The scheduling of parallel machines is a well-known problem in many companies. Nevertheless, not always all the jobs can be manufactured in any machine and the eligibility appears. Based on a real-life problem, we present a model which has three different machines, called as high, medium and low level respectively. The set of jobs to be scheduled on these three parallel machines are also distributed among these three levels: one job from a level can be manufactured in a machine of the same or higher level. But a penalty appears when a job is manufactured in a machine different from the higher level. Besides, there are release dates and delivery times associated to each job. The tackled problem is bi-objective with the criteria: minimization of the final date-i.e. the maximum for all the jobs of their completion time plus the delivery time-and the minimization of the total penalty generated by the jobs. In a first step we revisited possible heuristics to minimize the final date on a single machine. In a second step a heuristic is proposed to approximate the set of efficient solutions and the Pareto front of the bi-objective problem. All the algorithms are experimented on various instances.

Peer Reviewed