Applications of the Location Set-covering Problem

The location set-covering problem is extended to apply to three new situations. (1) The demands are assumed to occur continuously alone arcs of a network. (2) A mobile unit departs from one of the locations to be chosen and picks up the demand, providing service at a still more distant point. (3) New demands and sites occur over time.     

Product Differentiation and Location Choice in a Circular City*

Abstract. The paper analyzes spatial competition among firms that sell substitute and/or complementary products. The firms first choose locations on the perimeter of a circular city and then compete in quantities (à la Cournot). Both linear and convex (quadratic) transport costs are considered. In general, multiple location equilibria are encountered. Complete agglomeration, partial agglomeration, and complete dispersion are possible. Convex (quadratic) transport cost substantially shrinks the set of equilibria obtained under linear transport cost. In general, the results obtained for a larger number of firms selling complementary products are strikingly different from those obtained under a duopoly.     

Extensions to the Hub Location Problem: Formulations and Numerical Examples

Although a tremendous amount of analytical research is being conducted on the hub location problem, few models exist that extend the number of characteristics found in actual hub-and-spoke networks. Four extensions are presented in this paper: (1) a capacitated network model; (2) a minimum threshold model; (3) a model that endogenously determines the number of open hubs for the network; and (4) a model that incorporates a flow-dependent cost function for the spokes as well as the interhub links. Both the capacitated and the minimum threshold models drop the assumption of a completely interconnected network commonly found in hub location models. Numerical results show that total network costs are often minimized by closing a few interhub links. The third extension is the first known hub location model to determine the optimal number of hubs based on the needs of the network. In this model, the number of open hubs depends on the distribution of flows in the network and how cost effectively the flows can be moved across the network. Previous models that endogenously determined the number of open hubs utilized a fixed cost for establishing each hub in order to limit the number of hubs in the network. The final extension recognizes the potential of all links to amalgamate flows and includes a separate flow-dependent cost function for the spokes in addition to the one for the interhub links. Numerical results are shown for all four models.     

Use of the Mathematical Method in the Solution of a Location Problem

Cost minimization criteria are applied to a study of the optimal location of plants for the manufacture of service-industry machines, including street-cleaning equipment, laundry, and dry-cleaning machines. Future national and regional demand for such machines is estimated. The matrix technique is used to identify the economic region for which the aggregate cost of production and transportation of service-industry machines would be minimized. That region is found to be the Volga-Vyatka region, where the estimated cost of producing 315 million rubles worth of service-industry machines is put at 19.5 million rubles. The author does not necessarily exclude the location of manufacturing plants in other regions, if the purpose is to provide employment, as in areas of depleted mineral deposits of the Urals and the Donets Basin or in the agricultural districts of the Southwest and Central Asia.     

Aggregation Decomposition and Aggregation Guidelines for a Class of Minimax and Covering Location Models

Facility location problems often involve movement between facilities to be located and customers/demand points, with distances between the two being important. For problems with many customers, demand point aggregation may be needed to obtain a computationally tractable model. Aggregation causes error, which should be kept small. We consider a class of minimax location models for which the aggregation may be viewed as a second‐order location problem, and use error bounds as aggregation error measures. We provide easily computed approximate “square root” formulas to assist in the aggregation process. The formulas establish that the law of diminishing returns applies when doing aggregation. Our approach can also facilitate aggregation decomposition for location problems involving multiple “separate” communities.     

杜波依斯对解决美国黑人问题道路的探索

杜波依斯一生都在为争取黑人的平等权利而斗争。但是,在不同时期,他对美国黑人问题的认识不同,解决方案因而不断调整。     

An Interactive Approach to the Central Facility Location Problem: Locating Pediatric Hospitals in Warsaw

Most of the conventional approaches to the central facility location problem neglect the interaction of analyst and decision-maker during the locational choice process. This paper presents a new interactive approach to the central facility location problem. It is assumed that the problem is formulated by an analyst as a multiobjective optimization problem. Then the decision-maker searches for a satisfactory solution working directly with the computer system. The interactive procedure was implemented on IBM-PC XT/AT as the decision support system DINAS (Dynamic Interactive Network Analysis System) which enables the solution of various multiobjective location-allocation problems. DINAS has been successfully used for solving a real-world planning problem, namely for finding locations for pediatric hospitals in the Warsaw region.     

