Bi-objective dynamic multiprocessor open shop scheduling for maintenance and healthcare diagnostics

Abstract

This paper addresses a bi-objective dynamic multiprocessor open shop scheduling problem in which the simultaneous objectives of minimizing both the mean weighted flow time and the makespan are considered. This problem is commonly encountered in maintenance and healthcare diagnostic systems. Since it is NP-hard for both objectives, efficient heuristics are needed to quickly generate a set of non-dominated solutions that a decision maker would choose from. For this sake, two metaheuristic approaches based on the non-dominated sorting genetic algorithm (NSGA-II) and the multi-objective grey wolf optimizer (MOGWO) are developed in this paper. Both metaheuristics are hybridized with simulated annealing (SA) local search. Parameter tuning computational experiments are conducted first on a set of 30 small instances from the literature for which Pareto optimal solutions are known. Then, computational experiments on large randomly generated instances are conducted. Computational results for small instances show that the NSGA-II is capable of generating non-dominated solutions that are very close to the optimal Pareto front. Results also reveal that the performance of the NSGA-II is better in most of the cases compared to the MOGWO under different settings of the studied problem for both small and large instances. However, for large instances with large number of workstations and jobs, low loading level and high percentage of busy machines at the beginning of the schedule, the difference in performance between both metaheuristics is minor.