A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints
Minjiao Zhang, Simge Küçükyavuz, Saumya Goel
Management Science · 2014 · Volume 60 · Issue 5
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
Enable JavaScript for citation tools and additional paper interactions.