Scenario aggregation in single-resource production planning models with uncertain demand

Abstract

Abstract In this paper we present an application of the scenario aggregation approach proposed by Rockafellar and Wets to a simple standard multi-product multi-period production planning problem with uncertain demand and setup cost modelled by logical zero-one variables. The uncertainty in demand is expressed by a number of demand scenarios. As compared with more traditional approaches that require distributional assumptions and/or estimates of parameters from historical demand data, the scenario approach offers greater flexibility and makes it possible to take subjective information into account. The scenario aggregation principle and the corresponding progressive hedging algorithm offer a theoretically sound basis for generating consistent solutions for production planning models with uncertain demand. Since the production planning problem studied in this paper is of mixed-integer type the original scenario aggregation approach cannot be applied directly. However, since the integer variables in the prod...