A group of M machines for processing a set of jobs in a manufacturing system is often located in a serial line. An efficient strategy for locating these machines is desired such that the total travel distance or the cost of transporting the jobs is minimized. If an application requires more than one identical machine, the cost is minimized by flow distributions between machines. The problem of minimizing the travel distance that involves sets of identical machines is often formulated as a tertiary assignment problem. Finding an optimal solution for such a problem can be very complicated due to its combinatorial nature. This research proposes a two-stage solution methodology to ease the computation and to obtain a better solution. First, the problem of sets of identical machines is decomposed into sets of unique machines to find the machine assignment. Second, the task is to find the flow assignment by holding the machine assignment found in the previous stage. Results are encouraging and they are demonstrated through numerical examples and a set of test problems.
