Packing by Scheduling: Using Constraint Programming to Solve a Complex 2D Cutting Stock Problem

Abstract

We investigate the novel Two-stage Cutting Stock Problem with Flexible Length and Flexible Demand (2SCSP-FF): orders for rectangular items must be cut from rectangular stocks using guillotine cuts with the objective to minimize waste. Motivated by our industrial partner and different from problems in the literature, the 2SCSP-FF allows both the length of individual items and the total area of orders to vary within customer-specified intervals. We develop constraint programming (CP) and mixed-integer programming models, with the most successful coming from the adaptation of CP scheduling techniques. Numerical results show that this CP model has orders of magnitude smaller memory requirements and is the only model-based approach investigated that can solve industrial instances.