"A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints" by Minjiao Zhang

Article

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

Management Science (2014)

Minjiao Zhang
Simge Kucukyavuz
Saumya Goel

Abstract

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.

Keywords

chance constraints; branch-and-cut; multistage; probabilistic lot sizing; service levels

Disciplines

Publication Date

2014

Citation Information

Minjiao Zhang, Simge Kucukyavuz and Saumya Goel. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints" Management Science (2014)
Available at: http://works.bepress.com/minjiaozhang/4/