Abstract
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.
Highlights
Process planning and scheduling are two important functions in manufacturing systems [1]–[5]
The operation flexibility, the sequencing flexibility and the processing flexibility are handled properly by introducing suitable constraints or variables and more importantly, relative neutrosophic variables and some constraints are mapped into the determinacy and the indeterminacy parts
Due to the non-deterministic polynomial (NP)-hardness of the problem and the complexity in solving the problem using the proposed mixed integer linear programming (MILP) model, a variable neighborhood search (VNS) based memetic algorithm is proposed for the problem to seek more robust solutions
Summary
Process planning and scheduling are two important functions in manufacturing systems [1]–[5]. We try to take the advantage of neutrosophic numbers in expressing indeterminate information or ambiguity of people’s cognition; uncertain processing times in this paper are modelled as neutrosophic numbers and corresponding optimization method will be developed to capture a more robust scheduling scheme. Neutrosophic numbers are first introduced in meta-heuristic algorithms to model uncertain processing times Such optimization method has not been investigated in existing research publications. Due to the complexity in solving the MILP model as well as the problem itself, we develop an effective memetic algorithm where the problem specific N5 and Nm neighborhood structures in VNS local search method are considered to obtain more promising results Both the robustness criterion and the makespan criterion have been optimized in a weighted sum manner because in most cases the deterioration of the makespan criterion will occur if only the robustness is considered in the algorithm. The conclusion as well as some future research directions will be presented in the last section to finalize this paper
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