A number of mechanisms are explored for modelling equilibrium values of attractiveness terms in production-constrained spatial-interaction models. They include revenue and facility-size balancing, a differential-equation representation of profit maximisation, and mathematical-programming formulations. The different methods turn out to be closely related but offer different and complementary insights. Some dynamic properties of such equilibrium points are explored, including the identification of circumstances which generate discrete changes for smooth changes in parameters. A number of possible algorithms for calculating the points are described.

Geographic information systems (GIS) are becoming widespread in management and planning, affecting the very organization and operation of the planning process itself. In this paper we address the problems and potential of such systems, particularly in relation to the analytical, predictive, and prescriptive models on which strategic planning processes are based. Current GIS are not rooted in the sorts of functions which drive these processes and here we will identify the difficulties and possibilities for developing more appropriate GIS which are sensitive to the simulation, optimization, and design activities which define spatial planning. To this end we will describe the development of planning support systems (PSS) in which a wide array of data, information, and knowledge might be structured, and within which GIS develop ment must take place. We will identify the sorts of urban system and locational models which characterize strategic planning and whose data-demands might be accommodated using GIS. Our critique of GIS is positive and constructive in that we are concerned to embed GIS into planning processes in the most appropriate way. In conclusion we will identify a series of requirements which PSS must meet.

In the very nature of the title of this article, there are perhaps three major problems which ought to be clarified. First, perhaps, is the importance of the region, especially the "natural" region. This receives attention elsewhere in this symposium and is relatively the least important point in my discussion although it will deserve some attention. The second is the distinction between metropolitanism and other aspects of regionalism which are of importance especially from the economic point of view. This also requires some elaboration. Finally, there is the main problem to which this article is addressed, that is, the economic aspects of the metropolitan region itself. These economic aspects will be substantially clarified in the process of definition. DELINEATION OF THE "REGION" * This article being in the nature of a thoughtful but impressionistic review of the title problem, it has seemed impractical to select a few out of the growing body of references on the topic. The author is nonetheless indebted to the work of many in this field, and especially to the stimulating contacts provided with his colleagues and others through his work at the Institute for Urban Studies.

No abstract