Two-Stage Genetic Algorithm for Scheduling Stochastic Unrelated Parallel Machines in a Just-in-Time Manufacturing Context

Abstract

This paper considers a stochastic parallel machine scheduling problem in a just-in-time manufacturing context, in which its processing time can be described by a gamma or log-normal distribution. In order to obtain a high-performance schedule in a reasonable time, this work proposes a two-stage genetic algorithm with optimal computing budget allocation (OCBA) and improved Monte-Carlo Policy Evaluation (MCPE). In it, a genetic algorithm is selected as a main optimizer. An OCBA-based approach is developed to improve search efficiency, which is designed for two scenarios in a just-in-time manufacturing context. Different from most prior OCBA studies, this work considers that the stochastic processing time of jobs does not obey normal distribution. It extends the application area of OCBA by laying a theoretical foundation. A parameter control scheme based on MCPE is proposed, which aims to balance the global and local search in GA. To further enhance the efficiency and effectiveness of the proposed method, a two-stage framework is constructed. In the first stage, the performance is estimated roughly aiming at locating satisfactory solution regions. In the second stage, OCBA is incorporated to provide the reliable evaluation of excellent individuals. The theoretic interpretation of the proposed OCBA, and the convergence analysis results of the proposed method are presented. Various simulation results with benchmark and randomly generated cases validate that the proposed algorithm is more efficient and effective than several existing optimization algorithms. Note to Practitioners—A parallel machine scheduling problem under stochastic processing time is usually solved via meta-heuristic algorithms. However, their computational efficiency requires substantial improvement, especially for a stochastic optimization case that requires Monte Carlo sampling to estimate the actual objective function values in a precise manner. Most of them are parameter-sensitive, and choosing their proper parameters is highly challenging. For the first thorny issue, we develop an OCBA-based approach for determining the optimal numbers of simulations according to both prior knowledge and simulation results. In order to select proper control parameters of the proposed algorithm iteratively, we introduce a parameter control scheme based on MCPE. The combination of a meta-heuristic algorithm, OCBA and MCPE makes it possible to find high-quality solutions for the concerned scheduling problems in a short time. Theoretic analysis and numerical simulation results suggest that the proposed framework is valid and efficient. Hence, it can be readily applicable to practical systems, e.g., semiconductor manufacturing.