Minimizing the makespan and the system unavailability in parallel machine scheduling problem: a similarity-based genetic algorithm

This paper is devoted to ponder a joint production and maintenance problem. For solving the problem, a genetic algorithm named similarity-based subpopulation genetic algorithm (SBSPGA) is introduced. SBSPGA is presented based on a well-known evolutionary algorithm, the subpopulation genetic algorithm II (SPGA-II). Compared with the SPGA-II, the innovation of the SBSPGA could be divided into two parts: (1) using a similarity model for the elitism strategy and (2) performing the algorithm in just one stage. To tackle the maintenance aspect, reliability models are employed in this paper. The aim of this paper was to optimize two objectives: minimization of the makespan for the production part and minimization of the system unavailability for the maintenance part. To execute our proposed problem, two decisions must be made at the same time: achieving the best assignment of n jobs on m machines to minimize the makespan and determining the time at which the preventive maintenance activities must be performed to minimize the system unavailability. The maintenance activity numbers and the maintenance intervals are not fixed in advanced. Promising the acquired results, a benchmark with tremendous number of test instances (more than 5,000) is employed.