Locating cells with bottleneck machines in cellular manufacturing systems

Because of bottleneck machines, the assignment of machine-cells to locations is interrelated with the machines' relative locations, and it makes the problem complicated to solve optimally. This paper prescribes an assignment of machine-cells to linear locations in order to minimize the inter-cell material handling cost incurred due to bottleneck machines in a cellular manufacturing system. This problem is formulated as a quadratic assignment problem (QAP). The optimal results can be obtained for a limited size of QAP. A 3-pair comparison heuristic is devised to partially overcome the dimensional problem for solving a large example. Later, an improvement heuristic called the 'bubble search' technique is developed to obtain a better solution, followed by the development of a lower bound on the QAP problem. Numerical examples are presented to illustrate the two heuristic procedures. A comparison between the optimal and heuristic solutions is also provided to evaluate the performance of the heuristics. Empirical tests conducted on two sets of data yield impressive test results.