An efficient heuristic for the design of cellular manufacturing systems with multiple identical machines

In practice, in a manufacturing system, there are multiple machines of some machine types to meet the capacity requirement. Therefore, this factor should be taken into consideration in the design of cellular manufacturing systems. On one hand, this is a constraint to be satisfied for the cell formation problem, on the other hand, appropriate assignments of identical machines to different cells will reduce and simplify intercell flows. Thus, we should make use of this advantage in cell formation. The problem is that we do not know the specific machine within the identical machines that are to be used for the processing of an operation, and so it is difficult to assign operations to a specific machine within the group of identical machines. By using the information of operation sequences for each part type, we present a graphical model that can describe the part families with respect to the machine types of multiple machines. Thus, the identical machines can be assigned into different cells based on the part families without involving complex computation. With the model developed here, a merging-and-breaking heuristic is proposed to solve concurrently both the traditional cell formulation problem and the assignments of the identical machines to different cells. Three examples are taken to show the power and application of the approach.