective functions. The experimental results show that: (1)The algorithm can solve NEP or GNEP with a global optimal solution, and can deal with multidimensional, non-convex and other complex objective functions, and has certain wide applicability. (2)For NEP, compared with the state-of-the-art algorithm (NDEMO), this algorithm only needs less iterations and running time to obtain Nash equilibrium, and its efficiency is about twice that of NDEMO. (3)For GNEP, the algorithm can randomly select the initial point, not only can obtain the equilibrium solution, but also has better efficiency than other algorithms.
The main objective of this paper is to solve the equilibrium problem of complex objective functions such as nonlinear demand function and cost function in the non-cooperative continuous game model. A general algorithm for solving NEP or GNEP with a global optimal solution is given, which extends the classical non-cooperative game model, widens the application scope of Nash equilibrium in the real economy, and provides powerful research tools and new research objects. However, when the model contains multiple global solutions, the convergence conditions of the algorithm cannot be met, resulting in the solution failure. This is also the problem that this paper will study in the next step.

Manufacturer's Advertising Investment and Price Game Based on Platform Retailing

ZHAO Ju, CAO Yuanhong, SUN Cuiying, LI Xiaozheng

2023, 32(3):  43-49.  DOI: 10.12005/orms.2023.0078

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With the vigorous development of e-commerce, platform retailing is rapidly emerging, such as Amazon and Jingdong. More and more brands enter online retail platforms in the marketplace model (i.e., commission model), while platforms provide services for brands to broaden market demand. In the online retail environment, advertising investment is the most important way for e-commerce platform sellers to attract consumers. Online platforms use platforms' superior resources to push multi-channel advertising according to brands' advertising needs, and charge brands the corresponding level of advertising service fees. Therefore, brands who reside in the platform can purchase multi-channel advertising push services to increase the market competitiveness. In addition, in the era of e-commerce, many retail giants (e.g. Jingdong, Walmart, etc.) hold the dominant power in the supply chain system, while the power of brands is often asymmetrical. Based on the above background, this paper considers that two brands with asymmetric decision-making power consign two alternative products through the same retail platform, and studies the advertising investment and price game strategy of the brands under the platform's dominance and the decisions on advertising service pricing and consignment revenue sharing ratios for the retail platform. The literature about asymmetric power competition mainly focuses on price competition, but it does not consider the decision of advertising service level. As a more and more important product advertising service in business practice, it not only affects consumers' purchase choices, but also stimulates market demand. Under the asymmetric decision-making power structure, this paper studies the advertising service level decision-making and product pricing decision-making, which is of certain theoretical significance and practical value.
This paper constructs Stackelberg game model dominated by a retail platform and Stackelberg game model of two asymmetric brands. Decisions of the retail platform and the two brands are divided into three stages: In the first stage, the retail platform first decides the revenue sharing ratio of the unit product and the unit advertising service fee charged to the two brands. In the second stage, the leading brand decides its retail price and advertising level. In the third stage, after observing the decision of the retail platform and rival brand, the follower decides its retail price and advertising level. In this paper, we use exponential demand function to describe the market size of the two brands and obtain the refined Nash equilibrium solution by backward induction method. And the research results are analyzed by analytical method and example analysis method.
The study shows that, the advertising investment and price competition strategies of the two brands are affected by the first-mover advantage and cost advantage. The high-cost leading brand chooses the low advertising investment and low retail price strategy, while the follower chooses the high investment and high retail price strategy. The low-cost leading brand chooses the strategy of high advertising investment and low retail prices, while the follower chooses the strategy of low advertising investment and high retail prices. In addition, the increase in the elasticity coefficient of advertising service and cross price elasticity coefficient will intensify the competition of brand owners in price and advertising service level, and the retail platform will reduce the unit advertising service fee to attract more advertising investment from manufacturers and increase the proportion of revenue sharing. However, when the price elasticity coefficient increases, the retail platform will take the opposite strategy.

Evaluation of Comprehensive Competitiveness of Coastal Ports: An Extended MABAC Method Based on Cloud Model and Game Weight

LIU Peide, PAN Qian, ZHU Baoying, WANG Xiyu, WANG Dongyang

2023, 32(3):  50-55.  DOI: 10.12005/orms.2023.0079

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The seaward economy is the dynamic evolution of China's national economy from land to offshore, and from offshore to deep sea. As one of the bases for the development of seaward economy, ports connect land economy and ocean economy, and provides strategic resources and stable support for the 21st Century Maritime Silk Road to enhance international competitiveness. In recent years, with the development of the economy and the change in the world transportation structure, the accurate and reasonable evaluation of the comprehensive competitiveness of ports is a fundamental issue in exploring the development of the port itself. Scientific evaluation of the comprehensive competitiveness of ports can help the port clarify the current development situation, and improve the weak links of the port development while maintaining the development of the port's own advantages, so as to realize the improvement of the comprehensive competitiveness of the port and promote the sustainable development of the port. The current comprehensive competitiveness evaluation models of ports have disadvantages such as they cannot handle abnormal data, the weighting method cannot reflect expert information comprehensively, and the evaluation method is limited. In this context, it is of great theoretical significance and application value to improve the evaluation model of comprehensive competitiveness of ports and explore the influencing factors of comprehensive competitiveness of ports to develop port economy and promote high-quality development of ports. To break the limitation of the existing evaluation models of comprehensive competitiveness of coastal ports, firstly, this paper selects 18 ports of five port groups as sample ports and chooses 5 main indicators and 19 secondary evaluation indicators to establish a port comprehensive competitiveness evaluation index system. Then, to address the current existence of evaluation models with higher robustness to missing and anomalous data and the limitations of the model options available for solving the weights, this paper uses a backward cloud generator to generate cloud models (CMs) for data of ports from 2010 to 2019. And based on the obtained data, linguistic terms Best-Worst method (L-BWM) method is proposed to calculate the subjective weights by combining linguistic terms and Best-Worst method (BWM), cloud model-criteria importance though intercrieria correlation (CM-CRITIC) method is proposed to calculate objective weights by combining CM and criteria importance though intercrieria correlation (CRITIC). The combination weight calculation model of game theory is utilized to determine the combination weights of indicators. The model can minimize the deviation between the obtained combination weights and the subjective and objective weights in order to obtain relatively scientific combination weights in a reasonable and effective way, thus improving the quality of evaluation results. Simultaneously, CMs and the combined weighting method of game theory are applied to multi-attribute border approximation area comparison (MABAC) method to establish the MABAC port comprehensive competitiveness evaluation model. The model takes the distance between each alternative and the Bored approximation area (BAA) into account, along with the potential profit and loss values. In order to obtain more accurate and effective ranking results, uncertainty among decision-makers (DMs) and ambiguity in the decision-making environment are also taken into account. At the same time, the results of the model are stable, the computational process is simple and logical, and it can be combined with other methods. Finally, the model is applied to the comprehensive competitiveness evaluation and single-indicator analysis of 18 coastal ports in China from 2010~2019. The evaluation results indicate that the development level of domestic coastal ports is uneven and polarized at present. From the perspective of port groups, the Yangtze River Delta port group is at the forefront of development, the Pearl River Delta port group and the Bohai Bay port group are in the middle level of development on average, and the southwest coastal port group and the southeast coastal port group are relatively backward in development. The development level of port groups is highly differentiated. From the perspective of the ports in the group, Ningbo Zhoushan Port has the highest overall competitiveness, Shantou Port has relatively poor overall competitiveness, and Dalian Port has the closest development to the average development level of the sample ports. Meanwhile, based on the evaluation results of the comprehensive competitiveness of ports, this paper puts forward countermeasures for developing ports economy and improving the comprehensive competitiveness of ports from the factors affecting the comprehensive competitiveness of ports.

Study on Dynamic Game Between Consumer Finance Providers and Multiple Ownership Users

ZHANG Xinyu

2023, 32(3):  56-64.  DOI: 10.12005/orms.2023.0080

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More and more consumer finance enterprises focus on segmentation of consumption scenarios. This paper explores the relationship between two groups in consumer finance market from the perspective of dynamic game, that is, the provider of consumer financial installment products (CFIP) provides services and users can select the CFIP service automatically. Studies have shown that under certain conditions of infinite repeat games, there is a specific subgame perfect Nash equilibrium. The subgame of the finite-time repeat game is a perfect Nash equilibrium, which enables the same service portfolio for each of the CFIP at each stage, so that the CFIP can develop a grid-based service portfolio for different groups of users. In an ideal world, the CFIP can obtain a larger market share and benefit when it introduces a variety of differentiated, grid-based service combinations. Based on survey data, the simulation verifies the price monopoly status of the CFIP in the monopolistic market and the dynamic game process of various CFIP in the oligopoly market, and provides the method to develop service portfolio according to the characteristics of user groups. The management and marketing suggestions are given, which has a referential significance for CFIP to enhance corporate competitiveness and obtain stable growth returns.

Research on Robust Cooperative Dual Equilibria with Symmetric Strategy Uncertainty

LUO Guimei

2023, 32(3):  65-69.  DOI: 10.12005/orms.2023.0081

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In real life, people are not completely rational. Then when two competitors make decisions from their own selfish point of view at the same time, it is not always the best to maximize their own interests or minimize their own costs. On the other hand, there exist much uncertainty and incomplete information in a game. Based on the fact that there exists uncertainty in non-cooperative games or it is not always appropriate from one's own selfish perspective, we assume that competitors make decisions fromthe view of the lowest cost of the opponent and uncertainty. Then a robust cooperative dual equilibria model with strategy uncertainty for two players is introduced. In the model, each player wants to minimize the opponent's cost where he/she knows his/her cost matrix exactly while he/she can not evaluate his/her own strategy set accurately. Furthermore, the strategy set of each player can be estimated at a symmetric bounded closed set which is a subset of the mixed strategy set. In what follows, the robust optimization technology and dual theory are adopted. Then some results are obtained as follows:
When elements in his/her own uncertain strategy set are taken as l₂-norm, the problem of the lowest cost of the opponent can be transformed to a second-order cone optimization problem, while the problem of the lowest costs of both sides can be converted to a second-order cone complementarity problem. When the element in the uncertain strategy set is considered as l_1∩∞-norm, the corresponding problem of the lowest cost of the opponent can be transformed to a linear programming problem, and the problem of the lowest costs of both sides can be converted to a mixed complementarity problem. Finally, we present a numerical experiment to illustrate the reasonability and validity of the model. Furthermore, weshow that the model can be applied to the optimal reinsurance.
In the work, strategy uncertainty and cooperation are discussed at the same time. It can be regarded as a generalization and supplement of a non-cooperative bimatrix game.

