Heuristics for a Distributed Parallel Machine Assembly Scheduling Problem with eligibility constraints

In this paper we study a production scheduling problem with production and assembly stages. There is a set of distributed identical factories, each one with a set of unrelated parallel machines at the production stage and a single assembly machine in the assembly stage. Jobs have to be assigned to one of the distributed factories and processed by one of the unrelated parallel machines. Processed jobs are assembled into final products through a defined assembly program in the assembly stage. This problem is referred to as the Distributed Parallel Machine Assembly Scheduling Problem or DPMASP. Minimizing the makespan of the products in the assembly stage is considered as the objective. Because of technological constraints, some factories are bit able to process some jobs and empty machines at factories are permitted. We present a mathematical model, four simple, fast and high performing heuristics to solve the considered problem. CPLEX and GUROBI as two state-ofthe- art commercial solvers are used to solve the mathematical model. Comprehensive computational experiments and ANOVA statistical analyses are performed to evaluate the performance of the proposed mathematical model and heuristics. Our results show that the mathematical model is able to solve moderatelysized instances and some of the heuristics report solutions that are very close to optimality in negligible CPU times.