Optimal stock sizing in a cutting stock problem with stochastic demands

Abstract

One dimensional cutting stock problems arise in many manufacturing domains such as pulp and paper, textile and wood. In this paper, a new real life variant of the problem occuring in the rubber mold industry is introduced. It integrates both operational and strategical planning optimization: on one side, items need to be cut out of stocks of different lengths while minimizing trim loss, excess of production and the number of required cutting operations. Demands are however stochastic therefore the strategic choice of which mold(s) to build (i.e. which stock lengths will be available) is key for the minimization of the operational costs. A deterministic pattern-based formulation and a two-stage stochastic problem are presented. The models developed are solved with a mixed integer programming solver supported by a constraint programming procedure to generate cutting patterns. The approach shows promising experimental results on a set of realistic industrial instances.