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Different with the plain flexible job-shop scheduling problem (FJSP), the FJSP with routing flexibility is more complex and it can be deemed as the integrated process planning and (job shop) scheduling (IPPS) problem, where the process planning and the job shop scheduling two important functions are considered as a whole and optimized simultaneously to utilize the flexibility in a flexible manufacturing system. Although, many novel meta-heuristics have been introduced to address this problem and corresponding fruitful results have been observed; the dilemma in real-life applications of resultant scheduling schemes stems from the uncertainty or the nondeterminacy in processing times, since the uncertainty in processing times will disturb the predefined scheduling scheme by influencing unfinished operations. As a result, the performance of the manufacturing system will also be deteriorated. Nevertheless, research on such issue has seldom been considered before. This research focuses on the modeling and optimization method of the IPPS problem with uncertain processing times. The neutrosophic set is first introduced to model uncertain processing times. Due to the complexity in the math model, we developed an improved teaching-learning-based optimization(TLBO) algorithm to capture more robust scheduling schemes. In the proposed optimization method, the score values of the uncertain completion times on each machine are compared and optimized to obtain the most promising solution. Distinct levels of fluctuations or uncertainties on processing times are defined in testing the well-known Kim’s benchmark instances. The performance of computational results is analyzed and competitive solutions with smaller score values are obtained. Computational results show that more robust scheduling schemes with corresponding neutrosophic Gantt charts can be obtained; in general, the results of the improved TLBO algorithm suggested in this research are better than those of other algorithms with smaller score function values. The proposed method in this research gives ideas or clues for scheduling problems with uncertain processing times.

A neutrosophic set-based TLBO algorithm for the flexible job-shop scheduling problem with routing flexibility and uncertain processing times