Solving Stochastic Transportation-Location Problems by Generalized Benders Decomposition

The discrete Stochastic Transportation-Location Problem, a mathematical model that captures the impact of uncertainty on location decisions, is a mixture of the classical plant location problem and the stochastic transportation problem. With demand at each destination a random variable, the problem is to minimize the sum of expected holding and shortage costs, (linear) shipping costs, and fixed construction costs. We discuss the use of Generalized Benders Decomposition to solve the resultant mixed-integer nonlinear program; this technique yields (convex) stochastic transportation subprograms, whose optimal multipliers generate constraints (cuts) for a master integer location problem. The selection of optimal multiplier vectors likely to yield rapid convergence is emphasized. Limited computational experience is found to be encouraging.