A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
Formulating two-stage stochastic programs for interior point methods
Operations Research
Mixed 0-1 programming by lift-and-project in a branch-and-cut framework
Management Science
Discrete Mathematics
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
A scenario-based stochastic programming approach for technology and capacity planning
Computers and Operations Research
Reoptimization With the Primal-Dual Interior Point Method
SIAM Journal on Optimization
A Multi-Stage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty
Journal of Global Optimization
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
Capacitated Network Design with Uncertain Demand
INFORMS Journal on Computing
Commissioned Paper: Capacity Management, Investment, and Hedging: Review and Recent Developments
Manufacturing & Service Operations Management
Multiperiod capacity expansion of a telecommunications connection with uncertain demand
Computers and Operations Research
Duality gaps in nonconvex stochastic optimization
Mathematical Programming: Series A and B
Solving a class of stochastic mixed-integer programs with branch and price
Mathematical Programming: Series A and B
Selected Topics in Column Generation
Operations Research
Dual decomposition in stochastic integer programming
Operations Research Letters
An exact algorithm for IP column generation
Operations Research Letters
Optimal scenario tree reductions for the stochastic unit commitment problem
Proceedings of the Winter Simulation Conference
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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.