Multi-mode Robust Project Scheduling Optimization in Emergence Rescue with Stochastic Resource Breakdown

WANG Yanting, HE Zhengwen

2023, 32(3):  70-77.  DOI: 10.12005/orms.2023.0082

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In recent years, with the frequent occurrence of various types of emergencies such as COVID-19, fire, earthquake and so on, how to carry out emergency rescue effectively and efficiently has become a crucial research topic. Emergency rescue, however, is highly uncertain and dynamic due to complex environment and urgent resource deployment. According to a statistic data analysis, the main reason of the accident is that there is no flexible contingency plan to guide the rescue to go on in order and along with serious shortage of rescue materials and professional person. Existing contingency plans for emergencies have only concerned the establishment of the rescue organization, division of personal responsibility, but they can notgive specific guidance for resource and time scheduling. Therefore, developing a robust schedule before the accident plays a great role for emergency rescue. A stable and reliable rescue plan and its effective response can greatly reduce the risk of disaster diffusion and serious economic losses. By using the theory of project scheduling under uncertain environment, this paper studies the emergency rescue problem with random resources interruption. On the one hand, before the accident occurs, the proactive project scheduling method is used to develop a high robust baseline schedule to guide the rescue process to go on in order. On the other hand, once an accident occurs, the reactive project scheduling method is invoked to take appropriate strategies in response to disruptions in order to ensure the feasibility of the baseline schedule as far as possible and also the smooth development of the rescue work.
Based on this background, an emergency rescue scheduling optimization model is formulated with two sub-models included. The first sub-model tries to maximize total project robustness where both time buffer robustness and resource buffer robustness are considered under the constraint of renewable resources and project deadlines. The second sub-model indeed tries to minimize the adjustment losses once disruption occurs. The two sub-models are associated with the baseline schedule that the former provides an original baseline for determining the actual start time of activities, and the latter will adjust the baseline with the help of simulation tool at each disruption point. Through the integrated optimization of the above two sub-models, we can obtain the quantitative coordination between the preparation of emergency rescue plan and emergency disposal, and ensure the most effectively realization of the rescue objectives.
For the NP-hardness of the problem, an improved tabu search heuristic algorithm is developed where the solution is represented by an array of four lists, including an execution mode list, an activity list, a time buffer list and a resource buffer list. At the same time, in order to further improve the efficiency of the algorithm search, the algorithm neighbourhood search strategy is developed based on the characteristics of the solution representation. Then, the model and algorithm are applied to the case of a real blowout event in DG oilfield. In order to highlight the urgency and importance of emergency rescue, the accident case is mainly divided into three stages, and according to the changes of the key process data in the development of the accident, three stages are simulated respectively, and then the simulation results of different stages are analysed in detail. Moreover, the performance of the robustness baseline is compared with the actual schedule of the minimizing project makespan. The results show that the robust scheduling model can be used to arrange the schedule plan in emergency rescue, so that the activities can obtain appropriate and reasonable buffer and better resist the uncertain factors. Furthermore, when the baseline schedule has to be changed due to unexpected circumstances, the reactive scheduling research results can be used to adjust the baseline quickly and effectively, decreasing the total adjustment loss by about 20.4% compared with the makespan minimization model. It can be seen that through the cooperation of proactive and reactive scheduling methods applied in the emergence rescue, it can effectively improve the baseline robustness and strengthen its capability against resource disruption case, and moreover reduce the project loss to a greater extent. The conclusion of this paper can provide constructive adviceand flexible guidance for similar accident emergency rescue work. Although this paper has done some innovative work on the robust scheduling problem of emergency rescue projects, there is still a lot of problems that need to be solved. In the future, we should consider the scheduling problem of emergency rescue activities with preemptive rights. In the actual emergency rescue process, there are priorities among various activities, so it is also of great significance to consider the right of preemption.

Mathematical Model and Algorithm Design for Collaborative Vehicle Routing in Three-echelon Transportation with Complete Information Sharing

LYU Xiaohui, WANG Nengmin, YANG Zhen

2023, 32(3):  78-84.  DOI: 10.12005/orms.2023.0083

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Intercity goods distribution for e-commerce is usually realized in a three-echelon transportation network, where the delivery of goods from suppliers to customers passes two urban consolidation centres, one located in the origin city, and the other in the destination city, before arriving at the customers. In order to improve distribution efficiency, service quality, and reduce transportation costs, many cities in our country have carried out collaborative transportation pilot work, established resource-sharing urban consolidation centers, and constructed a collaborative three-echelon transportation network. The continuous development of digital platform technology provides information sharing foundation for collaborative transportation, reduces information asymmetry between logistics companies, integrates the supply and demand information of transportation requests, and reduces the empty load rate and improves transportation efficiency. The characteristics of transportation request delivery timeliness and mutual coupling in a three-echelon transportation network put forward new challenges for collaborative transportation. Based on the operation scenario of the digital platform providing information sharing for collaborative transportation, this paper studies a collaborative transportation problem in three-echelon transportation considering time windows constraints with the minimum of transportation cost. In this problem, all requests are served in a three-echelon transportation network, where goods are first delivered from suppliers located in a city (the city of origin) to their customers in another city (the city of destination) through two urban consolidation centers located at the outskirt of the two cities. Multiple shippers and customers are clustered in pick-up zones and delivery zones respectively. To handle the complicated linking constraints in a collaborative three-echelon transportation network, a multi-start iterated local search algorithm is proposed to obtain the approximate optimal solution of the problem. In the proposed algorithm, based on the coordination constraints among different echelons and the characteristic that each request in a three echelon transportation network must be served by the same carrier, the neighborhood structure is constructed by adding local branching constraints in local search operations and two perturbation strategies are adopted to select free variables in the perturbation operator. Extensive numerical experiment results have proved the effectiveness of the proposed algorithm, and demonstrated that in a three-echelon transportation network, collaborative transportation can significantly reduce the overall transportation cost. Moreover, the lower the proportion of reserved transportation requests, the more the number of transportation requests, and the larger the transportation network, the higher the possibility of collaboration among carriers, and the higher benefits can be achieved by collaborative transportation. This research enriches the study of collaborative transportation and provides quantitative decision support for carriers to solve the collaborative vehicle routing optimization problem in three-echelon transportation considering time windows with complete information sharing. However, this paper only considers the certain transportation requests, and ignores the randomness of transportation requests in the reality. Also, the proposed algorithm can only get approximate solutions for medium size and large size instances. In the future, the randomness of transportation requests should be considered when formulating a mathematical model and designing an algorithm to solve the problem with random transportation requests. In addition, accurate algorithms such as branch and cut algorithm and branch and cut and price algorithm can be adopt to obtain optimal solutions for this problem.

Optimal Price and Speed Decisions in Customer-intensive Service Systems with Boundedly Rational Customers

ZHANG Yu, WANG Jinting

2023, 32(3):  85-91.  DOI: 10.12005/orms.2023.0084

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Customer-intensive service systems are common in our daily life, such as personal care, healthcare and legal consulting. In such service systems, providing professional service requires a longer service time, which can increase customer satisfaction but also increase their waiting time. Therefore, setting an appropriate service rate is critical. When customers arrive at the service system, they decide whether to join the system based on their utility of entering the system. Due to customer limited cognitive ability, customers are usually boundedly rational and they cannot accurately estimate the utility of joining. They make the joining decisions according to their perceived service value and waiting cost. Further, servers are usually unreliable in reality and they may break down when providing service. So in this paper, we consider the customer-intensive service systems with boundedly rational customers and unreliable servers, and study the dilemma of service speed and service quality from the perspective of the service providers.
We consider a market with multiple competing service providers and each service facility is modeled by an M/M/1 queue with an unreliable server. When the server is working, it may break down. If the service of one customer is interrupted by the server's breakdown, the interrupted customer will wait in the system to resume service after the server is repaired. We assume the time between failures and the maintenance time follow exponential distributions. For the boundedly rational customers, we assume the random error in customer estimating the utility of joining follows a Gumbel distribution. Boundedly rational behavior of customers is then characterized by a logit choice model and we give their probability of choosing each server. In monopolistic and competitive situations, we investigate the revenue maximization problem of the service providers and consider the trade-off of revenue-optimal pricing and service rate. By adopting the sequential optimization approach, we derive the revenue-optimal decisions and prove their uniqueness. By comparing the optimal strategies under the two situations, we further study the effect of competition on customers' behavior, revenue-optimal decisions and the social welfare. Lastly, since customers are boundedly rational, they may enter the system even if their actual utility of joining is negative. So we study the sign of customer actual utility under the revenue-optimal decisions and give the condition that customer actual utility is positive.
By making comparisons between monopolistic and competitive situations, we find that competition may reduce the market share of each firm, but the total market share increases. Under competition, each firm sets a lower service rate to increase the service quality, but the manager may simultaneously raise the service price. Meanwhile, the social welfare increases in the competitive situation. Thus, in reality, the manager can take measures to encourage benign competition in the market, such as, providing compensation for enterprises to enter the market. From the perspective of customers, we find that when the market size is large enough, the revenue-optimal strategies lead to a negative utility for boundedly rational customers who enter the service system; however, when the market size is smaller, the revenue-optimal strategies can ensure a positive utility for customers. Similarly, there also exists a threshold of the failure rate such that customer actual utility of joining is positive when the failure rate is less than the threshold. The sign of customer actual utility changes from positive to negative with the increase of failure rate. Our work enriches the literature research on customer-intensive service systems and the findings in this paper provide a theoretical basis to optimize service operations in a competitive environment.
In this paper, we adopt the M/M/1 queue to model the customer-intensive service system and its tractability allows us to investigate the revenue-optimal decisions of the service providers. But the stylish model limits its practical applications. In the future we will extend this research to the queue model with general service times. Another extension is to characterize the boundedly rational behavior of customers by other methods rather than the logit choice model.

An Alternative Axiomatic Characterization of the Efficient Quotient Myerson Value

SHAN Erfang, ZENG Manchang

2023, 32(3):  92-96.  DOI: 10.12005/orms.2023.0085

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Acooperative game with transferable utility (TU-game) is a pair (N,v)consisting of a set N of players and a characteristic function v assigning a worth v(S) to each coalition S$\subseteq$N. The central question to be answered in cooperative game theory is how the value v(N) should be divided among the players N. The Shapley value (Shapley, 1953) provides a principled way to do this. However, it is assumed that all players can communicate with each other and also that all possible coalitions are feasible in the classical TU-game. Myerson(1977) modified this assumption by introducing restrictions in the communication among players through a graph. In this new setting, some of the coalitions become infeasible. Myerson, then, defined the graph-restricted game, and he proposed the Shapley value of the graph-restricted game as an allocation rule, now called the Myerson value, for TU-games restricted by graphs. Moreover, he presented an axiomatic characterization of the defined value using two properties: component efficiency and either fairness or balanced contributions. The component efficiency states that the worth of a component of the graph is distributed among its members. Thus generally the Myerson value is not efficient. However, in practice, the graph structure may not affect the formation of the grand coalition, but it will affect the bargaining power of players because of their different positions in the network. This prompts people to consider the effective extension of Myerson value. Several effective extensions of the Myerson value have been put forward in the literature.
Li and Shan(2020) introduced an efficient extension of the Myerson value, called the efficient quotient Myerson value, as a two-step value. The efficient quotient Myerson value proposed here distributes the worth of the grand coalition in two steps. Firstly, players within one component act collectively to bargain with other components, all components play the quotient game and obtain a payoff prescribed by the Shapley value. The surplus of the difference between the obtained payoff and the worth of the component is distributed equally among component members. An axiomatic characterization of the value for graph games is established. They show that the efficient quotient Myerson value is the unique allocation rule that satisfies quotient component efficiency, fair distribution of surplus within component and coherence with the Myerson value for connected graphs. Quotient component efficiency states that the sum of the payoffs obtained by the members within a component is equal to the Shapley value obtained by this component in the quotient game. The fair distribution of surplus within component property requires that any two members in the same component have the same payoff changes in the sub-game restricted on the component. The coherence with the Myerson value for connected graphs property suggests that each playerreceives the Myerson value in the connected graph games.
In this paper we introduce a new property, called quasi-fairness of surplus with quotient. This property means that breaking an link will exert the same influence on the quasi-payoffs of the two players associated with the link, that is to say, the quasi-payoff changes of the two players are the same, where the quasi-payoff of a player is the difference between his payoff in the original distribution rule and the amount of surplus assigned to the player. We show that the efficient quotient Myerson value can be axiomatically characterized by efficiency, quasi-fairness of surplus with quotient and coherence with the Myerson value for connected graphs. In addition, we compare this value with other allocation rules through an application example.

