A biary integer programming approach for simultaneous machine-part grouping in cellular manufacturing systems

Abstract

This paper presents the development of a comprehensive model and the identification of a suitable solution technique for evaluating the effectiveness of simultaneous part-machine groupings in cellular manufacturing systems. The objective function of the model is formulated as maximizing a unified measure of effectiveness evaluated as a weighted sum of fractions representative of the (negative of) total moves and in-cell utilizations. All of the operational constraints associated with setting-up a cellular manufacturing system are included in the model. These represent processing time requirements of parts on machines, sequence of operations, non-consecutive operations scheduled to be performed on the same machine, machine capacities, and the limitation set on the maximum number of machines that can be assigned to a cell. The model assumes that the desired number of manufacturing cells can be determined a priori by the management of the parts manufacturing company. The original model, formulated as a quadratic binary programming model, is subsequently converted into a linear binary programming model. The model is implemented by solving an example problem chosen from published literature, and the solution obtained is proven to be superior to that obtained from previous models.