Mathematical models and a heuristic method for the multiperiod one-dimensional cutting stock problem

Abstract

The multiperiod cutting stock problem arises in the production planning and programming of many industries that have the cutting process as an important stage. Ordered items are required in different periods of a finite planning horizon. It is possible to bring forward or not the production of items. Unused inventory in a certain period becomes available for the next period, all together with new inventory which may come to be acquired in the market. Based on mixed integer optimization models from the literature, extensions are proposed to deal with the multiperiod case and a residual heuristic is used. Computational experiments showed that effective gains can be obtained when comparing multiperiod models with the lot for lot solution, which is typically used in practice. Most of the instances are solved satisfactorily with a high performance optimization package and the heuristic method is used for solving the hard instances.