Shared Parking Match Model with PVR Service and Its Harmony Search

HE Shengxue

2023, 32(3):  97-103.  DOI: 10.12005/orms.2023.0086

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It is usually hard to match the supply of parking berth and the parking demand due to their different spatial and temporal distribution features. Sharing parking is an effective way to cope with the above problem by providing the slots unoccupied by its owner in a given time period for those with parking demand during the time period. Since it is very rare to supply a slot with a proper parking time window for every parking demand, the Parking Valet Robot (PVR) is adopted to deal with the above problem. PVR can move a car from a slot to another slot if the allowable parking time of the former slot is end. When using PVR, the related operation cost and the potential risk due to the using of PVR need to be considered. To solve the problem how to reduce the unnecessary translocation operation and lower the accident risk due to frequently translocation operation at the same time remaining the benefit of using PVR, this paper formulated a supply-demand matching optimization model that satisfies the reserved parking demand and designed a harmony search algorithm to solve the new model.
To formulate the sharing parking supply-demand matching problem, the parking demand time intervals and the slot supply time intervals were divided into small time slices which have the start and end time instants of the above time intervals as the delimiters. The matching of demand and supply in a given time slice is viewed as a music pitch. Put all the pitches in all time slices together to form the music harmony. Assume that the number of available supply slots is bigger than the number of vehicles with parking demand in every time slice. Obviously, the harmony defined as above is corresponding to a solution to the sharing parking supply-demand matching problem. From a given harmony, we can obtain the detailed parking schedule of any vehicle. The distance of moving during the slot change by PVR for a vehicle and the operational cost induced by slot change can be figured out easily. The sum of the total moving distance and the weighted operational cost of PVR will be used as the optimization objective. The constraints on the supply and demand of sharing parking represented by a series of similar constraints in all the time slices. The formulated model of sharing parking supply and demand matching with PVR is a nonlinear quadratic integer program. The model can be viewed as a special quadratic assignment model which is a well-known NP-hard problem. To solve the above model, the above-mentioned conceptions of pitch and harmony are used to design an effective harmony search algorithm. The key operation of pitch adjustment in harmony search algorithm is realized by swapping the positions of two vehicles parked in two slots in a time slice. The above swapping operation can avoid generating infeasible solution to the matching problem during the solving procedure if the original harmony composed of pitches of all the time slices is a proper one.
To verify the effectiveness and robustness of the proposed harmony search algorithm for the sharing parking matching problems, problems of different scales are employed in the numerical analyses. The results obtained by the new harmony algorithm are compared with those given by the classic genetic algorithm. The comparison demonstrated that the new harmony algorithm outperforms the genetic algorithm in terms of the final parking pattern with smaller operational cost and shorter moving distance. The utilization rate of the slots is greater than 80% for all the test problems except one. The computational time of the new harmony algorithm is only about 1 to 2 seconds for all the cases. The sensitivity analyses of the parameters showed the following conclusions: a. To increase the possibility of adjusting the new pitch can noticeably improve the final result; b. The number of adjusting a given pitch should be proper because a too small or too large one will generate a negative effect on the final result; c. The size of the harmony memory and the probability of using the known harmony have no obvious influence on the final result.

An Optimization Approach of Collaborative Distribution Considering Common Customers

LI Mengtao, DING Qiulei, LIU Kaijun

2023, 32(3):  104-110.  DOI: 10.12005/orms.2023.0087

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In the last kilometer of distribution, there is a situation where some distribution centers may provide distribution services to a particular public area or some co-customers at the same time, i.e. some customers require only one distribution center to provide distribution services, while some customers require multiple distribution centers to provide distribution services (customers who need multiple distribution centers to provide services are co-customers of the enterprise). When there are co-customers, the distribution routes of the two distribution centers will produce coupling(coupling points are common customer points), which leads to a great negative impact, such that repeated cross-over of distribution routes lead to high logistics transportation costs, low vehicle utilization, and traffic congestion; logistics service levels do not meet customer satisfaction standards and so on. Therefore, how to deal with the problem of inter-enterprise mutual customers is the key. This paper considers the situation of common customers in the distribution process, and puts forward the problem of considering the co-vehicle path of the common customer. Considering the collaborative vehicle routing problem of common customers, we can evaluate the potential benefits of cooperation between independent distribution centers. By calculating and comparing the benefits of each independent distribution center before and after cooperation, each independent distribution center may urge them to form a strategic cooperative relationship and make a cooperation plan. At the same time, the model can also be used to optimize the cooperation between existing enterprises.
The main research work of this paper is as follows: (1)In order to solve the situation of common customers, from the point of view of enterprises and customers, a kind of multi-distribution center and time window restrictions of VRP model is proposed. From the point of the enterprise, each distribution center is no longer limited to its own distribution customers. At the same time, from the customer's point of view, in order to meet the customer's requirements for time window and service quality, this paper takes the target function in the introduction of the penalty function into consideration. (2)The two-stage heuristic algorithm “classification before solution” is used to solve the problem. In the first stage, the algorithm of customer clustering using the transfer rules of ant colony algorithm is proposed, which classifies the common customers based on the distribution center, that is, the customers who are in need of multiple distribution centers are transferred to a distribution center to complete the distribution. In the second stage, the improved ant colony algorithm is used to solve the situation of each garage.
In order to evaluate the cost savings generated by this model, the results of the collaborative scheme and the results of the non-collaborative scheme are compared. The results show that the two schemes are basically consistent in terms of vehicle usage and average vehicle utilization, but under the collaborative scheme, both the cost of the respective distribution center and the overall cost of synergy are reduced in a certain degree. This shows that multi-distribution center coordination can reduce the distribution cost of the whole logistics system, which proves the rationality and effectiveness of the model.

Modelling and Optimization of Inspection and Imperfect Condition-based Maintenance for Non-renewable Warranty Products

WANG Liying, ZHANG Wenhua, YANG Yanmei, LING Xiaoliang

2023, 32(3):  111-115.  DOI: 10.12005/orms.2023.0088

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Warranty provides assurance to customers that manufacturers will provide compensation, through repair, replacement or refund, for purchased items that do not perform satisfactorily. To cope with the fierce market competition, attract and hold on customers, manufacturers usually promise to provide long-term and high-quality warranty services, which will entail an additional costto them. Maintenances play an important role in keeping products' performance and making sound decisions on maintenance strategies is an effective way of reducing warranty service costs. In industrial engineering, most products degrade gradually and operate at a lower performance level before complete failure. With the rapid development of computer-based monitoring technologies, condition-based maintenance has been widely used in reliability management and proven effective and economicalin reducing maintenance cost. Furthermore, over a period before the expiration of warranty period, the purpose of the manufacturer's maintenance activities is keeping the operation of the product, instead of improving it. Motivated by the aforementioned engineering practice, this paper focuses on products whose life can be divided into normal and defective stages and proposes an inspection and imperfect condition-based maintenance policy with residual warranty time threshold. Under the policy, the warranty period is divided into two stages: the inspection and preventive maintenance period and the residual warranty period. Over the inspection and preventive maintenance period, periodic inspections are carried outand periodic and imperfect maintenance activities will be performed if the product is identified to be in defective stage. Failures between two successive inspections are rectified using minimal repair. Over the residual warranty period, inspections are not performed and all failures are restored minimally.The virtual age model is used to quantify the level of imperfect maintenance activities. Two cases depending on whether imperfect maintenance activities are performed are discussed. The probabilities and the expected warranty costs for these two cases are derived by probability analysis method and based on them the average warranty cost over the whole warranty period can be obtained. To illustrate the effectiveness of the proposed policy, two comparison modelsare established. Under the first one, inspection and preventive maintenance activities are not performed and the remaining warranty period is not considered. Inspection and preventive maintenance activitiesare performed and the remaining warranty period is also not considered under the second model. Numerical examplesare given to demonstrate the application of the model. From the manufacturer's perspective, the inspection interval, the level of imperfect maintenance activities and the length of residual warranty period are optimized jointly such that the average warranty cost over the whole warranty period is minimized. The results of the numerical examples and contrastive analysis show that the joint optimization cansignifi can tly reduce the cost. The research can throw light on the warranty decision of complex and expensive products.In the current model, failures caused by performance degradations are considered. However, most products are subject to degradation and random shocks simultaneously. Warranty services aiming at external shockshave emerged, such as the “Protection Plus Mobile Elite”launched by Samsung, “iPhone Apple Care+” offered by Apple and so on.We can discuss the condition based warranty decision making for products that experience both degradations and external shocks. The decision analysis in this paper is made from the perspective of manufacturers. For future researches, warranty decision research based on game theory, which may balance the interests between producers and customers, are also worth discussing.

Dual-channel Supply Chain Contract Decision with Strategic Consumers

GUAN Zhenzhong, SHU Mengting

2023, 32(3):  116-122.  DOI: 10.12005/orms.2023.0089

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The popularity of the Internet and the rapid development of network technology have increased the channels for consumers to obtain information. More and more consumers not only rationally analyze the prices of different sales channels, but also make the decision of postponing purchase based on their own expectations. Strategic consumers increase the supply chain uncertainty. With the rapid development of e-commerce, online shopping has gradually evolved into a very important part of consumer life. Commodity sales have also broken through geographical and spatial restrictions. Many retailers provide goods to some consumers through third-party platforms such as Taobao and JD.com. Consumers also prefer to buy products through e-commerce channels. Traditional retailers usually consider opening online sales channels on the basis of the traditional offline channels. The retailer's profit is not only affected by the supplier's pricing, but also closely related to the type of supply chain contract. The emergence of online channel has increased the complexity of the supply chain, forming a dual-channel in which offline channel and online channel coexist. Dual-channel has aroused extensive discussion in the industry and academia, and has become an important research topic in supply chain management. This paper studies the selection of supply chain contract between the manufacturer and retailer when there are strategic consumers and retailer open online channel, and analyzes the change of retailers' dual-channel decisions under wholesale price contract and quantity discount contract.
We consider a supply chain consisting of a single manufacturer and a single retailer. Manufacturer sell goods to retailer based on the supply chain contract, and retailer resell products to strategic consumers. Retailer decide whether to add online sales channel according to the market. The model is divided into two stages. In the first stage, manufacturer and retailer choose to adopt wholesale price contract or quantity discount contract. In the second stage, retailers decide whether to add online sales channel. At the beginning of the first stage, consumers arrive at the market and make purchase decisions. Consumer can buy at most one unit of goods (purchase or give up). All consumers are strategic consumers. They foresee that retailers may add online channel, so they will strategically wait until the second stage of purchase, in order to obtain greater utility from online channel.
First of all, the paper solves the equilibrium solution of the game through the backwards-induction. Secondly, the paper compares the profits of the manufacturer and retailer in decentralize supply chain and centralizes supply chain under wholesale price contract and quantity discount contract, and discusses the optimal supply chain contract between the manufacturer and retailer. Then the paper studies the optimal decision of the manufacturer and retailer by analyzing the impact of different pricing of retailers' online and offline channel on the supply chain profit. The research results show that: (1)When the retailer does not open online channel, quantity discount contract can better coordinate the supply chain and increase the overall revenue of the supply chain. Whether in decentralized supply chain and centralized supply, supply chain profit under the quantity discount contract is not lower than that under the wholesale price contract. At this time, the profit distribution of the manufacturer and retailer is determined by the quantity discount coefficient. The upstream manufacturer with more dominant power in the supply chain is in an advantageous position discount contract. (2)When the retailer opens online channel, the wholesale price contract can better coordinate the supply chain discount contract. Under the wholesale price contract, the optimal pricing of retailer offline channel will increase, and the internal transfer price of online channel will decrease. When the parameters meet certain conditions, the supply chain profit under the wholesale price contract is higher than that under the quantity discount contract.
This paper mainly gets the following management enlightenment: (1)The manufacturer needs to consider consumers' foresight, patience and acceptance of online channel. The manufacturer can obtain the psychological expectation of strategic consumption on goods through sampling survey, award-winning questionnaire and customer return visit. (2)The retailer opening online channel needs to consider the opening cost of new channel, and also needs to pay attention to the impact of logistics and online platform credibility, on target customers. When strategic consumers prefer online channel and the reliability of online sales channel is high, both manufacturers and retailer will benefit from it.
The paper considers that all consumers in the market are strategic consumers, and does not consider the competitive situation of multiple manufacturers and retailers in the supply chain. The situation that strategic consumers and short-sighted consumers exist in the market can be regarded as the future research direction. Besides wholesale price contract and quantity discount contract, other supply chain contracts can also be used as research topics. For example, analysis of the impact of manufacturers' recovery contract and revenue sharing contract on retailers' opening of online channel.

