Geography

This paper examines two aspects of hierarchical urban models: the variations of total urban population and that of the urbanization ratio, in function of the number of hierarchical levels. Both variations are analysed through four categories of models. The comp!exity of the results suggests two approximations in order to make the analysis rvtore tr 5-table.

We present a theoretical model of residential growth that emphasises the path-dependent nature of urban sprawl patterns. The model is founded on the monocentric urban economic model and uses a cellular automata (CA) approach to introduce endogenous neighbourhood effects. Households are assumed both to like and to dislike the density of their neighbourhood, and are assumed to trade-off this density with housing space consumption and commuting costs. Discontinuous spatial patterns emerge from that trade-off, with the size of suburban clusters varying with time and distance to the centre. We use space–time diagrams inspired from 1D elementary CA to visualise changes in spatial patterns through time and space, and undertake sensitivity analyses to show how the pattern and timing of sprawl are affected by neighbourhood preferences, income level, commuting costs, or by imposing a green belt.

A recent body of research suggests that the spatial structure of cities might influence the socioeconomic characteristics and outcomes of their residents. In particular, the literature on neighbourhood effects emphasizes the potential influence of the socioeconomic composition of neighbourhoods in shaping individual's behaviours and outcomes, through social networks, peer influences or socialization effects. However, empirical work still has not reached a consensus regarding the existence and magnitude of such effects. This is mainly because the study of neighbourhood effects raises important methodological concerns that have not often been taken into account. Notably, as individuals with similar socioeconomic characteristics tend to sort themselves into certain parts of the city, the estimation of neighbourhood effects raises the issue of location choice endogeneity. Indeed, it is difficult to distinguish between neighbourhood effects and correlated effects, i.e. similarities in behaviours and outcomes arising from individuals having similar characteristics. This problem, if not adequately corrected for, may yield biased results. In the first part of this paper, neighbourhood effects are defined and some methodological problems involved in measuring such effects are identified. Particular attention is paid to the endogeneity issue, giving a formal definition of the problem and reviewing the main methods that have been used in the literature to try to solve it. The second part is devoted to an empirical illustration of the study of neighbourhood effects, in the case of labour-market outcomes of young adults in Brussels. The effect of living in a deprived neighbourhood on the unemployment probability of young adults residing in Brussels is estimated using logistic regressions. The endogeneity of neighbourhood is addressed by restricting the sample to young adults residing with their parents. Then, a sensitivity analysis is used to assess the robustness of the results to the presence of both observed and unobserved parental covariates.

This paper aims at showing how far the shape of a studied area influences the results of optimal location-allocation models. Simulations are performed on rectangular toynetworks with an equal number of vertices but with different length/width ratios. The case of merging two such networks into a common market is also considered. We limit our experience to the Simple Plant Location Problem (SPLP) which captures the fundamental trade-off of economic geography between accessibility and economies-of-scales. Results are analysed in terms of locations, allocations and costs. On the average, we confirm that regions that are elongated require a greater number of facilities that those with a compact shape; this effect however depends upon the way a region is merged into a common market (type of border; relative position). The results help at understanding how far an area (country/region) has larger development problems than others just because of its shape and/or of the way this area is linked within a common market (elongation of the country and length of the common border).

The single facility location problem 2. The p-median problem 3. Extensions (a) Maximum cost constraints (b) Capacity constraints (c) Budgetary constraint (d) Hierarchized systems of facilities 4. SPLP (a) The basic model (b) Some extensions 5. Covering problems (a) Set-covering problem (b) Maximal covering problem 6. The p-center problem CONCLUSIONS REFERENCES

This paper describes a study aimed at evaluating the capabilities of simulated annealing in dealing with complex, real-world multi-period location problems raised by school network planning in Portugal. The problems were formulated as mixed-integer linear optimization models. The models allow for facility closure or size reduction besides facility opening and size expansion, with sizes possibly limited to a set of pre-de®ned standards. They assume facility costs to be divided into a ®x component and two variable components, respectively dependent on facility size and facility attendance. Results obtained through the study indicate that simulated annealing can be a useful tool for solving these kinds of models.

We present a model that simulates the growth of a metropolitan area on a 2D lattice. The model is dynamic and based on microeconomics. Households show preferences for nearby open-spaces and neighbourhood density. They compete on the land market. They travel along a road network to access the CBD. A planner ensures the connectedness and maintenance of the road network. The spatial pattern of houses, green-spaces and road network self-organises, emerging from agents individualistic decisions. We perform several simulations and vary residential preferences. Our results show morphologies and transition phases that are similar to Dieletric Breakdown Models (DBM). Such similarities were observed earlier by other authors, but we show here that it can be deducted from the functionning of the land market and thus explicitly connected to urban economic theory.

This paper reconsiders the production-location problem (PLP) initiated by Moses. The PLP is extended to allow for the geographical substitution between input sources, which is likely to occur in an integrated market. An algorithm is then proposed to solve this problem. Finally, using numerical examples, it is shown that small variations in the elasticity of substitution of the production function may lead to substantial jumps in the optimal firm location.

The Simple Plant Location Problem (SPLP) consists in identifying a pattern of facilities among a set of potential sites so that the sum of the costs for opening the facilities and for supplying a group of geographically dispersed clients therefrom is minimized. It is posited in this framework that the locator rules on the allocation of the clients to the facilities. When the clients are free to decide upon which facility they will attend, their choices do not necessarily match the most economical supply pattern from the point of view of the locator. We suppose here that each client has a preference ordering on the list of potential sites whereby he determines his allocation out of any set of open facilities. This preference ordering depends on characteristics of the client, of the sites, and of the trip between the client's location and the sites. Mathematically, we translate the orderings into a set of constraints to be appended to the SPLP. This new problem, termed SPLPO, has a wide range of applications as shown by a series of examples. We present an algorithm for solving the SPLPO and extensive computational experiments are reported.

