An hybrid procedure for machine duplication in cellular manufacturing systems

Cellular manufacturing represents an effective and even more applied alternative in production system organization especially when line or batch-type production is not economically convenient or technically feasible. This is particularly true when a wide range of quite similar items need to be produced in small lot sizes with frequent and expensive setups. Cellular manufacturing is supported by the so-called cell formation problem whose aim is forming part groups to be assigned to manufacturing cells, composed by a defined subset of machines, so that the sum of intercellular flow costs and direct intra-cell costs is minimized. An effective approach to form manufacturing cells is based on cluster analysis and on the evaluation of similarity coefficients: machines are grouped by the application of clustering techniques and finally parts are assigned to clusters. The aim of this paper is to present a hybrid and original procedure for the cell formation problem based on cluster analysis and integer linear programming. In particular, an integer linear programming model optimizes and re-arranges the configuration of the cells as the result of the application of a hierarchical clustering algorithm. The proposed model evaluates the possibility of duplicating a machine in one or more cells in order to reach the best trade-off between direct cell costs and indirect costs caused by intercellular flows. As a result, all work areas are correctly designed with the optimal number of machines of each type and total production system cost is quantified. The presentation and discussion of the proposed approach is supported by the illustration of a significant case study which takes inspiration from the literature.