The Distributed Assembly Parallel Machine Scheduling Problem with eligibility constraints

In this paper we jointly consider realistic scheduling extensions: First we study the distributed unrelated parallel machines problems by which there is a set of identical factories with parallel machines in a production stage. Jobs have to be assigned to factories and to machines. Additionally, there is an assembly stage with a single assembly machine. Finished jobs at the manufacturing stage are assembled into final products in this second assembly stage. These two joint features are referred to as the distributed assembly parallel machine scheduling problem or DAPMSP. The objective is to minimize the makespan in the assembly stage. Due to technological constraints, machines cannot be left empty and some jobs might be processed on certain factories only. We propose a mathematical model and two high performing heuristics. The model is tested with two state-of-the-art solvers and, together with the heuristics, 2220 instances are solved in a comprehensive computational experiments. Results show that the proposed model is able to solve moderately-sized instances and one of the heuristics is fast, giving close to optimal solutions in less than half a second in the worst case.