Scheduling of job shop, make-to-order industries with recirculation and assembly: a MILP approach

This paper studies the performance of two Mixed Integer Linear Programming (MILP) models to solve scheduling problems in a flexible job shop environment with recirculation and assembly using a due-date-based objective function. The models convey different approaches both in the modelling of time (discrete and continuous approaches) as well as in the assignment of jobs to machines. In the discrete time formulation, time is modelled explicitly through a time index with no binary variables being required for machine assignment. In the continuous time formulation, modelling of time is implicit and jobs are assigned to machines through binary variables. The formulations are compared by scheduling a job shop system considered close to the reality of the mould making industry. Both models were tested for sets that range from 10 to 40 jobs to be scheduled and for operational scenarios of (1) a single machine per operation and (2) two or more machines in parallel per operation. As a main conclusion it can be stated that in the first scenario the continuous time formulation performs better than its discrete counterpart while in the second scenario the discrete time formulation outperforms the continuous one.