An Extended Mixed-Integer Programming Formulation and Dynamic Cut Generation Approach for the Stochastic Lot-Sizing Problem

Abstract

We present an extended mixed-integer programming formulation of the stochastic lot-sizing problem for the static-dynamic uncertainty strategy. The proposed formulation is significantly more time efficient as compared to existing formulations in the literature and it can handle variants of the stochastic lot-sizing problem characterized by penalty costs and service level constraints, as well as backorders and lost sales. Also, besides being capable of working with a predefined piecewise linear approximation of the cost function—as is the case in earlier formulations—it has the functionality of finding an optimal cost solution with an arbitrary level of precision by means of a novel dynamic cut generation approach. The online appendix is available at https://doi.org/10.1287/ijoc.2017.0792 .