Research on Information Acquisition and Sharing in Two Entry Modes

CAO Zonghong, XU Jie, MIN Jie, OU Jian

2023, 32(3):  123-130.  DOI: 10.12005/orms.2023.0090

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With the rapid development of community economy and information technology, the shortening of product update cycle has caused a rapid change in consumer demand. This means that consumer demand isuncertain and random. Closer to retail market, retailers are able to access consumer information and analyze real market demand through bearing the corresponding expenses. However, manufacturers usually are away from the retail market, so they are not capable of obtaining real market demand and only know the distribution of stochastic demand. In single-channel supply chain setting, some researchers have pointed out that it is optimal for retailer not to share real retail demand information with manufacturers. On the other hand, with the development of platform economy, many manufacturers introduce online direct channels to directly sell their product in addition to traditional retail channels. Online direct channels cause channel conflict and competition, which usually hurts retailers. In such case, manufacturers have become competitors for retailers. Thus, in a dual-channel supply chain setting, is it also optimal for retailers to share demand information with manufacturers. Retailers must focus on the issue of whether to share demand information with manufacturers.
In a dual-channel supply chain system, the manufacturer has multiple ordering modes to directly sell its product in the online direct channel. One is that the manufacturer can choose to determine the direct channel's sale quantity before the retailer determines ex-ante entry mode, and the other is as the same time as simultaneous entry mode the retailer sets the retail channel's sale quantity. Thus, which ordering mode should the manufacturer choose to maximize its profits?
To answer the above questions, this paper considers the two-level supply chain consisting of a single manufacturer and a single retailer based on stochastic demand. The manufacturer determines the order quantity of the direct sales channel in ex-ante entry mode or simultaneous entry mode. The retailer obtains the real market demand information by paying the fixed cost, but the manufacturer only knows the demand's distribution. Firstly, this paper discusses the optimal ordering decisions for the two partners and the condition under which the retailer is willing to obtain demand information and share it with the manufacturer given one of two modes, and analyzes the impact of the fixed cost on the optimal decisions information share strategy. Next, this paper discusses the optimal entry mode from the perspective of the manufacturer and retailer, respectively.
The results show as follows. (1)Given the ordering mode of direct sales channels, whether retailer obtains demand information depends on the acquisition cost. If the acquisition cost is not high, the retailer chooses to acquire information but not share it with the manufacturer, which means that the retailer can benefit from private demand information. If the acquisition cost is high, retailer chooses not to acquire demand information. (2)When the acquisition cost is low, even if the manufacturer bears the acquisition cost, the retailer is not willing to share demand information, because the information value is higher than the acquisition cost. The retailer is willing to share information unless the manufacturer bears the acquisition costs and gives part of information value subsidies to the retailer. When the acquisition cost is higher than the value of information, the cost-sharing contract becomes invalid. When the acquisition cost is moderate, the retailer can share demand information with the manufacturer if the manufacturer bears part of the acquisition cost, and the acquisition-cost-sharing contract can achieve Pareto improvement of both parties' profits. (3)The ex-ante entry mode is always optimal for the manufacturer. Under the strategy of not obtaining or obtaining and sharing information, the ex-ante entry mode is also optimal for the retailer. However, when the coefficient of variation of market size is not too small, that is, the deviation of market size is large or the average market size is small, the simultaneous entry mode is optimal for the retailer under the strategy of obtaining but not sharing information.

Coordination of Order-agriculture Supply Chain Based on CVaR under Option Contract

PENG Hongjun, YANG Meng

2023, 32(3):  131-136.  DOI: 10.12005/orms.2023.0091

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The order-agriculture has the advantages of reducing the risk of supply chain, promoting the modern agricultural machinery equipment application, improving agricultural production, reducing planting cost, improving farmers' market participation. However, the order-agriculture has many problems in practical application, the low performance rate is especially prominent. Reducing the default rate become the key to the healthy development of agriculture in the future. Option contract is an effective tool to improve the cooperation of supply chain members and avoid the risk of market price fluctuation. Introducing option contract in the order-agriculture supply chain is a powerful measure to improve the performance rate of the supply chain.
This paper considers an order-agriculture supply chain with a risk averse farmer and a risk neutral company under the random fluctuation of agricultural product prices. Based on the conditional value at risk (CVaR), we establish Stackelberg game model to study the optimal strategy and coordination of the supply chain. Firstly, we analyze the optimal production quantity decision of the farmer under the decentralized case. Secondly, we analyze the optimal production quantity decision of the order-agriculture supply chain under the centralized case, and compare it with the decentralized decision. Then, the option contract is introduced to analyze the coordination conditions of the order-agricultural supply chain and the pareto improvement range. Finally, the theorems and inferences are verified through numerical analysis.
The results show that, the production quantity and total benefits of both parties in the decentralized decision are lower than those in the centralized decision. With the risk aversion of the farmer, the production quantity and the benefit of the whole supply chain both reduce, and the higher the farmer's risk aversion, the lower the production quantity and benefits of both members. After the introduction of the option contract, when the option execution price is low, the production quantity and the farmer's benefit reduce with the increase of his risk aversion. When the option execution price is high, the production quantity and the farmer's benefit have no relationship with his risk aversion. When the farmer's risk aversion is very low, the option contract cannot achieve pareto improvement, while when the farmer's risk aversion is not very low, the pareto improvement range makes the benefits of the farmer and the company both higher than those under the decentralized case. Further research shows that the option contract cannot achieve the perfect coordination of the supply chain when the farmer's risk aversion is not too high, while it can fully coordinate the supply chain when the farmer's risk aversion is high. Besides, the pareto improvement range and perfect coordination range are both increase with the increase of the farmer's risk aversion.
　　In real life, farmers should actively buy option contracts from the company to avoid the risk of price fluctuation and improve the agriculture production quantity and benefits. To encourage farmers to buy option contracts, the company should set the option fee and option execution price according to farmers' risk aversion. Specifically, for farmers with low risk aversion, the company can reduce the option fee or increase the option execution appropriately. While for farmers with high risk aversion, the company may promote the option fee or reduce the option execution price. Furthermore, if farmers are with low risk aversion, it does no good to introduce option contract in the supply chain as a coordination mechanism. If farmers are with high risk aversion, the introduction of option contract is beneficial to both the company and farmers, and can achieve the perfect coordination of the supply chain. Nevertheless, this study only considers the uncertainty of the market price of agricultural products and farmers' risk aversion, the uncertainty of the market demand and companies' risk aversion can be further studied.

Application Research

Simulation Research on Grass-roots Organization Governance from the Perspective of Interpersonal Interactions

ZHANG Wenming, YANG Wenxiu, XU Jie

2023, 32(3):  137-142.  DOI: 10.12005/orms.2023.0092

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Suppose that n persons with their own behavioral characteristics live in a limited area. Some persons here are willing to be kind to others, while others choose to be selfish. Some are penny-pinching, while others may be weathercocks. When two persons meet, they will determine their behaviors according to their own behavior characteristics, and accordingly, obtain their own profits. What kinds of person will succeed in a long run?
To discuss the above problem, the agent-based simulation method is used to describe the interaction between persons in grass-roots organizations by using the repeated prisoner' dilemma model, where the different behavior characteristics of persons are modeled as strategies, and four simulation models with no manager, strongly supervised managers, weakly supervised managers, and no supervised managers are constructed, respectively.
In the no manager model, we design 12 strategies to depict the behavior of different persons and find that the “cunning men” get the highest profits. The reason may be that the persons of this strategy can not only ensure that they will not be retaliated by selfish persons but also benefit from friendly ones. It implies that no manager mechanism is not a suitable form for grass-roots organizations.
In the models with managers, managers are elected. Three sub-models are discussed below. In the model with strongly supervised managers, managers must always cooperate in the interaction with others. In this case, the “good men” with the always-cooperation-strategy, who are always cooperative with others, get the highest profits. It is may be that the election mechanism provides them with an important opportunity to be elected as managers to improve their profits. In the model with weakly supervised managers, some elected managers may choose to betray, while others still cooperate. Therefore, each strategy is changed into two strategies, for example, the always-cooperation-strategy is changed into two strategies: the really-always-cooperation-strategy, who is still cooperative after being elected as a manager, and the like-always-cooperation-strategy, who will betray after becoming a manager. The reason may be that although choosing betrayal can obtain high returns in a short period of time, the election mechanism makes it difficult for such agents in the future election, and as a result, the “good men” with the really-always-cooperation-strategy get the highest profits in this case. In the model with no supervised managers, some elected managers may not only choose to betray but also even encroach on the profits of others during their tenure. Although it is likely to lose the future election, elected managers still may have accumulated a lot of wealth by way of encroachment, which may be why the “hypocrites” with the like-always-cooperation-strategy get the highest profits in this case.
A good mechanism should be able to protect the interests of “good persons”. Therefore, from the perspective of individuals, the best mechanism is with strongly supervised managers, the second is with weekly supervised managers, the third is with no managers and the last is with no supervised managers. Furthermore, from the perspective of organizations, we compare the average profits of all persons under different mechanisms, and also find that the best mechanism is with strongly supervised managers, the second is with weekly supervised managers, the third is with no managers and the last is with no supervised managers. Whether from the perspective of individuals or organizations, the mechanism with supervised managers, especially with strongly supervised managers, is the most efficient organizational form since it can protect the interests of “good persons” and thus lead people to being “good”.

