Bi-objective optimization algorithms for joint production and maintenance scheduling under a global resource constraint: Application to the permutation flow shop problem

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Production scheduling and maintenance planning are two of the most important tasks that managers face before implementing their decisions on the shop floor. Another issue managers have to keep in mind is the proper allocation of various resources for production. These issues create difficulties in the planning process. In this paper, we propose a bi-objective model that integrates the three aforementioned issues and determines production scheduling, maintenance planning and resource supply rate decisions in order to minimize the make span and total production costs, which include total maintenance, resource consumption and resource inventory costs. Two meta heuristic methods were employed to find approximations of the Pareto optimal front in a permutation flow shop environment: The well-known non-dominated sorting genetic algorithm (NSGA-II) and a bi-objective adaptation of the particle swarm optimization (BOPSO). Additionally, a bi-objective randomized local search (BORLS) heuristic was developed in order to generate multiple non-dominated solutions along its search path. Two sets of computational experiments were conducted. In the first set, the performances of the two meta heuristics with purely random initial populations were compared, with results showing the superiority of BOPSO over NSGA-II. In the second set, the initial populations were enhanced with heuristically generated solutions from BORLS and the performances of BOPSO, NSGA-II and BORLS used as an independent search algorithm, were compared. In this instance, the algorithms performed evenly for large problems, with the BORLS method generating better solutions when total production cost is emphasized.