Two heuristics for the capacitated multi-period cutting stock problem with pattern setup cost

Abstract

This paper concentrates on a capacitated multi-period cutting stock problem. In the production process, multiple identical input rods can be bundled together and cut simultaneously. We say that these input rods are cut with the same pattern. Vanderbeck (2000) once noted that changing from one pattern to another involves significant setup times (to adjust for knife positions) and costs (e.g., those associated with waste from trial runs); thus, the pattern setup cost cannot be neglected. In this paper, we therefore consider the capacitated multi-period cutting stock problem with pattern setup cost. In this regard, we aim to determine the patterns and occurrence of such patterns in each decision period over the planning horizon in order to minimize the total cost, including the pattern setup, inventory holding, and material consumed costs. We present two mathematical models: the Gilmore-Gomory model and the Arc flow model. In addition, two heuristics are proposed: a column generation-based heuristic (CGH) and a dynamic programming-based heuristic (IDPH). Extensive experimental studies are executed based on randomly generated instances. The computational results show that the Gilmore-Gomory model works better than the Arc flow model for the capacitated multi-period cutting stock problem with pattern setup cost. Moreover, the two heuristics are comparable, as both can obtain high quality solutions. Statistical analyses are also performed to verify these conclusions.