Mitigating hard capacity constraints with inventory in facility location modeling

Although the traditional capacitated facility location model uses inflexible, limited capacities, facility managers often have many operational tools to extend capacity or to allow a facility to accept demands in excess of the capacity constraint for short periods of time. We present a mixed-integer program that captures these operational extensions. In particular, demands are not restricted by the capacity constraint, as we allow for unprocessed materials from one day to be held over in inventory and processed on a following day. We also consider demands at a daily level, which allows us to explicitly incorporate the daily variation in, and possibly correlated nature of, demands. Large problem instances, in terms of the number of demand nodes, candidate nodes, and number of days in the time horizon, are generated from United States census population data. We demonstrate that, in some instances, optimal locations identified by the new model differ from those of the traditional capacitated facility location problem and result in significant cost savings.