|edoc-Server der Humboldt-Universität zu Berlin|
Kavinesh J. Sing, Mighty River Power|
Andy B. Philpott, University of Auckland
R. Kevin Wood, Naval Postgraduate School
|Title:||Dantzig-Wolfe decomposition for solving multi-stage stochastic capacity-planning problems|
|Date of Acceptance:||07.03.2008|
Stochastic Programming E-Print Series |
|Editors:||Julie L. Higle; Werner Römisch; Surrajeet Sen|
|Complete Preprint:||pdf (urn:nbn:de:kobv:11-10086965)|
|Keywords (eng):||column generation, multi-stage stochastic mixed-integer program, branch-and-price, capacity expansion, Dantzig-Wolfe decomposition|
|Submitted in:||Operations Research|
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|We describe a multi-stage, stochastic, mixed-integer-programming model for planning discrete 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 scheme.” 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 6 stages and 243 scenarios, and corresponds to a deterministic equivalent with a quarter of a million binary variables.|
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