Closed-Form Solutions for Robust Inventory Management

• 成果类型: Article
• 署名作者: Mamani, Hamed; Nassiri, Shima; Wagner, Michael R.
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2015.2391
• 发表日期: 2017
• 页码: 1625-1643
• 关键词: Inventory Management; robust optimization; dynamic optimization; Central Limit Theorem

摘要

We propose and analyze robust optimization models of an inventory management problem, where cumulative purchase, inventory, and shortage costs over n periods are minimized for correlated nonidentically distributed demand. We assume that the means and covariance matrix of stochastic demand are known; the distributions are not needed. We derive closed-form ordering quantities for both symmetric and asymmetric uncertainty sets, under capacitated inventory constraints, in both static and dynamic settings. The behaviors of our robust strategies differ qualitatively depending on the symmetry of the uncertainty set. For instance, considering our simplest static problem, (1) if the uncertainty set is symmetric, then there is positive ordering in all periods, whereas (2) if the set is asymmetric, then there is a set of periods in the middle of the planning horizon with zero orders. We also link the symmetry of the uncertainty set to the symmetry of the demand distribution. Finally, we present encouraging computational results where our solution compares favorably to previously studied, more complex robust solutions.