Solving an Unrelated Parallel Machines Scheduling Problem with machine- and job-dependent setups and precedence constraints considering Support Machines

Abstract

Single-stage production planning problems are common in the academic literature and in real-world environments. One of the least studied scenarios in the literature for this environment is that with Unrelated Parallel Machines. In this work, this type of problem is inspired by a real station within the wind tower production process. The problem presents characteristics that have already been studied, such as mandatory precedences and setup times that depend on the machine and the job. However, a new and real feature is presented: the existence of “support machines”, which are machines that can continue to work but cannot complete jobs due to reduced capacity for some operational reason. In this case, instead of abandoning their work, support machines can still be used to assist other machines by performing partial jobs before handing them over to full-capacity machines for completion. This innovative concept of support machines, never before presented in this context of production planning, introduces a unique approach to dealing with reduced-capacity machines without sacrificing their operational potential. A Mixed-Integer Linear Programming (MILP) model is formulated to mathematically represent this problem.This work explores the impact of these support machines on production planning. For this purpose, Tabu Search and Simulated Annealing metaheuristics have been adapted for their solution, and a novel Constructive Heuristic has been developed based on the real and manual process currently performed in the aforementioned factory. These three algorithms are run and compared on a real database in order to minimise the makespan. Their analysis shows that although the use of support machines generally gives positive results, an improvement is not achieved in all cases. Furthermore, contrary to what might be expected, the use of full-capacity machines in the role of support machines sometimes improves completion times.