Minimizing Part Transfer Costs in Flexible Manufacturing Systems: A Computational Study on Different Lower Bounds

We address the problem of assigning operations to flexible machines in a manufacturing system in order to minimize handling costs associated to transferring parts between machines. We model this problem as a special discrete optimisation - related to minimum cut - problem on a graph. We use different mathematical programming tools, based on (i) relaxations of integer programming formulations or (ii) combinatorial models of the problem, to provide underestimations of its solution values. The latter ones are useful in exact solution algorithms based on enumeration schemes, like branch and bound or branch and cut. Extensive simulation experiments are carried out to test the performances of different lower bounds on the optimal solution values of our problem and of one more general variant (called metric labelling problem) which is well known in the literature.