Advances in Linear Stochastic Programming: the Two-level Decomposition Principle Via Dual Central Pricing

Multi-stage Stochastic Programming (MSP) has many practical applications for solving problems whose current resolution must be made while taking into account future uncertainty. A variety of methods exist for solving stochastic programming problems, among them are: direct methods such as simplex and interior point methods, and decomposition methods such as ACCPM (Analytic Center Cutting Plane Method), Dantzig-Wolfe and Benders decompositions, and L-shaped method. Moreover, approximation methods such as Monte Carlo simulation, as well as combinatorial heuristics are employed to solve this class of problems. In addition to extensive discussion on methods for solving multi-stage stochastic program, this book addresses two important production planning challenges namely, stochastic capacity planning; and stochastic in-house production and outsourcing planning. Problems are formulated as large-scale, Multi-stage Stochastic programs and solved implementing an innovative two-level, interior-point decomposition algorithm based on ACCPM.