A Robust Expected Makespan for Permutation Flow Shop Scheduling Depending on Machine Failure Rate

The environment of Flow Shop Scheduling Problems (FSSPs) to minimize the makespan of n jobs that have to be performed on m machines is considered. In real-world manufacturing systems nowadays, the uncertain circumstances to execute these jobs have an essential effect on the final scheduling scheme. This paper puts forward an integrated optimization heuristics that combine two distinct factors in flow shop scheduling. These factors are the variation in the processing times and the machine's reliability (machine failure rate), which must be considered to obtain optimal scheduling under stochastic assumptions. Two new approaches have been proposed in this work to achieve a robust expected makespan in the stochastic environment. The procedure is to add buffer time depending on the machine failure rate. Hence, the first procedure is to add buffer time to each operation in the mission according to the reliability of all machines (system reliability). The second one is to add buffer time to each operation depending on the reliability of each machine (machine reliability). For solving this problem with consideration to minimizing the expected makespan and maximizing the robustness simultaneously, the well-known (NEH) heuristic is implemented to schedule a set of jobs. Computational simulations are carried out with some well-studied problems taken from the OR-Library. Experimental results show that the proposed methods provide robust and efficient solutions. Moreover, the effects of some parameters on the optimization performance are discussed