Improved formulations to the hierarchical health facility location-allocation problem

In an earlier paper Calvo and Marks formulated the problem of locating various types of health facilities — and allocating different types and levels of demand to these facilities — as a zero-one integer programming model. Although the model has been widely referenced in the literature (as an example of a formulation which models the “ successively inclusive” hierarchical relationship), no solution algorithm has been developed to date. It is shown in this paper that the model is actually only “locally inclusive” and that it can be solved as a special case of another general, “successively exclusive,” model that is formulated and solved herein. Further, this paper contains a second model that corrects for a shortcoming in the Calvo and Marks model and solves for the “successively inclusive” hierarchical location-allocation problem.