Stochastic Dynamic Inventory Problem Under Explicit Inbound Transportation Cost and Capacity

• 成果类型: Article
• 署名作者: Zhang, Liqing; Cetinkaya, Sila
• 署名单位: Southern Methodist University; Southern Methodist University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2017.1625
• 发表日期: 2017
• 页码: 1267-1274
• 关键词: Optimal policy; setup costs; optimality

摘要

We study a practical generalization of the classical stochastic dynamic inventory problem where privately owned trucks with limited cargo capacity are used to transport the replenishment quantity. The resulting replenishment cost function also includes the traditional fixed setup cost, and it is known as a multiple setup cost structure, which leads to complicated cost-to-go functions in the problem of interest. We introduce the concepts of non-(Delta,C)-decreasing and non-(Delta,C)(NK)-decreasing, and we develop a sophisticated replenishment policy called the (Q, (s)over-right-arrow, (S)over-right-arrow) policy. We examine the sufficient conditions under which the new policy is optimal. Our results offer a detailed characterization of optimal policies and generalize the existing theory on the concepts of K-convexity and non-K-decreasing. In doing so, we are able to investigate a traditional stochastic inventory problem which has remained open in the literature for more than four decades.