An adaptive large neighborhood search for unrelated parallel machine scheduling with setup times and delivery times

Abstract

This paper investigates the problem of scheduling jobs on unrelated parallel machines, considering setup times and delivery times. The objective is to minimize the total weighted service time, which is the sum of the job’s completion time and delivery time. To address the problem, we introduce a mixed-integer programming model that is solved by the commercial solver CPLEX. Due to the NP-hardness of the problem, an adaptive large neighborhood search (ALNS) is developed to solve large-scale instances. The ALNS integrates effective operators and an initial solution generation method. Moreover, we propose a local search that consists of the problem’s lemmas and random variable neighborhood descent. To assess the performance of metaheuristic algorithms, a column generation algorithm (CG) is proposed. Afterwards, we carry out extensive numerical experiments on 4200 instances with up to 20 machines and 320 jobs. The results on small-scale instances show that the CG is capable of obtaining lower bounds tighter than those of the CPLEX, and ALNS is able to obtain solutions that are not inferior to the CPLEX in a very short time (0.33s). Furthermore, results on large-scale instances demonstrate that the duality gap between the upper and lower bounds of the ALNS is smaller than that of four state-of-the-art metaheuristic algorithms designed to solve similar problems.