An Integer Programming Approach for Linear Programs with Probabilistic Constraints
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Easy distributions for combinatorial optimization problems with probabilistic constraints
Operations Research Letters
The Express heuristic for probabilistically constrained integer problems
Journal of Heuristics
Improved integer programming approaches for chance-constrained stochastic programming
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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We consider a supply chain operating in an uncertain environment: The customers' demand is characterized by a discrete probability distribution. A probabilistic programming approach is adopted for constructing an inventory-production-distribution plan over a multiperiod planning horizon. The plan does not allow the backlogging of the unsatisfied demand, and minimizes the costs of the supply chain while enabling it to reach a prescribed nonstockout service level. It is a strategic plan that hedges against undesirable outcomes, and that can be adjusted to account for possible favorable realizations of uncertain quantities. A modular, integrated, and computationally tractable method is proposed for the solution of the associated stochastic mixed-integer optimization problems containing joint probabilistic constraints with dependent right-hand side variables. The concept of p-efficiency is used to construct a finite number of demand trajectories, which in turn are employed to solve problems with joint probabilistic constraints. We complement this idea by designing a preordered set-based preprocessing algorithm that selects a subset of promising p-efficient demand trajectories. Finally, to solve the resulting disjunctive mixed-integer programming problem, we implement a special column-generation algorithm that limits the risk of congestion in the resources of the supply chain. The methodology is validated on an industrial problem faced by a large chemical supply chain and turns out to be very efficient: it finds a solution with a minimal integrality gap and provides substantial cost savings.