Boosted Arc Flow Formulation Using Graph Compression for the Two-Dimensional Strip Cutting Problem

Abstract

Since the requirement for a material cutting process occurs in a wide variety of applied contemporary manufacturing, the cutting stock problem plays a critical role in optimizing the amount of raw material utilized in everyday production operations. In this paper, we address the two-dimension strip-cutting problem and implement the graph compression technique to improve the performance of the arc-flow formulation. The number of variables of the obtained mathematical model are substantially reduced. A comparative study on a large set of benchmark instances shows that our compressed model yields very good results for the non-unitary item demand case in contrast to the state-of-the-art mathematical models. Moreover, improved bounds are provided for 24 unsolved benchmark instances, among which 8 have been solved to optimality.