Dantzig-Wolfe Decomposition for Solving Multistage Stochastic Capacity-Planning Problems
成果类型：
Article
署名作者：
Singh, Kavinesh J.; Philpott, Andy B.; Wood, R. Kevin
署名单位：
University of Auckland; United States Department of Defense; United States Navy; Naval Postgraduate School
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1080.0678
发表日期：
2009
页码：
1271-1286
关键词：
摘要：
We describe a multistage, stochastic, mixed-integer programming model for planning capacity expansion of production facilities. A scenario tree represents uncertainty in the model; a general mixed-integer program defines the operational submodel at each scenario-tree node, and capacity-expansion decisions link the stages. We apply variable splitting to two model variants, and solve those variants using Dantzig-Wolfe decomposition. The Dantzig-Wolfe master problem can have a much stronger linear programming relaxation than is possible without variable splitting, over 700% stronger in one case. The master problem solves easily and tends to yield integer solutions, obviating the need for a full branch-and-price solution procedure. For each scenario-tree node, the decomposition defines a subproblem that may be viewed as a single-period, deterministic, capacity-planning problem. An effective solution procedure results as long as the subproblems solve efficiently, and the procedure incorporates a good duals stabilization method. We present computational results for a model to plan the capacity expansion of an electricity distribution network in New Zealand, given uncertain future demand. The largest problem we solve to optimality has six stages and 243 scenarios, and corresponds to a deterministic equivalent with a quarter of a million binary variables.