Impact of Corporate Compliance/Non-compliance on Remanufacturing Models Based on Carbon Trading

WANG Zhongze, XIA Xiqiang

2023, 32(3):  143-148.  DOI: 10.12005/orms.2023.0093

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In today's society, with the continuous improvement of the economic level, problems such as excessive energy consumption and global warming are getting worse. Excessive carbon dioxide emission is the root cause of climate change. To reduce carbon emissions and improve the social-ecological environment, the Chinese government has established the carbon trading market to promote sustainable economic development. Under this background, carbon emission rights have become an important resource invested by manufacturers in their production activities, and often have an impact on manufacturers' production and management decisions. At the same time, in the carbon trading market, all participants should fulfill the agreement of the carbon trading market, otherwise they will be punished. The establishment of a punishment mechanism can supervise the performance of enterprises, but it will also affect the profits of manufacturers and remanufacturers to a certain extent, so it is particularly important to reasonably set the penalty amount for an enterprise's non-compliance. At present, academic research on the influence of government subsidies and carbon tax policies on remanufacturing has made plentiful achievements, but there has been relatively little research on the influence of carbon trading on remanufacturing, and limited research on the influence of carbon trading on different remanufacturing modes. In this paper, to investigate the influence of the compliance and non-compliance of enterprises on different remanufacturing modes under carbon trading, we establish the game models of manufacturing or remanufacturing under three remanufacturing modes, namely, authorized remanufacturing, outsourced remanufacturing, and independent remanufacturing, and compare and analyze the three remanufacturing modes in the carbon trading market when the enterprises comply or fail to comply. This paper answers the following questions: How do three different manufacturing or remanufacturing modes affect the production decisions of original manufacturers and remanufacturers under the background of carbon trading? How does the fluctuation of carbon price affect the production behavior of these two manufacturers? What kind of remanufacturing mode does the original manufacturer choose for the maximum self-profit tendency? How do enterprises fulfill their obligations in the carbon trading market? What is the environmental impact of the enterprise's compliance or non-compliance in three manufacturing or remanufacturing modes?
Our main conclusions are as follows: First of all, in the background of carbon trading, the carbon trading price is positively related to the selling price of two products: it is negatively related to the production of new products, and when the carbon emission ratio of two products is greater than a certain threshold, the sales volume of remanufactured products is positively related to the unit carbon trading price. Secondly, the price per unit of new products is the same in authorized remanufacturing and outsourced remanufacturing modes, and the sales volume of new products is the same in authorized and independent modes. Thirdly, the original manufacturers tend to outsource the remanufacturing mode, and when the recycling coefficient of waste products and consumer preference for remanufactured products are greater than a certain threshold, the mutual benefits of original manufacturers and remanufacturers will be realized. Fourthly, in the case of only one production and operation cycle, when the ratio of penalty amount to carbon trading price is greater than a certain threshold, enterprises will choose to perform the contract, and the impact of compliance on the environment is smaller than the impact of non-compliance. Lastly, through the simulation analysis of remanufacturing engine-related case data, it can be seen that consumer consumption preference for green products will also affect enterprises' manufacturing and remanufacturing production decisions under the background of carbon trading. The increase in consumer preference for green consumption will promote the increase of the profit of the remanufacturer, and under the mode of outsourced remanufacturing and authorized remanufacturing, the income of the original manufacturer will also increase.
This study provides a theoretical basis for the government to establish a reasonable carbon trading price in the carbon trading market to promote coordination between enterprises in the carbon trading market and achieve a win-win situation. Simultaneously, the study provides a basis for the original manufacturer to choose which remanufacturing mode to realize the operation of its production activities, making the manufacturing and remanufacturing closed-loop supply chain run continuously and healthily. By doing so, the study effectively facilitates the realization of low-carbon emission reduction targets. Based on the above analysis, although this paper has a breakthrough compared with previous studies, there are still some shortcomings. For one, this paper only considers the production and operation decision-making in one carbon trading cycle but does not consider the situation in which the government reduces the carbon quota in the second year by the same amount if the enterprise is non-compliant. For another, this study only considers the trading mode of purchasing carbon emission rights in the carbon trading market and does not consider the way of purchasing carbon emission reduction in CCER projects. Future research should consider this method for a more comprehensive exploration.

Unstructured Data Driven Carbon Price Combined Forecast Based on Hybrid Decomposition-integration

LIU Jinpei, ZHANG Liaodan, ZHU Jiaming, CHEN Huayou

2023, 32(3):  149-154.  DOI: 10.12005/orms.2023.0094

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Carbon trading, as an effective mechanism for controlling carbon emissions, has generated a growing body of interest towards its trading price. Forecasting carbon trading price accurately is of vital significance. Not only can it assist investors in making informed decisions, but also it can aid governments in formulating scientifical carbon trading policies. However, the majority of the previous research on carbon trading price prediction generally builds prediction models based on historical data, and thus the forecasting results often exhibit significant hysteresis. Meanwhile, due to the complexity of carbon trading systems, time series of carbon trading price are endowed with characteristics such as non-linearity and high noise. Consequently, the promoting effect of a single decomposition integration method on forecasting accuracy is relatively limited. In sum, to enhance the forecast accuracy of the carbon trading price, it is of vital necessity to combine alternative source of information as well as various decomposition integration methods to construct the forecast model.
This research posits an unstructured data driven carbon price combined forecast model based on mixed decomposition and integration to forecast carbon trading price. First, relevant carbon trading unstructured data are obtained through Baidu Index and six corresponding main components are extracted by using principal component analysis (PCA). Second, empirical modal decomposition (EMD), variable modal decomposition (VMD) and wavelet transform (WT) are carried out respectively on the gained components and carbon trading price historical data, whose high frequency sequences, low frequency sequences and trend items are obtained after reconstruction. Then, based on the adaptive method, the self-regression integral sliding average model (ARIMA), Holt exponential smoothing method and artificial neural network (ANN) are selected to predict the high frequency sequence, low frequency sequence and trend item in combination with non-structural information. Furthermore, the predicted values from various forecasting methods such as ARIMA are integrated based on method of BP neural network. Meanwhile, the obtained forecasting results of the high frequency sequences, low frequency sequences and trend items are summed up to acquire the forecasting results of the carbon trading price decomposed by one of these three decomposition methods such as EMD. Eventually, the predicted values under these three decomposition methods are hierarchically integrated based on method of BP neural network again, and the final prediction results are obtained.
In an effort to test the predicting accuracy of the aforementioned model, we conduct an empirical analysis based on carbon trading price data from the carbon trading market in Hubei Province, China. Moreover, to further confirm the effectiveness of the proposed model, we compare its forecasting accuracy with seven other predicting models. Meanwhile, the prediction accuracy of these models is measured using five error evaluation metrics, including MAE, SSE, MSE, MSPE, and MAPE. Eventually, the result demonstrates that the values of the error indicators of our model are considerably smaller than those of the other models, indicating that the adoption of unstructured data, hybrid decomposition-integration method, as well as the combined forecast method can markedly improve the prediction accuracy of carbon trading price.
In summary, the proposed unstructured data driven carbon price combine forecast model based on mixed decomposition and integration provides with a new direction for constructing predicting models of carbon trading price as well as offers references for similar research. Based on this model, future research can further incorporate other sources of information such as structured data concerning carbon trading when predicting carbon trading price.

Multi-modal Data-driven Air Passenger Flow Integrated Forecasting Based on Internet Search Information

SUN Jingyun, YU Ting, HE Linyun

2023, 32(3):  155-162.  DOI: 10.12005/orms.2023.0095

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Airport passenger throughput mainly refers to the number of passengers carried by flights arriving and departing. On the one hand, the airport passenger throughput can directly reflect the size and passenger capacity of the airport. On the other hand, it can reflect the degree of social and economic development of the city and its surrounding areas. However, the internal resources of the airport are relatively limited. Check-in, baggage check tracking, safety checks, waiting point scheduling and emergency response strategies all depend on the space-time distribution of the unanticipated passenger flow. By predicting the airport passenger flow timely and accurately, the management can take a precaution measures, dispatch and arrange the airport resources effectively and reasonably. This way, the airport can save operating costs, reduce the waiting time of passengers queuing, and improve passenger satisfaction.
　In order to predict the airport passenger throughput with higher accuracy, this paper proposes anew “decomposition-reconstruction-integration” combined forecasting method based on internet search information. First, the mean impact value and time difference correlation analysis methods are employed to screen the internet keywords related to the airport passenger throughput, and the correlation between the search volume of each keyword and the original air passenger flow data is investigated to determine the best lag period, and then a comprehensive search index is constructed. Secondly, the ICEEMDAN data decomposition method is used to decompose the airport passenger throughput and comprehensive search index into several sub-modal sequences, which are reconstructed into high, medium and low frequency sequences according to the sample entropy value of the sub-sequences. Taking the different frequency components of the search index as auxiliary input information, we predict the high frequency and medium frequency sequences of the airport passenger throughput by using the BP neural network model optimized by the sparrow search algorithm (SSA-BP), while the low frequency sequence is predicted with autoregressive distributed lag model, and the ultimate forecasting value is obtained by integrating the predicted values of different frequency components with SSA-BP model.
　This paper focuses on the monthly passenger throughput of Xi'an Xianyang Airport and Chengdu Shuangliu Airport as the research object, takes the data from January 2011 to December 2019 (data from Wind database) as the sample set, and employs the search volume of the Baidu keywords which directly related to the airport or related to the corresponding urban scenic spots as the auxiliary prediction information. Through the empirical research, it is found that: (1)The prediction model based on the “decomposition-reconstruction-integration” framework has obtained smaller values in the three horizontal prediction indicators of RMSE, MAPE and MAE. (2)Compared with the model without Baidu search information, the model with Baidu search information has significantly improved the accuracy of horizontal and directional prediction. (3)Through further comparison of multi-step prediction results, it is found that the internet search information always has well auxiliary prediction ability for the passenger throughput of the two airports. Thus, the new combined forecasting model proposed in this paper can significantly improve the prediction accuracy and is strong in robustness. The prediction results of the model in this paper can provide certain decision-making reference for airport managers, and the proposed prediction method can also be used for short-term prediction of tourist flow in popular tourist attractions.

