The Distributed Parallel Machine and Assembly Scheduling Problem with eligibility constraints

In this paper we jointly consider several realistic scheduling extensions: First we study the distributed unrelated parallel machines problem where there is a set of identical factories with parallel machines in the 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 Parallel Machine and Assembly Scheduling Problem or DPMASP. The objective is to minimize the makespan in the assembly stage. Due to technological constraints, machines cannot be idle and some jobs can be processed only in certain factories. 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 experience. Results show that the proposed model is able to solve moderately-sized instances, and that one of the heuristics is fast, giving optimal solutions close to optimum in less than half a second in the worst case.