A mathematical programming model for cellular manufacturing system controlled by kanban with rework consideration

This research studies the cellular manufacturing system (CMS) controlled by kanban mechanism which defective items are produced in any production run of each product and rework is carried out to transform them into serviceable items. We consider and compare two different policies for rework where in the first policy rework is completed within the same production cycle and in the second policy rework done after N production cycles. Recently Aghajani et al. (2012) explain policy 2 and proposed a mixed-integer nonlinear programming (MINLP) model for this policy. In order to minimize total cost, MINLP model was developed for policy 1 to find simultaneously the optimal number of kanban, batch size, and number of batches. The cost function includes the cost of setup, holding, and transportation. Due to the high combinatorial structure of the problem, particle swarm optimization (PSO), and simulated annealing (SA) algorithms as meta-heuristic methods are proposed to solve the problem and numerical experiments are conducted to demonstrate the efficiency of the proposed algorithms. It is shown that both PSO and SA result are in a near optimal solution but the PSO algorithm gives a better performance than the SA method. Also, sensitivity analysis is carried out to study the effect of defective rate, holding cost, and setup cost variations on the total system cost is discussed the performance of these policies in different conditions.

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