Approaches to the general cell formation problem

It has long been recognized that productivity in manufacturing plants can often be increased by producing similar products in manufacturing cells. This involves: (i) assigning parts to individual machines and (ii) forming machines into manufacturing cells. These two activities have traditionally been carried out separately. However most solution procedures for (i) above, utilize a solution to (ii), and vice versa. Here we present a new model that deals with (i) and (ii) simultaneously. We then extend this model to allow for the reassignment of operations to different machine types by incorporating machine type modification costs. Such modification enables additional machine types to process certain parts, with view to reducing inter-cell travel. The cost of such modifications must be balanced by the consequent reduction in inter-cell travel cost. The extended model specifies which individual machines should be modified to enable them to process additional part types, part-machine assignment, and the grouping of individual machines for cell formation. The objective is to minimize the sum of the machine modification costs and the inter-cell travel. We call this endeavour the General Cell Formation Problem. Computational experience with the models indicates that they are likely to be useful additions to the production engineer’s toolkit.