A mathematical model for the product mixing and lot-sizing problem by considering stochastic demand

Abstract

The product-mix planning and the lot size decisions are some of the most fundamental research themes for the operations research community. The fact that markets have become more unpredictable has increaed the importance of these issues, rapidly. Currently, directors need to work with product-mix planning and lot size decision models by introducing stochastic variables related to the demands, lead times, etc. However, some real mathematical models involving stochastic variables are not capable of obtaining good solutions within short commuting times. Several heuristics and metaheuristics have been developed to deal with lot decisions problems, in order to obtain high quality results within short commuting times. Nevertheless, the search for an efficient model by considering product mix and deal size with stochastic demand is a prominent research area. This paper aims to develop a general model for the product-mix, and lot size decision within a stochastic demand environment, by introducing the Economic Value Added (EVA) as the objective function of a product portfolio selection. The proposed stochastic model has been solved by using a Sample Average Approximation (SAA) scheme. The proposed model obtains high quality results within acceptable computing times.

Keywords

• Lot Sizing
• Product-mix planning
• Stochastic demand
• EVA
• Sample average approximation