Developments in Mathematical Programming Models and Their Impact on the Spatial Allocation of Educational Resources

economic ideas about competition which require instantaneous clearance of the market for school places. Such apparently gross imperfections might easily be interpreted as a cue to abandon modelling altogether. However, on closer inspection, it is apparent that Sayer's arguments gain much of their momentum from a dialectic which begins by taking a Utopian view of a model's power to explain reality and then gloats when these ideals are not met in practice. Those who actually construct theories of the space economy usually take a more conservative view which sees a model as nothing more than a mathematical simplification of reality imbued, by impUcation, with imperfect and approximate explanatory mechanisms. The discovery of seemingly better mechanisms is the major task and, given these more relaxed ground rules, modelling educational resource allocation has made progress both in the way important educational criteria have been added to their design and in the signs that static equilibrium analysis might be replaced by a more dynamic approach based on the analysis of models of the form described by equations (19 -23) . The technical advances made in the construction of resource allocation models should not be allowed to detract from the caution that must be taken with their implementation. For example, the reconciliation of equity and efficiency ascribed to a location-allocation model arises from its internal functioning, consequently the results might turn out to be quite different from those expected by an educational planner interested in pursuing policies that promote social justice. Even when the planner is directly involved in the modelling process, which is the object of a goal programme, the same conflict of interest still arises because his actions are confined to the limits imposed by the programme's structure. Moreover, significant costs and benefits are often ignored in the model's design. Dear (1978), writing about the changes that have overtaken the theory of urban public facility location since Tietz (1968) advocated its development, notes how 'neighbourhood associated extern­ alities' and 'user-associated external effects' have been largely ignored in model design. He describes the way the location of a new mental institution has a doubleedged neighbourhood effect which, though positive for the local patient, is usually felt to be negative by the resident. Similarly, Bondi (1985) notes how a school's role extends beyond its educational significance to act as an out of hours community centre, a funcfion which is often crucial to deprived inner city areas whose declining populations make them susceptible to the closure of public facilities. Such neigh­ bourhood effects are essentially non-monetary and, for this reason, have eluded the programming framework. However, to conclude on an optimistic note, it is worth recording that the modelling of scale economies (a 'user-associated external effect') has progressed considerably since Dear described the failure of location-allocation problems to take them into account. School of Geography, University of Manchester, UK