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

Minjiao Zhang (), Simge Küçükyavuz () and Saumya Goel ()
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Minjiao Zhang: Department of Integrated Systems Engineering, Ohio State University, Columbus, Ohio 43210
Simge Küçükyavuz: Department of Integrated Systems Engineering, Ohio State University, Columbus, Ohio 43210
Saumya Goel: Department of Integrated Systems Engineering, Ohio State University, Columbus, Ohio 43210

Management Science, 2014, vol. 60, issue 5, 1317-1333

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.Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2013.1822 . This paper was accepted by Dimitris Bertsimas, optimization .

Keywords: chance constraints; branch-and-cut; multistage; probabilistic lot sizing; service levels (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (9)

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