Default Prediction of Credit Bond in China Based on Stacking Algorithm Integrated Model

LIU Xiao, ZHOU Rongxi, LI Yuru

2023, 32(3):  163-170.  DOI: 10.12005/orms.2023.0096

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Many scholars pay more attention to financial risk warning analysis of debt default, and the comprehensive impact analysis of cross-level and multi-angle influencing factors is less. The existing bond default data is obviously unbalanced, and the overall number is relatively small, and the acquisition of data information becomes difficult. The research of credit risk models and the mining of various models have shortcomings in model setting. In the face of the increasingly serious trend of credit debt default in China, how to effectively predict it so as to achieve timely supervision in advance and prevent risk aggregation has important theoretical significance and application value.
We select the data of credit bonds that have defaulted between January 1, 2014 and September 30, 2019, and the bonds that have been in normal existence for two years or more as the normal sample, including 453 default samples. We select the default bond data in the period from May 2019 to September 2019, and intercept the bond data in the last five months of the normal existing bond data. A total of 411 bonds contain 90 default samples, as the prediction sample data of the evaluation model. Through the analysis of the causes of the default cases of credit bonds in China and the review of relevant literature, the indicator system of bond default is constructed from the four dimensions of bond qualification, debt subject, financial data and macro factors. First of all, the Pearson correlation coefficient and Spear-man correlation coefficient are used to test the correlation between default and 43 consecutive indicators, and the importance score of their impact degree is ranked. The stochastic forest algorithm model is used to determine the optimal parameters of the continuity indicators, and the model training and evaluation are carried out by eliminating the indicators one by one to obtain the optimal impact factor combination. Secondly, the underlying algorithm is built by weighted fusion, and a certain algorithm is combined as a secondary algorithm, and the output of the former is used as the input of the latter to build a two-level Stacking model, which can improve the prediction results. Therefore, based on the comparative analysis of seven algorithms from different angles, three algorithms are selected as the underlying algorithms: Random Forest algorithm, Gradient Boosting Decision Tree algorithm and Bayes algorithm. We also combine the Logical Regression algorithm as the secondary training algorithm fusion. A bond default prediction model based on Stacking algorithm integration is constructed.
The optimization algorithm based on Random Forest finds that when 18 and 37 influencing factors are selected, the prediction results inside and outside the sample reach equilibrium. The results of the bond default prediction model based on the Stacking algorithm integration show that, first, the overall accuracy of the double Stacking algorithm integration is improved by 1% to 8% compared with the single integration at the bottom. Secondly, the evaluation of the Stacking algorithm integration model with different index numbers shows that the constructed index system improves the prediction level. Thirdly, the selection method of the underlying algorithm based on the internal and external prediction balance of the sample is effective and desirable. When the underlying algorithm with relative disadvantages is included separately, it will gradually affect the stability of the model. In the study of bond default, the fitness of information gain analysis is better than that of distance measurement analysis. The distance analysis between samples is not suitable for judging the level of bond default, so we should try to avoid the instability of the distance measurement analysis when constructing the integrated model.
The research results can provide technical support and reference for China's bond market risk management. In the model comparison used in this paper, only a few classic algorithms are used to compare the model results. However, the improvement of various algorithms is constantly advancing. At the same time, for the learning algorithm with higher complexity, the corresponding data ratio should also be improved. The Stacking algorithm has a variety of fusion methods. Different fusion methods can achieve different performance, and also can obtain different research perspectives and ideas. Therefore, there are still many research perspectives on this method.

Product Market Competition, Risk-taking and Corporate Investment Efficiency

DU Jinzhu, HU Wenxiu

2023, 32(3):  171-176.  DOI: 10.12005/orms.2023.0097

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The inefficiency investment of listed companies has always been a persistent disease plaguing the capital market. Product market competition is one of the factors affecting market efficiency. The degree of product market competition affects the investment behavior of enterprises, and even determines the investment scale of enterprises to some extent. The market competitiveness of enterprises' products also continues to affect the subsequent investment ability and business performance of enterprises. Product market competition can alleviate the problem of information asymmetry, enable investors and analysts to obtain corporate information from corporate financial reports and other channels, and improve information transparency. The Sixth Plenary Session of the 18th Communist Party of China Central Committee clearly state that we should “through effective market competition, improve the efficiency of resource allocation; actively promote scientific and technological innovation, enhance core competitiveness”, which provides policy basis for improving the market competitiveness of Chinese listed companies and optimizing the efficiency of resource allocation. Risk-taking reflects a company' risk preference in investment decisions. Companies with a high level of risk-taking usually give up less risky investment projects with high uncertainty, greater returns and potential value, while companies with a low level of risk-taking tend to choose short-term investment projects with low risks. There are differences in project investment risks faced by different companies, leading to great differences in their willingness to take risks, which reflects the degree of risk avoidance and coping ability of companies. At the same time, the Sino-US trade war and Huawei' 5G ban have also posed more severe challenges to China'economic transformation and enterprise development. Therefore, under this realistic background, to explore the relationship between product market competition and corporate risk taking can not only expand the existing theoretical research results, but also has important practical value. At the same time, under the trend of the globalization of American financial crisis and the deepening of the supply-side reform, it is of great practical significance to further study the mechanism of the influence of risk assumption on the investment efficiency of companies.
This article uses the China's A-share listed companies from 2009 to 2019 as a research sample to examine the impact of product market competition on corporate investment efficiency, and introduces risk-taking as a mediating variable to explain the specific path of product market competition affecting corporate investment efficiency. The test results show that product market competition can effectively alleviate the over-investment and restrain the under-investment, thereby improving the corporate investment efficiency; product market competition can significantly increase the level of corporate risk-taking, thus supporting the “governance effect” of product market competition; the risk-taking behavior also has a significant effect on the improvement of corporate investment efficiency. Meanwhile, the risk-taking behavior can play an important mediating effect in the relationship between product market competition and corporate investment efficiency.
The conclusion of this paper not only improves the existing literature on the product market competition effect, but also provides a new research idea for the product market competition effect. In the new normal of China' economic development and the process of promoting supply-side structural reform, companies should reasonably balance the relationship between risk taking and investment efficiency, so as to smoothly realize economic transformation and upgrading and maintain long-term competitive advantages.

Multi-objective Performance Prediction of Turboshaft Engine Based on Bayesian Network

WANG Ning, WANG Yuhang, CAI Zhiqiang, ZHANG Shuai

2023, 32(3):  177-183.  DOI: 10.12005/orms.2023.0098

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The turboshaft engine is a kind of highly complex and precise thermal machinery, which is usually used as the power source of helicopter. Its performance directly affects the reliability and safety of flight missions. Turboshaft engines require a very high level of manufacturing. Typically, a qualified turboshaft engine requires two performance parameters: power and critical section temperature. However, in practice, it is difficult to manufacture an engine that can pass a single test run, often requiring several attempts after reassembly. Accurate and effective prediction of turboshaft engine performance can help to anticipate risks, which is important to improve the reliability of the helicopter and ensure the safe completion of the mission, as well as to guide the production process to improve the qualification rate. In recent years, with the development of computer technology and the rise of artificial intelligence and big data, Bayesian networks are increasingly used in the fields of data analysis and machine learning. Bayesian networks are a new type of probabilistic graphical model that combines the advantages of probability theory and graph theory to make the complex systems under study clear and understandable and to quantify, reconstruct and reason about complex systems. In the turboshaft engine performance prediction problem studied in this paper, two performance parameter target variables need to be considered together, which requires simultaneous determination of whether the two target variables of a turboshaft engine to be predicted can satisfy their respective qualifying conditions. Considering the practical research background, this paper combines each of the three multi-objective transformation strategies with Bayesian networks to construct a multi-objective performance prediction model for turboshaft engines, extend and improve the plain Bayesian classifier, and realize the prediction and analysis of multi-objective classification problems in the Bayesian network model. In this paper, based on the collected data of a certain type of turboshaft engines, according to the manufacturer's suggestions, four attribute variables that affect the two performance indicators of turboshaft engine — power and key section temperature are extracted firstly, which are the dimensions of part 1, part 2 and part 3, and the temperature. Then, three multi-objective transformation strategies, target generation, binary association and classifier chain, are introduced and combined with Bayesian networks respectively to construct three multi-objective performance prediction models (TG_NB, BR_NB, CC_NB) based on different strategies for turboshaft engines. Finally, to compare the performance of these multi-objective performance prediction models, while considering the validity of the results. In this paper, decision tree models, logistic regression models, and random forest models (TG_DT, TG_LR, TG_RF) are developed in conjunction with the objectives. The accuracy of each model is compared and validated so that the optimal model can be selected to effectively predict the performance of the turboshaft engine. Since the TG_NB model transforms the original dataset by target generation before modelling, and the new target variable integrates the dependencies of the two old target variables, and performs the most outstandingly in all three performance indicators. Meanwhile, compared with the other two models, TG_NB is presented as a single classifier with a simple and more interpretable model, which improves the modelling speed and prediction speed. Due to the limitation of experimental data, we have not yet considered the possibility of deformation of parts under extreme temperature. In future studies, we will collect more data and explore the effect of external temperature on the part dimensions.

Extension and Selection of Linear Dimensionless Methods in Group Evaluation

GUO Yajun, NGUYEN THai Hoc, GONG Chengju, ZHENG Hong

2023, 32(3):  184-190.  DOI: 10.12005/orms.2023.0099

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Comprehensive evaluation is the important research director of management science and engineering, system engineering, and information science. And it is an important premise of scientific decision-making. In comprehensive evaluation, eliminating the impacts of the different dimensions corresponding to the evaluation index is a key process in a complete comprehensive evaluation activity. The existing dimensionless treatment methods are developed for traditional static evaluation problems which do not consider the factor of the number of experts or decision-makers. However, using the common linear dimensionless treatment methods to deal with the index data given by multiple decision makers directly will change the size relationship between raw data, and further use of the dimensionless data for evaluation activity will lead to unreasonable and even error evaluation results. Therefore, extending the common linear dimensionless treatment methods to the group evaluation deserves research. Aiming at this problem, we find that the index data is not the unique variable when using the common linear dimensionless treatment methods to group evaluation directly is the important reason.
To solve this issue, based on the six kinds of commonly used linear dimensionless treatment methods, we first define the problem, and further extend the six dimensionless treatment methods. So, the extended standardized treatment method, the extended extremum treatment method, the extended linear proportional method, the extended normalization method, the extended vector normalization method, and the extended efficiency coefficient method, are obtained. The significant features of the six extended methods are that only the index data is variable when using these methods for group evaluation. This solution is also suitable for dynamic evaluation which further considers the time factor in evaluation. We secondly analyze the properties of the six extended linear dimensionless treatment methods. In this process, two new properties, the lateral monotonic property, and the single variable property are proposed, which are the necessary properties the linear dimensionless treatment methods should meet when considering group evaluation. And a total of eight properties are proposed to analyze the six extended methods. We find that all these six extended methods fulfill the longitudinal monotonicity property, the lateral monotonic property, the single variable property, and the variance ratio invariance property. And there is no linear dimensionless treatment method satisfying all eight properties because they only satisfy one of the interval stability and total constancy properties. We thirdly analyze how to select the six linear dimensionless treatment methods. We use the coefficient of variation to measure the size of the original information retained by the dimensionless index information. And we find that the coefficient of variation of each index data processed by the linear proportional method, normalization method, and vector normalization method has not changed. The efficacy coefficient method can adjust the values of the translation coefficient and amplification coefficient so that the coefficient of variation of each index data processed by the efficacy coefficient method does not change. From the comparison of the coefficient of variation, the linear proportional method, normalization method, vector normalization method, and efficacy coefficient method are superior to the extreme value method and standardization method. Because only measuring the amount of information retained in the original index data after dimensionless index information from the perspective of coefficient of variation cannot compare and select the linear proportion method, normalization method, vector normalization method, and efficacy coefficient method, according to the different weighting methods, through the comparison of the variance of the dimensionless index data and the variance of the original index data, the principle of dimensionless method selection is to retain the variance of the original indicator data as much as possible after dimensionless. Based on this principle we find that among these three methods, the normalization method is the best method when the sum of all the data corresponding to the same evaluation index is more than one. If the value of the amplification coefficient is appropriate, the efficiency coefficient method is the best linear dimensionless treatment method. And when the minimum value of the special point is taken and the minimum value is less than or equal to one, the linear scaling method is the best linear dimensionless method in the linear scaling method, normalization method, and vector normalization method. We finally use a numerical example to illustrate the effectiveness of this method. And this numerical example proves that extending the common six linear dimensionless treatment methods is really necessary and will help improve the evaluation quality.
In the future, we will construct some new linear dimensionless treatment methods suitable for dynamic evaluation, and we will also research some nonlinear dimensionless treatment methods based on the regulation of the specific evaluation background.

