Location-Allocation Models and their Development

Abstract

Location-allocation modelling studies, primarily applied to facility Location problems, have rapidly increased and extensively spanned a wide range of disciplines in the past three decades. In Japan, facility location models have attracted the attention of planning-oriented researchers from architecture, city engineering, operations research, and of a few geographers. This paper has three aims: first, to introduce location-allocation models to Japanese geographers; second, to review the development of new literature on representing decision-making behavior, uncertainty in the environment and the multi-objective formulation; and, third, to identify the tasks of models in chiefly geographical research.In general, location-allocation models are classified into three problems: the p-median problem which minimizes the aggregate distance or time from demand point i to facility j; the p-center problem which minimizes the maximum distance from i to j; the covering problem where coverage is required (the set covering problem) or optimized (the maximal covering location problem). These models on a network are formulated as a linear programming or a mixed-integer programming. Due to the computational complexity of these problems, several heuristic solution methods have been developed and demand data aggregation methods to eliminate errors in the aggregation process have been proposed.With improved solution methods and increasing computational speed, location-allocation models have been adapted to complex and realistic location problems. A variety of facility problems and developed models are summarized in the following categories: First, considering the characteristics of a facility, models are diversely formulated by the type of facility, the existence of constraint on capacity and the hierarchy of the facility system. Second are the facilities-location methods, including free location, adding locations to an existing network, or restructuring of networks (Hodgart, 1978), which are linked to dynamic locational problems. The above options are mainly concerned with “location”and selected by a single-location decision-maker. However, the third“allocation” option is controlled by two decision-makers, namely, the locator and allocator (Leonardi, 1981). Various types of decision-making behavior will be represented by several allocation patterns. Fig. 3 shows the classification of allocation systems that contains nearest-neighbor allocation, probabilistic allocation, intermediate trips, combined and round trips, routing trips and the hub-facility problem. Later, realistic models reflecting an uncertain environment are presented. Uncertainties arise from the stochastic nature of demand, travel time, service provision and the competitive environment in the private sector. Finally, it is demonstrated that multi-objective location-allocation models solve the complexity of decision-making faced in realistic facility location planning.Most applications of location-allocation models typically placed emphasis on facility location planning. Location-allocation models will provide, if we geographers as location analysts seek another way to use models, valuable tools by wich well-defined location theories, especially central place theory, may be formulated as operational and normative models. Accordingly I propose two tasks for location-allocation models as follows:1) use of location-allocation models as a decision support system for facility location planning;2) use of location-allocation models as a spatial analysis tool. The latter task can be adapted to geographers interests and demonstrate spatial analysis including theoretical insights in understanding real-world spatial organization. In addition, linked with geographic information systems (GIS), location-allocation models could create more interactive tools.