A Fuzzy Approach to Determine Production Lot Size for Capacitated Single-Stage Production Process with Fuzzy Demand
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Abstract
This paper addresses the production lot size problem for a fuzzy single-stage, multiple -item, capacitated lot-sizing model in the context of unrelated parallel machines, known as the F-CLSPP model. This problem is particularly useful for SMEs or new product production planning, where there is a lack of historical quantitative data, and the available data comes primarily from expert experience. In this paper, the problem is formulated as a fuzzy mixed-integer programming model in the form of a dynamic lot size and scheduling problem. To make the F-CLSPP model mathematically solvable, a chance-constraint programming concept and a possibility approach are proposed to transform it into an equivalent crisp CLSPP model. The fuzzy constraints are converted into equivalent crisp constraints using the extension principle, allowing the model to be solved with basic software. This procedure and model are tested with an illustrative numerical example, and the results demonstrate that this approach can provide valuable production planning information and assist in decision-making based on the confidence level in the data.
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References
Toledo, F. M. B. & Armentano, V. A. (2006). A Lagrangian-Based Heuristic for the Capacitated Lot-Sizing Problem in Parallel Machines. European Journal of Operational Research, 175, 1070-1083.
Fiorotto, D. J., et al. (2015). Hybrid Methods for Lot Sizing on Parallel Machines. Computers and Operation Research, 63, 136-148.
Kim, T. & Glock, C. H. (2018). Production planning for a two-stage production system with multiple parallel machines and variable production rates. International Journal of Production Economics, 196, 284–292.
Toledo, F. M. B. & Armentano, V. A. (2006). A Lagrangian-Based Heuristic for the Capacitated Lot-Sizing Problem in Parallel Machines. European Journal of Operational Research, 175, 1070-1083.
Jans, R. (2009). Solving Lot-Sizing Problems on Parallel Identical Machines using Symmetry-Breaking Constraints. INFORMS Journal on Computing, 21, 123-136.
Rostami, M., et al. (2015). Multi-Objective Parallel Machine Scheduling Problem with Job Deterioration and Learning Effect under Fuzzy Environment. Computer and Industrial Engineering, 85, 206-215.
Alimian, M., et al. (2022). Solving a parallel-line capacitated lot-sizing and scheduling problem with sequence-dependent setup timecost and preventive maintenance by a rolling horizon method. Computers & Industrial Engineering, 168, 105-119.
Yildiz, S. T., et al. (2023). Variable neighborhood search-based algorithms for the parallel machine capacitated lot-sizing and scheduling problem. Journal of Engineering Research, 14(2), 49-58.
Bismut, J. M. (1978). An introductory approach to duality in optimal stochastic control. Society for Industrial and Applied Mathematics Review, 20(1), 62-78.
Ding, X. & Wang, C. (2011). A novel algorithm of stochastic chance-constrained linear programming and its application. Mathematical Problems in Engineering, 1, 1-17.
Chotayakul, S. & Punyangarm, V. (2016). The Chance-Constrained Programming for the Lot-Sizing Problem with Stochastic Demand on Parallel Machines. International Journal of Modeling and Optimization, 6(1), 56-60.
Charnes, A. & Cooper, W. W. (1959). Chance-constrained programming. Management Science, 6(1), 73-79.
Ketsarapong, S. & Punyangarm, V. (2010). An application of fuzzy data envelopment analytical hierarchy process for reducing defects in the production of liquid medicine. Industrial Engineering and Management System, 9(3), 251-261.
Ketsarapong, S., et. al. (2012). An experience-based system supporting inventory planning: a fuzzy approach. Expert Systems with Applications, 39, 6994-7003.
Cox, E. (1994). The fuzzy systems handbook: a practitioner’s guide to building using and maintaining fuzzy systes. Boston: AP Professional.
Liang, T. F. & Cheng, H. W. (2009). Application of fuzzy sets to manufacturing distribution planning decisions with multi-product and multi-time period in supply chains. Expert Systems with Applications, 36, 3367–3377.
Halim, K. A., et. al. (2011). Fuzzy production planning models for an unreliable production system with fuzzy production rate and stochasticfuzzy demand rate. International Journal of Industrial Engineering Computations, 2(1), 179–192.
Mandal, N. K. et. al. (2005). Multi-objective fuzzy inventory model with three constraints: a geometric programming approach. Fuzzy Sets and Systems, 150(1), 87–106.
Chang, H. C. et. al. (2006). Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand. European Journal of Operational Research, 16(9), 65–80.
Garg H., et. al. (2023). Optimization of fuzzy inventory lot-size with scrap and defective items under inspection policy. Soft Computing, 27, 2231-2250.
Lertworasirikul, S. et. al. (2003). Fuzzy data envelopment analysis (DEA): A possibility approach. Fuzzy Sets and Systems, 139(2), 379–394.