Machine duplication and part subcontracting in the presence of alternative cell locations in manufacturing cell design

In this paper a model and a solution algorithm are reported to simultaneously deal with the processes of machine duplication and part subcontracting in the presence of two significant design issues in cellular manufacturing systems: (i) alternative cell locations; and (ii) the maximum number of machines assigned to a cell. As the problem, formulated as a polynomial programming model, is shown NP-hard in the strong sense, a higher-level heuristic algorithm based upon a concept known as ‘tabu search’ is presented. An example (small) problem is solved to demonstrate the functionality of the algorithm. Additionally, the small problem is solved for its optimal solution under different scenarios, both with linear single-row and linear double-row layout arrangements, and the solutions obtained are shown to match with those obtained with the heuristic algorithm. A comparison of six different versions of tabu search-based heuristics (TSH 1–TSH 6) is performed to investigate the impact of long-term memory and the use of fixed versus variable tabu-list sizes. A carefully constructed statistical experiment, based on randomised complete-block design, is used to test the performance on three different problem structures, classified as small, medium and large. The results show that TSH 6 with variable tabu-list size and long-term memory based on minimal frequencies is preferred for the single-row layout, while TSH 4 with variable tabu-list size and no long-term memory is preferred for the double-row layout. When subject to budgetary restrictions, the proposed approach can be used by parts manufacturing companies to determine which of the following three actions should be undertaken for each bottleneck part: bottleneck part left as in the initial solution, all the bottleneck machines connected to it are duplicated, or the part subcontracted.