Variable capacity sizing and selection of connections in a facility layout

The variable capacity sizing and selection of connections in the facilities design context is discussed (to the best knowledge of the authors) for the first time in the open literature. A connection is defined as the connected part that links different sets of departments through which some interdepartmental material flows must go. The goal of the problem is to select the location and capacity of the connections (and to assign the flows) so as to minimize the sum of the fixed connection installation costs and material movement cost in the material handing system. Mathematical programming formulations are presented for continuous and discrete capacity options. For the continuous unbounded capacity case, we prove that it can be reduced to the uncapacitated fixed charge facility location problem. For the discrete capacity case, a Lagrangian relaxation-based solution approach is developed. It provides a 'good' feasible solution as well as a lower bound for assessing the optimality gap. Computational results are reported. Our findings indicate that the discrete version of the problem can be effectively solved with the Lagrangian heuristic.