Solving large-scale requirements planning problems with component substitution options

Abstract

This paper presents an approach for solving large-scale requirements planning problems with substitution options. The requirements planning with substitutions (RPS) problem, developed by Balakrishnan , A., & Geunes, J (2000) is defined as follows: consider a set of made-to-order products, each requiring at least one component for production. Every product has a preferred component for use in production, but can draw from a set of substitute components at a (per unit) substitution cost. Given the product demands over a finite horizon, determine the component production and substitution quantities in every period that minimize total component production, substitution, and holding costs. We show that under fixed plus linear (variable) production costs, this problem can be posed as an uncapacitated facility location problem, and extremely effective solution methods for this problem class can be employed to quickly solve RPS problems. Comparison of this (heuristic) approach with the (optimal) shortest path algorithm proposed by Balakrishnan, A.,& Geunes, J (2000) using a consistent test problem set shows that the facility location reformulation approach produced an optimal solution for every instance tested in a fraction of the time. We further demonstrate that the proposed approach has the potential to handle much larger problem instances than the shortest path algorithm.