基于非对称成本的设计竞赛博弈模型及奖金设置

论从项目业主的角度出发，利用博弈论和信息经济学理论和方法，在竞赛参与人成本不对称条件下，建立了一个项目业主和多个设计竞赛参与人组成的设计竞赛博弈模型；并在竞赛参与人成本函数分别为线性函数、凹函数和凸函数的条件下，研究对项目业主最优的竞赛奖金设置，研究表明：对于项目业主最优的奖金设置是单项奖金的方式。     

Reverse contests

We study two forms of a reverse contest. In reverse contest A the designer imposes a punishment such that the agent with the highest effort who caused the greatest damage is punished. Conversely, in reverse contest B, the designer awards a prize to the agent with the lowest effort who caused the smallest damage. We analyze the behavior of the agents in both contest forms and demonstrate that asymmetry of the players' payoff functions does not necessarily yield different expected payoffs.     

随机R＆D竞赛模型及最优参与人选择

运用博弈理论，建立随机R＆D竞赛博弈模型，对该模型下竞赛参与人与项目业主的行为策略进行分析，并从项目业主的角度出发，给出了对项目业主最优的竞赛参与人选择。     

考虑即时采购价格的物流服务供应链优化

物流服务市场的不确定性会影响物流服务供应链的服务水平和收益。在考虑随机即时采购价格以及基础物流提供商在正常情况和应急情况下具有不同物流能力投资成本的情形下,引入期权机制研究不确定市场环境下物流服务供应链的优化决策,以提高物流服务供应链柔性和降低市场不确定性带来的风险。构建物流服务供应链的期权契约模型,采用Stackelberg博弈理论和优化算法分析和求得物流服务集成商的最优期权采购和即时采购策略,以及基础物流提供商的最优物流能力投资策略。结果表明即时采购价格将影响基础物流提供商和物流服务集成商的决策。最后通过数值分析研究即时采购价格的不确定程度对物流服务集成商和提供商的优化策略和利润的影响。     

The best banking strategy when playing The Weakest Link

The paper uses dynamic programming to investigate when contestants should bank their current winnings in the TV quiz show, ‘The Weakest Link’. It obtains the optimal strategy for the team as a whole and then looks at two possible reasons why the contestants tend to use other strategies in reality.     

低碳环境下供应链差异化定价与协调机制研究

以低碳和普通产品两个制造商和一个零售商组成的两级供应链系统为研究对象,探讨了供应链的差异化定价与协调机制问题。求解得到了两制造商和零售商的最优定价策略及可行的低碳产品生产成本范围。研究发现:1)分散决策的差异化定价策略无法达到供应链协调;2)在可行的低碳产品生产成本范围内,低碳产品制造商、零售商和整个供应链系统的利润都随低碳产品生产成本的增加而减少,只有普通产品制造商的利润随低碳产品生产成本的增加而增加。因此,降低低碳产品生产成本是促进低碳产品推广的关键。针对分散决策造成供应链效率损失的情况,采用Shapley值法进行协调,并给出了契约协调机制。最后,通过算例分析了消费者价格敏感性变化和低碳产品生产成本上升对最优决策和供应链利润的影响。     

碳交易规制下信息不对称供应链的减排和低碳推广博弈研究

论文在碳交易规制下,研究单一制造商和双零售商组成的供应链减排与低碳推广决策以及零售商对制造商的成本信息分享问题,分析了零售商对制造商分享成本信息的条件,及不同情形下的制造商减排和零售商低碳推广策略。研究发现:零售商的最优低碳推广水平只与自身相关参数有关,零售商只有在自身低碳推广效率足够高时才会与制造商分享信息;制造商最优减排量随消费者低碳意识、碳交易价格、零售商低碳推广效率及其不确定性增大而提高,随零售商之间竞争程度提高而降低;无论零售商是否对制造商分享成本信息,供应链成员的最优利润随零售商之间竞争程度提高而增加,随消费者低碳意识、碳交易价格提高而提高;零售商低碳推广效率的不确定性越大则制造商的最优利润越低,零售商的最优利润越高;仅一家零售商分享成本信息时,制造商无法通过转移支付使另一家零售商与其分享信息。     