The Influence of Data Aggregation on the Stability of p-Median Location Model Solutions

Location planning often makes use of data in an aggregate form without a clear understanding of the consequences. Although research has been directed toward addressing aggregate data usage in location planning, there have been conflicting findings on the stability of location model solutions obtained using aggregated data. This paper analyzes the question of location model solution stability from a somewhat different perspective than previous researchers in that locational configurations identified for aggregate data are evaluated using the original disaggregate data. Analytical results demonstrate that a high level of solution stability does exist when aggregated data are utilized. Further, this analysis is based upon the use of what can be expected to be worst case aggregation approaches. This suggests that the use of aggregate data is adequate for conducting locational studies.     

Tradeoffs between Local Taxes and Government Spending as Determinants of Business Location*

Abstract. This paper investigates the effects of local fiscal policy on the location decisions of 3,763 establishments that began operations in Maine between 1993 and 1995. Empirical results, estimated from Poisson and negative binomial regression models, indicate that businesses favor municipalities that spend high amounts on public goods and services, even when these expenditures are financed by an increase in local taxes. This suggests that a local fiscal policy of reduced government spending, to balance a tax cut, may attract fewer new businesses than a policy featuring additional spending and higher taxes.     

Approximating the Length of Vehicle Routing Problem Solutions Using Complementary Spatial Information

Accurately estimating the length of Vehicle Routing Problem (VRP) distances can inform transportation planning in a wide variety of delivery and service provision contexts. This study extends the work of previous research where multiple linear regression models were used to estimate the average distance of VRP solutions with various customer demands and capacity constraints. This research expands on that approach in two ways: first, the point patterns used in estimation have a wider range of customer clustering or dispersion values as measured by the Average Nearest Neighbor Index (ANNI) as opposed to just using a Poisson or random point process; second, the tour coefficient adjusted by this complementary spatial information is shown to exhibit statistically more accurate estimations. To generate a full range of ANNI values, point patterns were simulated using a Poisson process, a Matern clustering process, and a simple sequential inhibition process to obtain random, clustered, and dispersed point patterns, respectively. The coefficients of independent variables in the models were used to explain how the spatial distributions of customers influence the VRP distances. These results demonstrate that complementary spatial data can be used to improve operational results, a concept that could be applied more broadly.     

The Location Choice of Employment‐based Immigrants among U.S. Metro Areas*

Abstract. This paper examines the initial location choice of legal employment‐based immigrants to the United States using Immigration and Naturalization Service data on individual immigrants, as well as economic, demographic, and social data to characterize the 298 metropolitan areas we define as the universal choice set. Focusing on interactions between place characteristics and immigrant characteristics, we provide multinomial logit model estimates for the location choices of about 38,000 employment‐based immigrants to the United States in 1995, focusing on the top 10 source countries. We find that, as groups, immigrants from nearly all countries are attracted to large cities with superior climates, and to cities with relatively well‐educated adults and high wages. We also find evidence that employment‐based immigrants tend to choose cities where there are relatively few immigrants of nationalities other than their own. However, when we introduce interaction terms to account for the sociodemographic characteristics of the individual immigrants, we find that the estimated effects of location destination factors can reverse as one takes account of the age, gender, marital status, and previous occupation of the immigrants.     

On a Class of Map Transformations

This paper considers contiguity preserving map transformations (or cartograms) that have a preassigned arcal scale. Because for each such scale it is possible to construct infinitely many transformations, this paper investigates restrictions under which such cartograms are possible. It is shown that it is possible to construct transformations that preserve the location of boundaries and of any finite number of predefined points. However, these cartograms are often quite distorted. Different types of distortions and suitable measures are discussed.     

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