This paper describes a dynamic (multi-period) optimization model that has recently been used in Portugal to formulate planning proposals for the evolution of several school networks. This eort follows the extension of elementary education from 6 to 9 years as decided by the Government in 1986, and gradually implemented since then. The model allows for facility closure or size reduction, as well as facility opening and size expansion, with sizes limited to a set of pre-de®ned standards. It assumes facility costs are divided into a ®xed component and two variable components, dependent, respectively, on capacity and attendance.

A residential location model derived from urban economics is combined with the geometry of a multifractal Sierpinski carpet to represent and model a metropolitan area. This area is made up of a system of built-up patches hierarchically organised around a city centre, and green areas arranged in an inverse hierarchical order (large open-spaces in the periphery). An analytical solution is obtained by using a specific geographic coding system for computing distances. The values of the parameters used in the model are based on the French medium sized metropolitan areas; a realistic benchmark is proposed and comparative-statics simulations are performed. The results show that the French peri-urbanisation process (which took place from 1970 onward) can be explained by an increase in income and a reduction in transport costs. Nevertheless, changes in household preferences, in particular an increased taste for open spaces, can also contribute to urban sprawl by making the gradient of land rents less steep and by making peripheral household locations more desirable.

Facility location analysis deals with the problem of locating one or several facilities with regard to existing facilities and clients in order to optimize some economic criterion. In this survey, we consider specifically the problem of selecting one or several points of a network in order to optimize a function which is distance-dependent with respect to given points of the network. Minisum and minimax problems, where the objectives are to minimize respectively the sum or the maximum of different functions of distances, are reviewed. We also discuss models integrating more economic variables, such as prices, and putting more emphasis on the decision making context, particularly the competitive location models. Discrete models, for which the set of possible locations is finite and which have received the most attention of practionners, are presented as well.

Public services occupy an important place in modern societies. We are born in a hospital, we go to school, we benefit from transportation infrastructures and emergency services, we communicate by mail, telephone and Internet, we go to a city hall for anything to do with civil status, our household garbage is collected, we are buried in a cemetery, etc. One of the challenges facing contemporary society is to reach a correct adequacy between its members' needs and the services that they offer. This adequacy has several facets and concerns: the identification of needs, the selection of those that should be satisfied, the way in which service providers will be organized and controlled, the arbitrage between users, the funding of these activities, the impact on the physical and human environment, etc. All these issues open the door for large debates in political, social, economic, ethical, etc., areas. A question of particular interest to the geographer throughout these discussions is the spatial adequacy between supply and demand, which means the choice of the location of the services and their geographical coverage. The goal of this chapter is to show how operations research methods can provide answers to these questions. The problem is prevalent in economically developed regions. Indeed, most of these regions are faced with huge budget (and debt) control problems that require, in principle, the best possible allocation of public money. Moreover, because of the emergence of supranational institutions (European Union, NAFTA, etc.), many Chapter written by Dominique PEETERS and Isabelle THOMAS.

Using Belgian microdata, we assess the impact, on a hedonic regression, of the distortions arising from the choice of either a specific zoning system or the delineation of the study area. We also evaluate the biases that arise when spatial effects are not accounted for. Given that the dependent variable is interval-coded, controlling for spatial dependence in this context is challenging. We address this problem with two alternative strategies. Firstly, we use the Gibbs Sampling algorithm to estimate spatial econometric models which extends the interval regression model. A major drawback of this approach is that the implied estimation is proned to the endogeneity biases inherent to our hedonic regression model. To circumvent the endogeneity issues triggered by the first estimation strategy, we also use a two-stage estimation procedure with locational fixed effects. In all specifications, results are sensitive to the Modifiable Areal Unit Problem (MAUP) and to the choice of the delineation of the study area. Moreover, they confirm the existence of substantive spatial dependence. Conversely to the previous results with a negative elasticity for the percentage of the area covered by agriculture and a positive elasticity for the potential accessibility to jobs, the second approach implies opposite effects for those two variables. This indicates that dwellings close to agricultural areas and with a lower accessibility to the main employment centers are highly demanded and that endogeneity biases are not negligible.

We consider the location of a profit-maximizing. single-plant firm in a continuous space with a finite number of local markets. Five different spatial price policies are considered: (i) spatial discriminatory pricing. (ii) uniform delivered pricing. (iii) uniform mill pricing. (iv) zone pricing. and (v) mixed pricing where clients have the choice between pickup or delivery. Global optimization methods are proposed for solving the corresponding problems and numerical experiments are reported on. Kr~~ords: Firm location. spatial price policies. global optimization.

This article presents an economic decision model for planning in public education, considering the satisfaction of the total demand for education in a municipality and the annual cost involved in the system. Given a set of established schools in a municipality and possible new locations, the aim of the model is to find the optimal supply in terms of which schools should be kept open or closed, which grades (or year levels) should be made available and the number of classes that should be provided within each such grade to meet student demand. The model includes specific information about curriculum requirements in terms of the number of hours per year per subject to be provided for each grade level. The objective function essentially seeks to minimize the total fixed and variable costs to schools, which mainly relate to human resources (principal and direction, teaching, administrative, and support staff). We propose an integer optimization model for solving this problem and we apply it to two large municipalities in Chile.