Scheduling parallel extrusion lines

Abstract

This paper introduces the problem of scheduling jobs on parallel plastic extrusion lines where each line is composed of one or more than one extruder. Although there are some similarities between the introduced problem and the non-identical parallel machines scheduling problems with sequence-dependent setup times, limited additional resources and machine eligibility restrictions, the problem considered in this paper is a generalization of the parallel machine scheduling problem. This is because in parallel machines scheduling each job requires only one machine but in our case some jobs require more than one machine. Thus, our problem reduces to the parallel machine scheduling problem if all jobs require only one machine. This paper describes the problem of scheduling parallel extrusion lines, its industrial context, and develops a mixed-linear formulation to model the problem. This formulation allowed solving instances of up to 15 jobs. In addition, we developed four metaheuristics: a simulated annealing algorithm, a tabu search heuristic, a genetic algorithm, and a greedy randomized adaptive search procedure. These metaheuristics can be used to solve real-life instances of the problem. A numerical experiment shows that the proposed metaheuristics produce excellent solutions. Some of the proposed simulated annealing adaptations and of the tabu search heuristics obtained solutions with less than 2% deviation from the optimum.