Group shops scheduling with makespan criterion subject to random release dates and processing times

• Published in: Computers & operations research Vol. 37; no. 1; pp. 152 - 162
• Main Authors: Ahmadizar, Fardin, Ghazanfari, Mehdi, Fatemi Ghomi, Seyyed Mohammad Taghi
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 2010; Elsevier; Pergamon Press Inc
• Subjects: Ant colony algorithm; Applied sciences; Exact sciences and technology; Group shop scheduling problem; Heuristic; Inventory control, production control. Distribution; Job shops; Makespan; Mathematical programming; Operational research and scientific management; Operational research. Management science; Optimization algorithms; Production scheduling; Random processing times; Random release dates; Random variables; Scheduling; Scheduling, sequencing; Simulation; Stochastic models; Studies; Group shop scheduling problem; Random release dates; Makespan; Simulation; Ant colony algorithm; Random processing times; Lower bound; Job shop; Processing time; Scheduling; Modeling; Particle swarm optimization; Stochastic programming; Heuristic method; Open systems; Flow shop; Swarm intelligence; Random variable; Discrete event system; Execution time
• DOI: 10.1016/j.cor.2009.04.002
• ISSN: 0305-0548

This paper deals with a stochastic group shop scheduling problem. The group shop scheduling problem is a general formulation that includes the other shop scheduling problems such as the flow shop, the job shop and the open shop scheduling problems. Both the release date of each job and the processing time of each job on each machine are random variables with known distributions. The objective is to find a job schedule which minimizes the expected makespan. First, the problem is formulated in a form of stochastic programming and then a lower bound on the expected makespan is proposed which may be used as a measure for evaluating the performance of a solution without simulating. To solve the stochastic problem efficiently, a simulation optimization approach is developed that is a hybrid of an ant colony optimization algorithm and a heuristic algorithm to generate good solutions and a discrete event simulation model to evaluate the expected makespan. The proposed approach is tested on instances where the random variables are normally, exponentially or uniformly distributed and gives promising results.