Strategic and Tactical Planning Models for Supply Chain: An Application of Stochastic Mixed Integer Programming

Stochastic mixed integer programming (SMIP) models arise in a variety of applications. In particular they are being increasingly applied in the modelling and analysis of financial planning and supply chain management problems. SMIP models explicitly consider discrete decisions and model uncertainty and thus provide hedged decisions that perform well under several scenarios. Such SMIP models are relevant for industrial practitioners and academic researchers alike. From an industrial perspective, the need for well-hedged solutions cannot be overemphasized. On the other hand the NP-Hard nature of the underlying model (due to the discrete variables) together with the curse of dimensionality (due to the underlying random variables) make these models important research topics for academics. In this chapter we discus the contemporary developments of SMIP models and algorithms. We introduce a generic classification scheme that can be used to classify such models. Next we discuss the use of such models in supply chain planning and management. We present a case study of a strategic supply chain model modelled as a two-stage SMIP model. We propose a heuristic based on Lagrangean relaxation for processing the underlying model. Our heuristic can be generalized to an optimum-seeking branch-and-price algorithm, but we confine ourselves to a simpler approach of ranking the first-stage decisions which use the columns generated by the Lagrangean relaxation. In addition to providing integer feasible solutions, this approach has the advantage of mimicking the use of scenario analysis, while seeking good “here-and-now” solutions. The approach thus provides industrial practitioners an approach that they are able to incorporate within their decision-making methodology. Our computational investigations with this model are presented.