Mathematical models and decomposition algorithms for makespan minimization in plastic rolls production

We study an optimization problem that originates from the packaging industry, and in particular in the process of blown film extrusion, where a plastic film is used to produce rolls of different dimensions and colors. The film can be cut along its width, thus producing multiple rolls in parallel, and setup times must be considered when changing from one color to another. The optimization problem that we face is to produce a given set of rolls on a number of identical parallel machines by minimizing the makespan. The problem combines together cutting and scheduling decisions and is of high complexity. For its solution, we propose mathematical models and heuristic algorithms that involve a nontrivial decomposition method. By means of extensive computational experiments, we show that proven optimality can be achieved only on small instances, whereas for larger instances good quality solutions can be obtained especially by the use of an iterated local search algorithm.