Bi-objective optimisation for integrated scheduling of single machine with setup times and preventive maintenance planning

This paper deals with an integrated bi-objective optimisation problem for production scheduling and preventive maintenance in a single-machine context with sequence-dependent setup times. To model its increasing failure rate, the time to failure of the machine is subject to Weibull distribution. The two objectives are to minimise the total expected completion time of jobs and to minimise the maximum of expected times of failure of the machine at the same time. During the setup times, preventive maintenance activities are supposed to be performed simultaneously. Due to the assumption of non-preemptive job processing, three resolution policies are adapted to deal with the conflicts arising between job processing and maintenance activities. Two decisions are to be taken at the same time: find the permutation of jobs and determine when to perform the preventive maintenance. To solve this integrated problem, two well-known evolutionary genetic algorithms are compared to find an approximation of the Pareto-optimal front, in terms of standard multi-objective metrics. The results of extensive computational experiments show the promising performance of the adapted algorithms.