A Memory-Efficient Implementation of Multi-Period Two- and Multi-Stage Stochastic Programming Models

The objective of this paper is to describe a method of implementing multi-period two- and multi-stage Stochastic Programming (SP) models with exogenous uncertainty that is modeling-platform and programming-language independent. The proposed implementation approach generates an implicit extensive form of the SP model in contrast to an explicit formulation, which explicitly accounts for the sequence of decisions, thus introducing redundant variables and constraints in the model. The efficiency of the proposed implementation approach with respect to memory usage, thus problem size, is achieved with the introduction of three sets of auxiliary parameters in the mathematical formulation of the deterministic equivalent stochastic program. The three parameters capture the non-anticipativity condition, the mapping between scenarios and stages, and the structure of the scenario tree in terms of ancestor nodes without explicitly modeling each node individually. A real-world multi-product, multi-period network planning optimization model is used to illustrate the effectiveness of the proposed implementation approach.