A Three-Stage Optimization Algorithm for the Stochastic Parallel Machine Scheduling Problem with Adjustable Production Rates

Abstract

We consider a parallel machine scheduling problem with random processing/setup times and adjustable production rates. The objective functions to be minimized consist of two parts; the first part is related with the due date performance (i.e., the tardiness of the jobs), while the second part is related with the setting of machine speeds. Therefore, the decision variables include both the production schedule (sequences of jobs) and the production rate of each machine. The optimization process, however, is significantly complicated by the stochastic factors in the manufacturing system. To address the difficulty, a simulation-based threestage optimization framework is presented in this paper for high-quality robust solutions to the integrated scheduling problem. The first stage (crude optimization) is featured by the ordinal optimization theory, the second stage (finer optimization) is implemented with a metaheuristic called differential evolution, and the third stage (fine-tuning) is characterized by a perturbation-based local search. Finally, computational experiments are conducted to verify the effectiveness of the proposed approach. Sensitivity analysis and practical implications are also discussed. Hindawi Publishing Corporation

A Monte Carlo simulation based chaotic differential evolution algorithm for scheduling a stochastic parallel processor system

“…An iterated greedy heuristic was also designed to generate a sequence of schedules by iterating over a constructive heuristic using destruction and construction mechanisms. Zhang (2013) devised a three-stage algorithm for solving a parallel machine scheduling problem with random processing and setup times and adjustable production minimizing the tardiness of jobs and set the machine speeds. Cheng et al (2013) proposed a mixed integer programming model and an ant colony optimization method to address the problem of scheduling parallel batching machines with jobs of arbitrary sizes with identical capacity and processing velocity.…”

“…We found few research papers (Weber, 1982;Arnaout et al 2006;Zhang, 2013;Torabi et al, 2015) considering uncertain processing times within parallel processor scheduling problem. As can be seen, these existing papers considered a diffused range of assumptions and/or solved the problem just via a specific distribution function or by fuzzy assumptions.…”

Scheduling an Energy-Aware Parallel Machine System with Deteriorating and Learning Effects Considering Multiple Optimization Objectives and Stochastic Processing Time

“…Al-Khamis et al [18] focused on the uncertain due dates when solving a PMSP. Zhang [19] used the random processing time and adjustable production rate in a PMSP.…”

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