A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints

• 成果类型: Article
• 署名作者: Zhang, Minjiao; Kucukyavuz, Simge; Goel, Saumya
• 署名单位: University System of Ohio; Ohio State University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2013.1822
• 发表日期: 2014
• 页码: 1317-1333
• 关键词: chance constraints; branch-and-cut; multistage; probabilistic lot sizing; service levels

摘要

In this paper, we consider a finite-horizon stochastic mixed-integer program involving dynamic decisions under a constraint on the overall performance or reliability of the system. We formulate this problem as a multistage (dynamic) chance-constrained program, whose deterministic equivalent is a large-scale mixed-integer program. We study the structure of the formulation and develop a branch-and-cut method for its solution. We illustrate the efficacy of the proposed model and method on a dynamic inventory control problem with stochastic demand in which a specific service level must be met over the entire planning horizon. We compare our dynamic model with a static chance-constrained model, a dynamic risk-averse optimization model, a robust optimization model, and a pseudo-dynamic approach and show that significant cost savings can be achieved at high service levels using our model.