基于期望损失厌恶的供应链期权契约协调研究

以一个损失厌恶销售商与一个损失中性供应商组成的两级供应链为背景,利用期望损失厌恶理论对销售商在期权契约下的最优采购策略进行了研究,并证明了期望损失厌恶理论能有效克服传统基于前景理论的研究中因参考点外生且固定假设带来的弊端。在此基础上,进一步给出了供销双方在期权契约下实现协调共赢的条件,分析了销售商损失厌恶程度,期权契约价格等参数对供应链协调共赢机制的影响。结果显示：销售商的损失厌恶偏好并不会改变权利金分配整体供应链利润的作用,但会增强销售商分享收益的能力,改变供销双方利润或效用水平对权利金,产品销售价格和生产成本的敏感程度,且较高的损失厌恶偏好还会阻碍供销双方协调共赢目标的达成。     

制造商为小本经营情况下零售商购货机制的合同设计

考虑零售商采用逆向拍卖方式到个小本经营的制造商处购货,研究供应链中如何设计合同使得零售商单位时间的支出费用最低,采用最优控制的方法和委托代理理论中的显示原理,得出零售商的最优购货机制,同时给出两个简单的购货机制——打分拍卖机制和固定生产时间下的价格拍卖。结果表明由制造商承担的制造费用越多,零售商的进货价格越高;在简单机制下,制造商承担制造费用的大小并不影响最优生产率的制定。     

Consumer returns reduction and information revelation mechanism for a supply chain

In this paper, we develop two revelation mechanism models of a supply chain consisting of one manufacturer and one retailer under asymmetric information, where the retailer provides store assistance (SA) to reduce consumer returns rate and increase demand. Under full information, we find that a higher returns rate or returns handling cost increases the SA level if the market scale is sufficiently high. In the demand information asymmetry model, we find that: (i) the low-type retailer (facing a low demand) has no incentive to distort demand information while the high-type retailer may report wrong information; (ii) the manufacturer would like to design a menu of wholesale price-order quantity contract to induce truthful demand information and the manufacturer pays an information rent to the high-type retailer if the returns rate or returns handling cost for the retailer is sufficiently low; (iii) asymmetry of information does not change the monotonicity of the unit wholesale price in the retailer’s type, and information asymmetry decreases the retail price but increases the SA level. Unlike the demand information asymmetry model, a higher retailer’s returns handling cost expands the effects of information asymmetry on the retail price and the SA level, and using revelation mechanism decreases the channel profit if the retailer’s returns handling cost is sufficiently high under the returns rate information asymmetry model.     

The stochastic generalized bin packing problem

The Generalized Bin Packing Problem (GBPP) is a recently introduced packing problem where, given a set of bins characterized by volume and cost and a set of items characterized by volume and profit (which also depends on bins), we want to select a subset of items to be loaded into a subset of bins which maximizes the total net profit, while satisfying the volume and bin availability constraints. The total net profit is given by the difference between the total profit of the loaded items and the total cost of the used bins. In this paper, we consider the stochastic version of the GBPP (S-GBPP), where the item profits are random variables to take into account the profit oscillations due to the handling operations for bin loading. The probability distribution of these random variables is assumed to be unknown. By using the asymptotic theory of extreme values a deterministic approximation for the S-GBPP is derived.     

Mathematics classroom instruction excellence through the platform of teaching contests

In this study, we aimed to examine features of mathematics classroom instruction excellence identified and valued through teaching contests in the Chinese mainland. By taking a case study approach, we focused on a prize-winning lesson as an exemplary lesson that was awarded the top prize in teaching contests at both the district and the city level. The analyses of the exemplary lesson itself revealed important features on the lesson’s content treatment, students’ engagement, and the use of multiple methods to facilitate students’ learning. These features are consistent with what the contest evaluation committees valued and what seven other mathematics expert teachers focused in their comments. The Chinese teaching culture in identifying and promoting classroom instruction excellence is then discussed in a broader context.     

Optimal Contract Design of Supplier-Led Outsourcing Based on Pontryagin Maximum Principle

This paper provides a supplier-led outsourcing model to maximize the supplier’s profits based on a principal-agent framework with both asymmetric cost information and uncertain market demand information described by continuous random variables. The salvage value of the unsold product is processing-cost dependent. By converting the proposed model, which is a dynamic optimization problem, to an optimal control problem, we obtain the analytical form of the optimal supplier outsourcing contract composed of the wholesale price and the transfer payment by applying Pontryagin’s maximum principle. It is shown that the optimal contract is directly related to the supplier’s beliefs about the manufacturer’s unit cost and the salvage value function. The Pontryagin’s maximum principle-based solution method serves as a powerful tool to support the decision making for the best sourcing strategy, and it provides analytical insights for outsourcing management. Finally, numerical examples are presented to illustrate the validness of the theoretical results.     

