Optimum loading of machines in a flexible manufacturing system using a mixed-integer linear mathematical programming model and genetic algorithm

• Published in: Computers & industrial engineering 2012-03, Vol.62 (2), p.469-478
• Main Authors: Abazari, Amir Musa, Solimanpur, Maghsud, Sattari, Hossein
• Format: Article
• Language: English
• Subjects: Algorithms; Flexibility; Flexible manufacturing systems; Genetic algorithm; Genetic algorithms; Integer programming; Machine loading problem; Mathematical analysis; Mathematical models; Mathematical programming; Optimization; Process planning; Studies
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/j.cie.2011.10.013

► We study optimum allocation of workload on machines in an FMS. ► We present an accurate and practical way to calculate system unbalance in an FMS. ► A mathematical model is proposed considering different parameters in machine loading. ► A genetic algorithm has been developed to solve the proposed model. ► Solving benchmark problems indicates supremacy of the proposed genetic algorithm. Machine loading problem in a flexible manufacturing system (FMS) encompasses various types of flexibility aspects pertaining to part selection and operation assignments. The evolution of flexible manufacturing systems offers great potential for increasing flexibility by ensuring both cost-effectiveness and customized manufacturing at the same time. This paper proposes a linear mathematical programming model with both continuous and zero-one variables for job selection and operation allocation problems in an FMS to maximize profitability and utilization of system. The proposed model assigns operations to different machines considering capacity of machines, batch-sizes, processing time of operations, machine costs, tool requirements, and capacity of tool magazine. A genetic algorithm (GA) is then proposed to solve the formulated problem. Performance of the proposed GA is evaluated based on some benchmark problems adopted from the literature. A statistical test is conducted which implies that the proposed algorithm is robust in finding near-optimal solutions. Comparison of the results with those published in the literature indicates supremacy of the solutions obtained by the proposed algorithm for attempted model.