Robust scheduling of parallel machines considering total flow time

Abstract

An effective approach to structuring uncertainty and making decisions under uncertain conditions is the robustness approach. The robust scheduling approach tries to create a schedule that minimizes the effect of disturbances caused by uncertainty during the operation on the objective function of initial scheduling. The present research was an attempt to study the problem of maximizing the probability that the total flow time does not exceed a predetermined limit in identical parallel machines while the processing time of each job is stochastic. In order to find an optimal solution to this problem, several theorems were proposed. The proposed theorems considerably reduced the search space and resulted in a branch and bound method to the problem with a specific branching scheme. Moreover, development of theorems to determine the dominance set along with introduction of dominance rules, an upper bound, and a lower bound helped find optimal solutions to the problems of 45 jobs and 5 machines. In addition, it was found that the method proposed in this paper for several machines is more effective than the methods developed for a single machine.