Hierarchical location-allocation problems: A classification scheme

In the literature, the p-median problem has been well studied. For the p-median problem our objective is to locate p facilities among n(? p) locations such that the total weighted travel distance is minimized. In the problem formulation, it is tacitly assumed that the facilities are of one type.In many practical situations, systems that provide products/services generally consist of k( ? 2) distinct types of facilities. In such problems, we would like to locate p_i type i facilities, i = 1, 2, … k, among n ( ? Σ_i^k = ₁p_i) available locations. Here also our objective may be to locate these facilities such that the ‘total weighted travel distance’ is minimized. What makes these problems difficult and interesting is that the extension of the p-median problem formulation and solution procedures to these problems is not always obvious, easy or straightforward. The problem formulation and solution procedures depend upon the hierarchical relationship among the facility types and the flow of goods and services allowed among them.In this paper we attemp to classify the hierarchical location-allocation problems.