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Process planning and scheduling are two crucial components in a flexible manufacturing system. Lots of novel meta-heuristics have been applied to the integrated process planning and scheduling (IPPS) problem for an efficient utilization of manufacturing resources; nevertheless, the tricky part in real life stems from the uncertainty in processing times. Existing publications regarding IPPS problems mainly focus on cases with nominal or fixed processing times; nevertheless, processing time fluctuations will certainly result in an intolerable deviation between the actual makespan and the nominal one. This research focuses on the IPPS problem with uncertain processing times to hedge against the uncertainty in makespan. The novel neutrosophic numbers are first introduced to model the uncertain processing times. A neutrosophic number based mixed integer linear programming (MILP) model is established; due to the non-deterministic polynomial (NP)-hardness and the complexity in solving the model, a variable neighborhood search (VNS) incorporated memetic algorithm (MA) is then developed to facilitate more robust solutions. In the proposed algorithm, the nominal makespan criterion and the deviation (robustness) criterion have been considered in a weighted sum manner. The well-known Kim's benchmark is adopted to test the performance of the proposed algorithm and different degrees of fluctuations are also defined in experiments. Computational results reveal that the VNS based local search method is powerful in capturing promising solutions; competitive solutions with superior nominal makespan and robustness have been obtained. This research presents a novel perspective or methodology to seek more robust solutions for the uncertain IPPS problem.

A Neutrosophic Number-Based Memetic Algorithm for the Integrated Process Planning and Scheduling Problem With Uncertain Processing Times