A tabu search algorithm for Unspecified Parallel Machine scheduling with shift consideration

Abstract

This paper addresses the Unspecified Parallel Machine Flexible Resource Scheduling (UPMFRS) problem with shift consideration, focusing on assigning jobs to parallel machines while accounting for shifts and worker breaks, a practical aspect often overlooked in the literature. In this problem, teams of workers are treated as machines, and the duration of each job depends on the number of workers assigned to the team. We propose a two-stage algorithm combining bin-packing with a job scheduling heuristic to generate initial solutions. In the first stage, jobs and resources are allocated to active teams, while in the second stage, jobs are scheduled for each team. Then, the initial solutions are refined using a novel tabu search algorithm designed to handle the complexities of the problem. Our tabu search integrates neighborhood exploration techniques and strategic move selection to avoid local optima. The proposed algorithm’s performance is compared with the exact methods, the branch and cut in CPLEX, and the state-of-the-art bilinear branch and check (BBCh) algorithm. Numerical experiments indicate that our tabu search algorithm generates high-quality solutions. When these solutions are used as a warm start for BBCh (hybrid BBCh), BBCh’s performance is significantly enhanced. While BBCh alone and CPLEX can solve instances with up to 35 jobs, tabu search and the hybrid BBCh successfully handle problems with up to 100 jobs. These results confirm that the hybrid approach, with the high-quality solutions provided by our tabu search algorithm, is highly effective, practical, and reliable for large-scale scenarios while maintaining reasonable computational times.