随机弹性需求下供应链销售价格与提前期联合决策及协调机制

研究了市场需求随机且对销售价格及提前期敏感的条件下,供应链如何制定最优的销售价格、提前期以及库存因子使得利润最大化。首先,分析了集中决策与分散决策供应链的最优决策,发现集中决策与分散决策模式下的提前期与库存因子是相同的,但分散决策下的销售价格更高、期望利润更低,且分散决策与集中决策供应链的利润之比随着需求对价格的敏感程度的增大而增大。然后建立了收入共享与成本分担的协调机制,并分析了其最优决策。研究发现,协调决策机制可以有效地压缩提前期,并能同时使供应链达到帕累托改进,但不能达到完美协调,而且还发现协调决策下制定的最优销售价格比分散决策要低。最后通过数值计算对三种供应链决策模式下的绩效进行了比较分析,结果表明供应链利润随着需求方差增大而减小,提前期压缩程度随着材料成本承担比例增大而增大。上述结论可以为企业制定销售价格与提前期决策以及企业间的协调提供有益的指导。     

Firms' R&D decisions under incomplete information

The paper considers a patent race in which firms do not know their relative positions. In this setting, firms that start in the same position proceed at the highest possible speed; and if one firm has an initial advantage it preempts the rival, but at the cost of dissipating a significant part of its monopoly rent. So the paper shows that incomplete information in a patent race leads to rent dissipation. The latter is higher, the higher the value of the prize and the lower the cost of R&D. Thus, for innovations that provide relatively high profits the time to discovery is shortened, but the social losses are likely to be high, due to duplication of effort.     

最佳组队方案及模型

本文以选择队员参加大学生数学建模竞赛的组队问题为背景,利用层次分析和动态规划等方法给出了一个最佳组队方案及模型。     

确定性需求连续生产模型下的最优保理融资策略

保理是融资机构基于供应链上下游企业之间实际发生交易而给予供应链卖方企业的一种短期融资。基于连续生产模型研究了资金约束制造商的最优保理融资策略。考虑保理时间决策对融资成本和需求损失的影响,比较了固定期保理和即时保理两种策略下制造商的利润。研究发现,固定期保理策略下的最优保理时间随着其边际利润的增加而提前,而随着保理费率上升、应收款账期延长、自有资金增加而延迟。数值研究结果发现,保理商最优保理费率随着应收账款账期延长而降低。     

Risk sharing and information revelation mechanism of a one-manufacturer and one-retailer supply chain facing an integrated competitor

This paper develops an information revelation mechanism model of a one-manufacturer and one-retailer supply chain facing an outside integrated-competitor under demand uncertainty. We investigate how the manufacturer designs a wholesale price-order quantity contract to induce the retailer to report his risk sensitivity information truthfully. We try to explore the effects of the outside competitor and the risk-sharing rule on the optimal price-service level decisions of the retailer and the optimal wholesale prices of the manufacturer. We find that the strategic interaction plays an important role in the effect of risk sensitivity on the order quantity for the retailer. When the fraction of the risk cost shared by the manufacturer is sufficiently large (small), the optimal wholesale price for the high risk-averse retailer is higher (lower) than that for the low risk-averse retailer.     

Supply chain scheduling with receiving deadlines and non-linear penalty

We study the operations scheduling problem with delivery deadlines in a three-stage supply chain process consisting of (1) heterogeneous suppliers, (2) capacitated processing centres (PCs), and (3) a network of business customers. The suppliers make and ship semi-finished products to the PCs where products are finalized and packaged before they are shipped to customers. Each business customer has an order quantity to fulfil and a specified delivery date, and the customer network has a required service level so that if the total quantity delivered to the network falls below a given targeted fill rate, a non-linear penalty will apply. Since the PCs are capacitated and both shipping and production operations are non-instantaneous, not all the customer orders may be fulfilled on time. The optimization problem is therefore to select a subset of customers whose orders can be fulfilled on time and a subset of suppliers to ensure the supplies to minimize the total cost, which includes processing cost, shipping cost, cost of unfilled orders (if any), and a non-linear penalty if the target service level is not met. The general version of this problem is difficult because of its combinatorial nature. In this paper, we solve a special case of this problem when the number of PCs equals one, and develop a dynamic programming-based algorithm that identifies the optimal subset of customer orders to be fulfilled under each given utilization level of the PC capacity. We then construct a cost function of a recursive form, and prove that the resulting search algorithm always converges to the optimal solution within pseudo-polynomial time. Two numerical examples are presented to test the computational performance of the proposed algorithm.