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An important element in the integration of the fourth industrial revolution is the development of efficient algorithms to deal with dynamic scheduling problems. In dynamic scheduling, jobs can be admitted during the execution of a given schedule, which necessitates appropriately planned rescheduling decisions for maintaining a high level of performance. In this paper, a dynamic case of the multiprocessor open shop scheduling problem is addressed. This problem appears in different contexts, particularly those involving diagnostic operations in maintenance and health care industries. Two objectives are considered simultaneously—the minimization of the makespan and the minimization of the mean weighted flow time. The former objective aims to sustain efficient utilization of the available resources, while the latter objective helps in maintaining a high customer satisfaction level. An exact algorithm is presented for generating optimal Pareto front solutions. Despite the fact that the studied problem is NP-hard for both objectives, the presented algorithm can be used to solve small instances. This is demonstrated through computational experiments on a testbed of 30 randomly generated instances. The presented algorithm can also be used to generate approximate Pareto front solutions in case computational time needed to find proven optimal solutions for generated sub-problems is found to be excessive. Furthermore, computational results are used to investigate the characteristics of the optimal Pareto front of the studied problem. Accordingly, some insights for future metaheuristic developments are drawn.

Bi-Objective Dynamic Multiprocessor Open Shop Scheduling: An Exact Algorithm