Dynamic Patent Quality Evaluation Method Based on Interval-valued Intuitionistic Fuzzy Score Function

WEN Haili, XIA Fei

2023, 32(3):  191-197.  DOI: 10.12005/orms.2023.0100

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Multi criteria decision making with intuitionistic fuzzy sets is a hot topic in the field decision making in recent years. Intuitionistic fuzzy sets use membership degree, non-membership degree and hesitation degree to represent fuzzy decision information, which can more flexibly represent and process fuzzy information. Because of the difficulty of determining the three critical degrees, Atanassov further extends the concept of intuitionistic fuzzy set and proposes interval valued intuitionistic fuzzy sets, which has been widely used in logistics management, energy analysis, decision-making analysis and many other fields. The score function of interval intuitionistic fuzzy sets is an important way to transform interval fuzzy values into accurate values. However, the score function of interval intuitionistic fuzzy sets also has the problems of anti-intuitionistic scoring results and ignoring interval information, which affect the reliability and objectivity of group preference aggregation. Therefore, this paper first proposes an improved score function based on set pair theory on the basis of analyzing the defects of the existing scoring function of interval intuitionistic fuzzy sets. Secondly, based on the improved scoring function of interval intuitionistic fuzzy sets, this paper designs an interval intuitionistic fuzzy dynamic group decision-making model based on the scoring function, and applies it to patent quality evaluation, providing a good information fusion framework for patent quality evaluation. From the perspective of application, patent quality evaluation involves many disciplines, with strong cross cutting in knowledge fields, and the trend of diversified evaluation indicators is increasingly obvious. Therefore, patent quality evaluation is usually a multi-attribute group decision-making problem involving multiple experts. Through the analysis of the existing evaluation index system, this paper intends to evaluate the patent quality from three aspects: patent technology level, patent transformation benefits, and patent protection regulations.
　　In this paper, based on the analysis of the shortcomings of the existing score function of interval intuitionistic fuzzy sets, an improved score function based on set pair theory is proposed; Secondly, based on the improved score function of interval intuitionistic fuzzy sets, this paper designs an interval intuitionistic fuzzy dynamic group decision-making model based on the scoring function, and applies it to patent quality evaluation, providing an effective information fusion framework for patent quality evaluation. This paper intends to evaluate patent quality from three aspects: patent technology level, patent transformation benefits, and patent protection regulations. Among them, (1)Technology level is the core indicator of patent quality, which can reflect the endogenous quality of a patent. According to the Patent Law, a patent can only be granted if the technology has novelty, creativity and practicability. (2)The benefit of patent transformation refers to the sum of the economic value generated by the application of a patented technology in the market process. It is the embodiment of the market value of the patented technology and the ultimate destination of the patented technology: it is transformed into productivity, generates economic benefits and contributes value to the society. (3)Patent protection regulations are the basic conditions to ensure the quality of patents and provide strong legal protection for innovation subjects or patent holders.
This paper summarizes the existing score functions of interval intuitionistic fuzzy sets, and analyzes the shortcomings of the existing score functions from two aspects: whether the evaluation value can follow the decision-maker's intuition and whether the evaluation value can reflect the interval fuzzy information. In order to improve the scoring and ranking ability of score function for interval intuitionistic fuzzy sets, based on the concept of set pair potential, this paper proposes an improved score function for interval intuitionistic fuzzy sets, and proves that it satisfies the basic intuition of decision makers. Driven by group consensus, this paper designs an interval intuitionistic fuzzy information fusion model based on scoring function, and applies it to the patent quality evaluation model, and achieves good evaluation results.

Research on Subsidy and Guarantee Mechanism in the Government-led Agricultural Supply Chain Finance

LU Qihui, XU Tingting, LI Shuang, XIAO Di

2023, 32(3):  198-205.  DOI: 10.12005/orms.2023.0101

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The problem of difficult and expensive financing of credit funds restricts the development of agriculture in China。The government adopts different measures to support the sustainable development of agriculture,including loan subsidy and policy-based guarantee mechanism. Most research on agricultural supply chain finance discusses the issues on performance, risk management, financing and return of supply chain finance. Few research studies the choice of financing strategy in agricultural supply chain. In addition, most current literature on government subsidies and policy guarantees uses empirical research methods to qualitatively describe concepts and values. Therefore, in the context of uncertain output, this paper uses the modeling method to study the subsidy and guarantee mechanism in government-led agricultural supply chain finance. By theoretically analyzing the value of government subsidies and policy guarantees on the entire agricultural supply chain and its members, our study provides a reference for the strategic choices of governments and banks. This study complements and develops the existing government-led risk management theory.
This paper establishes a single-cycle two-level supply chain model composed of a farmer,a core enterprise (referred to as company), a bank and a government. Assume that before production, the farmer does not have initial funds and needs to borrow from banks, and the company's operation is not subject to financial constraints. When the company places an order to the farmer, the wholesale price is determined, and the farmer accordingly determines the amount of agricultural production input. This paper assumes that the production cost function of the farmer is a quadratic function, including the productioncost for the production unit of agricultural products and the effort cost of the farmer to produce agricultural products, such as the time, energy, and technical input spent on production. The uncertainty of the output of agricultural productsis affected by natural factors. We assume that the random output factors of agricultural products follow a two-point distribution. When agricultural production is normal, the farmer will not default. When the production of agricultural products is affected by unfavorable conditions, the purchase fee paid by the company to the farmer may not be enough to repay the principal and interest of the bank's loan, and then the farmer may default. When the company buys all agricultural products produced by the farmer, the company only considers the cost of agricultural product acquisition, but does not consider the residual value of agricultural products, so the purchase volume (sales volume) is equal to the output volume. This article assumes that all supply chain members are risk-neutral.
Our study shows that under the circumstances of government subsidy, when the random output factor is higher and the loan interest rate is lower, the higher the loan interest subsidy rate, the higher the profit and social welfare of farmers, companies, and banks. In the guarantee mode, the reduction of guarantee rate is beneficial to the development of the farmer and society. Finally, we find that government subsidy reduces the financing cost of the farmer, but the real beneficiaries are the bank。However, policy-based guarantee mechanism reducing the bank's risk and loan interest rate, indirectly reduces the farmer's financing costs, and increases the profit of the farmer, company and social welfare.

Spatiotemporal Pattern Analysis of Industrial Green Development and Its Obstacle Factors in Beijing-Tianjin-Hebei

WANG Shaohua, LIU Ye, ZHANG Wei

2023, 32(3):  206-212.  DOI: 10.12005/orms.2023.0102

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The greening of the industry is the core of the green development of Beijing, Tianjin, and Hebei, and also the main carrier to promote the construction of ecological civilization, of which the green development of the industry is the top priority. To recognize the current situation of industrial green development in Beijing, Tianjin, and Hebei, and identify the obstacle factors, it is necessary to make a scientific and reasonable measurement of industrial green development in Beijing, Tianjin, and Hebei, which can promote the systematization and standardization of industrial green development measurement, and also provide a theoretical basis for different regions to tailor their policies and measures for industrial green development. However, the concept of “green development” has not been explicitly introduced in the international academic community, and since Pearce first proposed the “green economy” in 1989, the focus has been on ecosystems, economic-ecological systems, and economic-ecological-social systems. The measurement of green development has also emerged in three ways: First, using a single indicator to characterize. Second, incorporating resources and environment into the production function, and calculating green total factor productivity by treating pollution emissions as non-desired output. Although the research has made great progress, it still holds the view of weak sustainability. Third, as theresearch progresses, the construction of a comprehensive index system for green development becomes an accepted approach. On this basis, current research has examined the relationship among green development and environmental regulation, technological innovation, capital, labor, energy, industrial structure, FDI, urbanization level, and investment in education, mainly using econometric methods, with more and more attention being paid to the industry and regional differences of the influencing factors. Although more authoritative green development index systems have been constructed in the literature, they are mostly evaluated at relative levels and lack absolute levels. And there are few targeted studies on Beijing-Tianjin-Hebei, a major national strategic development region, and industry, an important sector, in terms of research objects. Although the barrier factors can be extracted by analyzing the temporal trend of green development level or regional variability, and the barrier factors can also be summarized by identifying the influence direction, influence effect and significance of the influencing factors, the existing studies have less analysis of the contribution degree of the barrier factors, ignoring the dynamic and spatial variability of the barrier factors and their barrier degree.
Therefore, this paper refers to the authoritative evaluation index system and constructs the industrial green development index system based on the connotation of green development of resource, environment and economic coordination. Taking into account both subjective and objective methods, the weights are calculated using AHP and the improved entropy weighting method that introduces time variables. On this basis, grading criteria are set, and the relative level and absolute level of industrial green development in Beijing, Tianjin, and Hebei from 2012 to 2018, as well as the barrier degree of barrier factors, are measured and temporal trends are summarized by combining the unconfirmed model and the improved barrier degree model, and a time-weighted vector is further introduced to describe the spatial pattern. The results show that: First, the level of industrial green development in Beijing, Tianjin and Hebei is rising year by year and has reached C1 level; most of the top-ranked cities are located in the “atrium” area near Beijing and Tianjin, while the bottom-ranked ones are mainly located in the “bottom of the heart” area of the aorta; the cities in higher grades are located in the center of the “heart” near Beijing and Tianjin, while the lower-ranked cities are located in the “tip” and “bottom” of the heart. Second, research input intensity, electricity consumption per unit of GDP, energy consumption per unit of industrial value-added, and outward orientation are the key obstacle factors for the overall industrial green development of 13 cities in Beijing, Tianjin, and Hebei; and their obstacle degrees are all on an increasing trend.

Management Science

Research on the Strategies of Farmers Cooperative with the Introduction of Branded Enterprise

CAO Yu, LIU Yingzhi, YI Chaoqun

2023, 32(3):  213-219.  DOI: 10.12005/orms.2023.0103

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In recent years, farmers' cooperatives have developed rapidly in China, but at present, China's farmers' cooperatives are still in the primary stage of development. Most agricultural products are relatively primary agricultural products, with low added value and insufficient brand-building capacity. Farmers' cooperatives can increase the added value of agricultural products and cultivate brand agricultural products by introducing agricultural products enterprises. However, when should the farmers' cooperatives introduce agricultural products enterprises? After introducing of agricultural products enterprises, the choice of the optimal cooperation mode of farmers' cooperatives is worth studying. Currently, the research on agricultural brands is mainly based on empirical research, but more quantitative research is needed. Only a few scholars have studied the impact of the brand effect on the optimal decision of the supply chain based on the game model. However, the relevant research under the “cooperative+enterprise” model does not consider the influence of brand effect on the decisions of the supply chain entities.
This paper constructs two kinds of agricultural product sales models, namely, cooperatives facing the market and “cooperative+enterprise”, compares and analyzes the optimal pricing and quality decisions in three different cooperation models, namely, wholesale price contract, cost-sharing contract and revenue-sharing contract, under the “cooperative+enterprise” model, and discusses the impact of the brand effect on the optimal introduction strategy and optimal cooperation model of cooperatives. Considering the influence of brand effect on the cooperative's decision to introduce enterprises, it is assumed that the cost of processing and branding construction of enterprises is zero. Finally, through numerical simulation, Europe analyzes the influence of brand effect on the strategic choice of farmers' cooperatives introducing agricultural products enterprises, the optimal cooperation mode after introducing agricultural products enterprises, the optimal quality level of cooperatives and the optimal price decision.
The research finds that the brand effect and the cooperation mode between cooperatives and enterprises will affect the cooperative's enterprise introduction strategy. Cooperatives can cultivate brand agricultural products by introducing agricultural products enterprises, but cooperatives are not always motivated to introduce agricultural products enterprises. In particular, when the information and trust advantages of brand agricultural products are relatively small, it is more beneficial for the cooperative to adopt the direct marketing mode. In contrast, the introduction of agricultural products enterprises is not beneficial to the cooperative. It is further found that the introduction strategy of cooperative enterprises is affected by the cooperation mode between cooperatives and enterprises. After the introduction of enterprises into cooperatives, the cooperation mode of revenue sharing contract is the most beneficial to cooperatives, followed by the cooperation mode of cost-sharing contract. The greater the information or trust advantages of brand agricultural products, the more motivated the cooperatives are to provide high-quality agricultural products. Further analysis of the optimal quality under three different cooperation modes shows that cooperatives are more motivated to provide high-quality agricultural products under the revenue-sharing contract. Finally, the validity of the proposed conclusions is verified by numerical simulation analysis. The research results can provide effective theoretical support for optimizing the optimal decision-making of farmers' cooperatives and promoting the construction of agricultural branding.
This paper considers the situation of information asymmetry. In fact, information asymmetry is common among supply chain members, so we can consider the situation of information asymmetry in the future. At the same time, we can also consider the characteristics of the agricultural product supply chain, such as stochastic output.

