A linear programming embedded genetic algorithm for an integrated cell formation and lot sizing considering product quality

• Published in: European journal of operational research Vol. 187; no. 1; pp. 46 - 69
• Main Authors: Defersha, Fantahun M., Chen, Mingyuan
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16-05-2008; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Cellular manufacturing; Cost reduction; Exact sciences and technology; Genetic algorithm; Genetic algorithms; Integrated approach; Inventory control, production control. Distribution; Linear programming; Manufacturing cells; Mathematical models; Mathematical programming; Operational research and scientific management; Operational research. Management science; Product quality; Production planning; Studies; Product quality; Cellular manufacturing; Genetic algorithm; Production planning; Cell formation; Production quality; Model following; Linear programming; Lot sizing; Modeling; Search algorithm; Production management; Non linear model; Simplex method; Production cost; Mathematical programming
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2007.02.040

Production lot sizing models are often used to decide the best lot size to minimize operation cost, inventory cost, and setup cost. Cellular manufacturing analyses mainly address how machines should be grouped and parts be produced. In this paper, a mathematical programming model is developed following an integrated approach for cell configuration and lot sizing in a dynamic manufacturing environment. The model development also considers the impact of lot sizes on product quality. Solution of the mathematical model is to minimize both production and quality related costs. The proposed model, with nonlinear terms and integer variables, cannot be solved for real size problems efficiently due to its NP-complexity. To solve the model for practical purposes, a linear programming embedded genetic algorithm was developed. The algorithm searches over the integer variables and for each integer solution visited the corresponding values of the continuous variables are determined by solving a linear programming subproblem using the simplex algorithm. Numerical examples showed that the proposed method is efficient and effective in searching for near optimal solutions.