Manufacturing cell formation in the presence of lot splitting and multiple units of the same machine

Abstract

We present a realistic cell formation problem in the design of cellular manufacturing systems which includes three important features. First, when multiple units of a machine type are considered due to processing time requirements, the model accounts for assigning the units to different cells if such an assignment contributes to reducing material handling costs. Second, the model accounts for the possibility of performing two or more nonconsecutive operations of a part on the same machine. Finally, the model allows for splitting the lot into two if the total workload required of a part's operation on a machine exceeded its daily unit capacity expressed in manned hours. We refer to this feature as ‘lot splitting’. Consequently, the operation required of each split lot of the part can be performed on a separate unit (machine). The model formulated for the problem falls into the class of generalized quadratic binary programming models. As the problem is shown NP-hard in the strong sense, a higher level heuristic algorithm based upon a concept known as tabu search is presented. Results obtained from solving an example problem demonstrate the application of the proposed algorithm when either of the two features—lot splitting or nonconsecutive operations, exist. The applicability of the proposed algorithm has further been extended to solving a test problem consisting of both features—lot splitting and non-consecutive operations. The results obtained show a reduction of ⩽ 50% in total moves (material handling costs) between the initial solution and the final best solution.