Political Capability of MNE, Overconfidence of CEO and Political-risk Taking of OFDI

SHI Ruxin, DU Xiaojun, ZHANG Zheng

2023, 32(3):  220-226.  DOI: 10.12005/orms.2023.0104

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In recent years, the overall scale of Chinese OFDI has gradually increased. In the choice of OFDI location, more and more MNEs show the preference of political risk. For example, China's investment in 65 countries which is along the “the Belt and Road” is mainly distributed in Asia and Europe, with 60.4% locations of high political risk. This shows that more and more MNEs tend to invest in locations of high political risk, that is, MNEs tend to undertake political risk in OFDI. This paper takes the MNEs' OFDI location choice of high political risk as the core issue, and discusses the mechanism of political-risk undertaking of MNEs' OFDI by integrating the factors affecting the heterogeneity of MNEs at the organizational and individual levels. Unlike the existing literatures, which study the political-risk undertaking of MNEs' OFDI from the organizational or individual level of enterprise heterogeneity alone, this paper realizes the integration of the two levels, and constructs a theoretical model of the impact of the organizational level of MNEs' political ability and the individual level of CEO overconfidence on the political-risk undertaking of MNEs' OFDI. It is proved that MNEs are more willing to undertake political risks in OFDI due to the expectation of opportunities in the location of high political risk. This expected effect mainly depends on the impact of the political ability of MNE on the value maintenance and value creation of MNE. The explanation of the transmission mechanism of CEO overconfidence not only effectively responds to “how the political ability of the MNE at the organizational level can promote the political-risk undertaking of the MNEs' OFDI”, but also gives a tentative answer to “how the CEO's cognition at the individual level can realize the connection with the organizational level”, It not only overcomes the limitations of studying the impact of the organizational and individual levels of MNEs heterogeneity on the political-risk undertaking of OFDI, but also provides a solid micro-basis for the research on the political-risk undertaking of MNEs' OFDI, which is a supplement and improvement to the research on the political-risk undertaking of MNEs' OFDI.
This paper takes the OFDI events of A-shares firms in 2008~2019 as the research objects to explore the impact of MNEs' political capacity on the political-risk undertaking of MNEs' OFDI, and introduces the overconfidence of CEO as the intermediary variable of the impact of MNEs' political capacity on the political-risk undertaking of MNEs' OFDI, and constructs a complete model of political risk of MNEs' OFDI. At the same time, based on the nature of MNEs' ownership and the distance of political risk between the host country and the home country, the samples are grouped to test the heterogeneity of the impact of MNEs' political capacity on the political-risk undertaking of MNEs' OFDI.
The empirical results show that: The stronger the political ability of MNE, the more inclined they are to invest in the location with high political risk. The overconfidence of CEO plays an intermediary role in the relationship between the political ability of MNE and the political-risk undertaking of MNEs' OFDI, that is, the political ability of MNE will promote the increase of the overconfidence of CEO, and the higher the overconfidence of CEO, the more inclined the MNEs are to invest in the location with high political risk. The further analysis finds that the different ownership nature of MNE and the different distance of political risk between the host country and the home country will have different effects on the research conclusion. The political ability of state-owned MNE will promote MNEs to invest in location of high political risk, and the intermediary effect of overconfidence of CEO is established, while the political ability of private MNE has no significant impact on the political risk of MNEs' OFDI. When the distance of political risk between the host country and the home country is small, the political ability can promote MNEs to invest in location of high political risk, and the intermediary effect of overconfidence of CEO is established. When the distance of political risk between the host country and the home country is large, the above conclusion is not established.

General Core and Its Axiomatic Characterization

KONG Qianqian, HAN Weibin, XU Genjiu

2023, 32(3):  227-232.  DOI: 10.12005/orms.2023.0105

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An important issue in cooperative games is to divide the worth of the grand coalition among all players. For this purpose, various solutions have been proposed. As a famous solution in the cooperative game theory, the core has captured a lot of attention. It is an imputation set in which all coalition excesses are non-positive. Since the coalition excessis a concept that is used to evaluate the complaint of coalitions towards a given imputation in a cooperative game, no coalition has the incentive to deviate from the cooperation once the players receive a core allocation.From this point of view, the core is an important solution to stabilize the cooperation. This solution has been successfully applied to solve the problems of interest or product distribution in fields including economics, political science and operational research. However, the limitations of the core will occur in the following circumstances: (1)Except for the coalition excess, one would want to access the complaint of a coalition via other different ways, such as the per-capita excess, the envy excess, the optimistic excess, etc. (2)Instead of evaluating the coalitional complaint, one would be more willing to intuitively evaluate the complaint of one player, which has actually been done by many scholars who proposed the player excess, the per-capita player excess, etc. (3)The complexity of reality creates the necessity to study the stabilization of other types of games, such as cooperative games with coalition structure, cooperative with nontransferable utilities, non-cooperative games, etc.
In view of the above circumstances, this paper generalizes the core to an arbitrary pair(Π,F)∈Ω, where Ω is a class of potential “decision spaces”, Π is a topological space and for every j∈M,F_j is a component of F, which is a real continuous function on the domain Π. F_j could be treated as a general complaint function. The general core is a set that collects the topological space such that every coordinate of F is nonpositive. As a consequence, we make it possible to apply the general core in several other conflict situations. Moreover, analogous to the conclusion that the nucleolus belongs to the core whenever the core is nonempty, we prove that the general core contains the general nucleolus whenever the general core is not empty.
　　The main part of this paper is devoted to presenting an axiomatic characterization of the general core to illustrate its reasonability and fairness. The main result in this paper is Theorem 1, in which the general core is characterized by four axioms: Non-discrimination, Non-positive Redundancy, Reduction of the Scope, and Invariance with respect to Max/Min. Non-discrimination says that if M is an empty set, then the solution is made up of the whole topological space. Non-positive Redundancy argues that the solution keeps unchanged if we delete a non-positive coordinate of F. Alternatively, Non-positive Redundancy means that non-positive coordinates of F have no effect on the solution itself. Reduction of the Scope states that a set is never contained in the solution if there exists a coordinate of F on such a set that is never smaller than a given positive number. Invariance with respect to Max/Min implies that the solution is the same if we replace two coordinates of F with their maximum and minimum and keep the other coordinates unchanged. In order to make the above axioms be valid, we assume that the topological space is closed when we delete some coordinates of F or when we operate the maximal and minimal operators on F. Besides, we also prove the logical independence of the four mentioned axioms.
　　Last, various applications of the general core are listed in Section 4. When F's coordinatesare the coalition excesses or the per-capita excesses, Propositions 2, 3, and 4 present respectively that the general core could (1)reduce to some classical solutions, such as the union between the k-core and k-anticore, etc, (2)reduce to some sets, such as the pre-imputation set or the imputation set, etc, (3)reduce to the core on various games, such as the cooperative games with coalition structures, the cooperative games with graph structures or the cooperative games with nontransferable utilities, etc. Proposition 5 gives a refinement of the core when F is restricted to the vector whose coordinates are the sum excesses. These propositions show the relationships between the general core and cooperative game solutions, which is of great significance in revealing the inner connection of these cooperative game solutions.
　　As have shown, a characterization of the core is given for abstract function F, the abstract space Π and the abstract dimension restriction M in this paper. One future work could focus on the characterizations for some specific functions, specific spaces, and specific dimension restrictions. We could also study some other general solutions, such as the general bargaining set, the general stable set, and so on.

Group Purchase Pricing Strategy for Innovative Products Based on Online Community Learning Mechanism

ZHANG Peng, REN Weihao, MEI Lei, LI Wen

2023, 32(3):  233-239.  DOI: 10.12005/orms.2023.0106

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The pricing strategy is the key to successfully launching innovative products. Traditional pricing strategies are skimming pricing and penetration pricing. Skimming pricing can gain high profits but keep potential consumers out of market and hinder market development efficiency, while penetration pricing can rapidly capture market share at the expense of profits. With the development of online community, however, a new business model, named group purchase, has been devised and the working mechanism is as follows: Make the group purchase price slightly lower than the evaluation of innovative products by the consumers who are concerned about the new products and willing to pay high price for early adoption in order to activate their perception of consumer surplus (consumer surplus is additional benefit that consumers receive because they are paying less for commodity than what they were willing to pay). Early adopters have to recruit adequate buyers before the deadline if they want the consumer surplus. As a result, they prefer to spread product knowledge and share their experience with potential consumers who have little product information in online community. Through community interaction and learning, potential consumers improve their evaluation of innovations and join the group purchase. In this way, group purchase pricing strategy can not only ensure the ideal profits with relatively high price, but also influence more potential consumers to buy new products due to community learning effect. Compared with traditional skimming pricing and penetration pricing, the group purchase pricing strategy based on online community learning mechanism can achieve an effective balance between the profits rate and the market share under certain conditions. In order to explore these necessary conditions, this paper studies the influencing factors on optimal profits and sales of group purchase pricingstrategy compared with skimming pricing and penetration pricing. The research may contribute to enriching the theory of pricing strategy for innovative products and helping firms achieve an effective balance between the profit rate and the market share for innovative products.
Firstly, online community learning effect influencing individual purchase decision model is established according to online community learning mechanism and Bayesian formula andoptimal profits and sales models of group purchase pricing are constructed. Secondly, based on the above work, the profit comparison model of group purchase pricing vs. skimming pricing and the sales comparison model of group purchase pricing vs. penetration pricing are constructed respectively. Lastly, we conduct simulation experiments on these models by using MATLAB software, and explore the factors that influence group purchase pricing to become dominate strategy.
Firstly, community learning effect is positively correlated with community size, community activity, community identity and community interaction efficiency, and negatively correlated with heterogeneity of community members. Secondly, through simulation experiments, we find that the maximum profits and sales of group purchase pricing for innovative products are positively correlated with community size, community activity, community identity and community interaction efficiency, and negatively correlated with heterogeneity of community members. Lastly, when community size, community activity, community identity and community interaction efficiency are higher than a certain threshold and heterogeneity of community members is below a certain threshold, the group purchase pricing strategy can achieve an effective balance between the profit rate and the market share for innovative products and become the dominant strategy. The research results will help firms employ group purchase pricing strategy to launch innovative products successfully.