A mathematical programming approach for dealing with exceptional elements in cellular manufacturing

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Abstract
Many researchers have suggested methods for developing manufacturing cells (machines cells/part families). However, few of these methods have addressed the possible (in actuality, highly probable) existence of exceptional elements in the solution. Exceptional elements are bottleneck machines and exceptional parts that span two or more manufacturing cells. This paper presents a mathematical programming model that deals with exceptional elements. An initial solution is developed using any of the numerous cell formation procedures. Any exceptional elements that can be eliminated by changing the design or the process plans of the parts are eliminated. Then, the mathematical programming model is solved to determine how best to deal with the remaining exceptional elements. The mathematical programming model considers three important costs: (1) intercellular transfer; (2) machine duplication; and (3) subcontracting. The model is an optimizing model that can recognize possibly advantageous mixed strategies ignored by previous approaches.

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