Joint parallel-machine scheduling and maintenance planning optimisation with deterioration, unexpected breakdowns, and condition-based maintenance

The joint optimisation of production scheduling and maintenance planning can significantly decrease production interruptions (or stoppages) and, simultaneously, improve production stability and enhance the reliability and availability of equipment and machines. This paper studies the joint optimisation of production schedules and CBM plans in a parallel-machine production setting. The machines are subject to deterioration, unexpected breakdowns, and deterioration-based failures. The reliability of the machines is modelled as a multi-state system in which two deterioration thresholds are introduced to initiate maintenance and prevent deterioration-based failures. An integrated optimisation model is proposed to solve this new problem. The proposed model employs Markov chains to formulate machines’ reliability and a matrix-based approach to estimate the expected processing times, energy consumption, and maintenance costs. Then, a mixed-integer programming model is proposed that jointly optimises production schedules and maintenance plans by minimising a weighted sum objective function that includes expected lateness, maintenance, and energy consumption costs. A genetic algorithm (GA) is used to solve the new problem, and extensive computational experiments are performed to test the performance of the proposed GA. The results show the superiority of the proposed GA for all the test problems compared to two well-known metaheuristics.