回购与缺货成本下的连续时间报童模型

doi:10.3969/j.issn.1005-3085.2023.01.006

工程数学学报 ›› 2023, Vol. 40 ›› Issue (1): 83-96.doi: 10.3969/j.issn.1005-3085.2023.01.006

回购与缺货成本下的连续时间报童模型

张未未

惠州学院数学与统计学院，惠州 516007

出版日期:2023-02-15 发布日期:2023-04-11
基金资助:
惠州学院校立项目 (91801).

The Continuous Time Newsvendor with Return and Shortage Cost

ZHANG Weiwei

School of Mathematics and Statistics, Huizhou University, Huizhou 516007

Online:2023-02-15 Published:2023-04-11
Supported by:
The School Establishment Project of Huizhou University (91801).

摘要/Abstract

摘要：

对带回购策略与缺货成本的连续时间报童模型，研究了其最优订购策略与批发价策略，使得生产商和零售商期望收益最大化。在零售价格依赖需求过程与零售价格外生的两种情形下，讨论了带回购策略和缺货成本对连续时间报童均衡策略的共同影响。运用随机最大值原理研究了以上问题均衡策略的存在唯一性，讨论了均衡策略满足的条件，在价格外生情形下得出结论：回购策略与缺货成本的共同作用，使得零售商的最优订购量和供应商的最优批发价格均提高很多。最后，通过数值算例做了最优批发价格与最优订购策略的敏感度分析，具体例子验证了已得结论。

关键词: 连续时间报童模型, Stackelberg博弈, Hamilton函数, Ornstein-Uhlenbeck过程, 随机最大值原理, 回购策略

Abstract:

The equilibrium strategy is considered for a continuous-time newsvendor problem with the return policy and shortage cost. In the continuous-time newsvendor problem, the supplier and the retailer want to find the optimal strategy to maximize the expected terminal profit. An optimization problem is studied which is a continuous-time newsvendor problem with return policy and shortage cost. By using the principle of stochastic maximum, the existence and uniqueness of the equilibrium strategy are proved for this optimization problem and the conditions are obtained, which assure the equilibrium strategy. When the retail price is exogenous, the combined effect of the return policy and the shortage cost are proved to increase a lot the optimal order quantity of the retailer and the optimal whole sale price of the supplier. The numerical analysis shows the sensitive about the optimal wholesale price and the optimal order strategy.

Key words: continuous time newsvendor model, Stackelberg game, Hamilton function, Ornstein-Uhlenbeck process, stochastic maximum principle, return policy

中图分类号:

张未未. 回购与缺货成本下的连续时间报童模型[J]. 工程数学学报, 2023, 40(1): 83-96.

ZHANG Weiwei. The Continuous Time Newsvendor with Return and Shortage Cost[J]. Chinese Journal of Engineering Mathematics, 2023, 40(1): 83-96.

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回购与缺货成本下的连续时间报童模型

The Continuous Time Newsvendor with Return and Shortage Cost

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