A Mixed Integer Model for Unrelated Parallel Machine Scheduling with Job Deteriorating Effect

Maintenance planning has been widely applied in manufacturing systems to improve production efficiency. In some real cases, job processing times may change over time, but they are mostly assumed to be constant in the scheduling literature. Hence, in this article, a mixed integer model is developed to optimize scheduling jobs on unrelated parallel machines with reliability-based maintenance and job deteriorating effects. The proposed model considers a reliability-based maintenance system and multi-stage quality cost and starts a time-dependent deteriorating effect. Based on the assumptions, if machines work in undesirable conditions, quality reduction and quality cost increment would occur. According to the start time-dependent deteriorating effect, the processing time of each job is a function of its start time. The problem is modeled by an integer linear programming method. Computational experiments are performed on various numerical instances to show the model’s effectiveness.