A constraint programming-based iterated greedy algorithm for the open shop with sequence-dependent processing times and makespan minimization

Abstract

In this paper, a novel variant of the open shop scheduling problem where the jobs have sequence-dependent processing times is addressed. The performance measure considered is the minimization of the length of the schedule (makespan). This problem arises in several real-life settings and, particularly, our work is inspired in scheduling samples in a quality control laboratory where a series of tests have to be performed in different equipment – being irrelevant the order in which these tests are performed –, and the time required to perform the tests depends on the previous sample tested. For this problem, we compare the results of a Mixed-Integer Linear Programming (MILP) model with those from a Constraint Programming (CP) model specifically proposed for the problem, showing that the latter yields better results. Given the NP-hard nature of the problem, in order to obtain good – but not necessarily optimal – solutions within reasonable computational effort, we propose a matheuristic consisting of an Iterated Greedy Algorithm hybridized with a reconstruction phase based in executing the CP model with a partial solution. The results of the computational experiments carried out on 160 instances based on established datasets show the ability of the matheuristic to solve large-sized instances, in contrast with exact (i.e. MILP and CP) models. Our proposal outperforms the most efficient approximate procedures from related problems that have been adapted to the problem under consideration. A subsequent statistical analysis is carried out to prove the statistical significance of these results.