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This paper addresses the groups of permutable operations method. This method is a flexible scheduling approach to hedge against uncertainties and is composed of a proactive/reactive phase. The proac-tive phase consists of computing a set of solutions (schedule) to a scheduling problem, leaving the choice of executing one of these solutions during the reactive phase according to the current state of the shop floor. During the reactive phase, the remaining decisions have to be made in real-time. The worst-case evaluation of the remaining solutions is a decision-aid parameter used during the reactive phase in order to control the final schedule from exceeding a worst-case performance. While the existing literature only tackles the worst-case evaluation of the groups of permutable operations, this paper deals with its best-case evaluation. For solving this problem, a new lower bound calculating this parameter in polynomial time is proposed. The computational efficiency of this parameter in a reactive algorithm exhibits very good performance. Moreover, the experiments show the robustness of this evaluation allowing this parameter to be used in an unstable job shop environment.

Evaluation of a new decision-aid parameter for job shop scheduling under uncertainties