Bounding the search space of the population harvest cutting problem with multiple size stock selection

In this paper we deal with a variant of the Multiple Stock Size Cutting Stock Problem (MSSCSP) arising from population harvesting, in which some sets of large pieces of raw material (of different shapes) must be cut following certain patterns to meet customer demands of certain product types. The main extra difficulty of this variant of the MSSCSP lies in the fact that the available patterns are not known a priori. Instead, a given complex algorithm maps a vector of continuous variables called a values vector into a vector of total amounts of products, which we call a global products pattern. Modeling and solving this MSSCSP is not straightforward since the number of value vectors is infinite and the mapping algorithm consumes a significant amount of time, which precludes complete pattern enumeration. For this reason a representative sample of global products patterns must be selected. We propose an approach to bounding the search space of the values vector and an algorithm for performing an exhaustive sampling using such bounds. Our approach has been evaluated with real data provided by an industry partner.