Facility Location with Changing Demand Levels

The paper identifies six strategies that may be considered by a planner in the location of public facilities over time. All the strategies share the common goal of producing the optimal locational arrangement at the end of a specified planning period, where optimality is defined in terms of cost minimization. However, the paths taken by each toward the optimal arrangement differ markedly. The analysis focuses on two main questions. The first is a comparison at any given point in time of the demand levels that result from implementing the various strategies. The second is a consideration of the relative costs involved in instituting two of the strategies. The appendix supplies the proofs of the main theorems derived for the demand level comparisons.     

The Location-Production-Allocation Problem With Nonlinear Production Costs

This paper develops a location-production-allocation model for the multiplant producer selling under the conditions of nonlinear production costs and a uniform pricing system. The primary goals of this paper are to incorporate the following criteria into a model: (1) production factors and location factors should be synthesized into a location-production-allocation problem; (2) the production function is nonlinear, implying economies and diseconomies of scale; (3) a systems approach should be utilized to solve for a global optimum. Within the context of these criteria, equilibrium conditions are derived for a location-production-allocation model. Finally, a heuristic technique to solve this problem is derived from the equilibrium conditions.     

LOCATION AND SPATIAL PRICING FOR PUBLIC FACILITIES

ABSTRACT. Past analysis of public facility location has generally assumed a single goal, such as cost minimization or welfare maximization, and exogenous spatial pricing. This paper considers optimal facility location under a variety of goals. Furthermore, the facility manager is allowed to engage in freight absorption so that the delivered price to consumers need not reflect actual transportation costs. A systematic interaction among management goals, freight absorption, and the optimal size and spacing of public facilities is found.     

MILL AND UNIFORM PRICING A COMPARISON*

ABSTRACT. In this paper we examine profit, price, output and welfare under mill and uniform pricing in a monopolistic spatial market with nonlinear demand, a general consumer distribution function, and a general transportation cost function. We show that if demand is convex (concave) then the optimal uniform price minus the average unit transportation cost is lower (higher) than the optimal mill price, output under uniform pricing is lower (higher) than output under mill pricing, and welfare under uniform pricing is lower (higher) than welfare under mill pricing, provided other respective conditions are satisfied.     

Optimal Number of Hierarchical Facilities with Failures

This article proposes a continuous approximation model for determining the number of hierarchical facilities when lower level facilities are subject to failures. The average distance from customers to the nearest open facility is derived for two types of customer behavior. The optimal number of facilities that minimizes the average distance is then obtained. The analytical expression for the optimal number of facilities demonstrates how the location of facilities, the failure probability, and the customer behavior affect the optimal hierarchy and the average distance. The result shows that introducing the hierarchy can reduce the average distance if the failure probability is small and the penalty for failing to use facilities is large. The model provides a fundamental understanding of the optimal hierarchy and is useful for designing hierarchical facility systems.     

Duopoly prices under congested access*

Abstract. Consider two firms, at different locations, supplying a homogenous good at constant marginal production cost. Consumers incur travel costs to the firm for each unit purchased, and the travel costs increase with the amount of travel to each firm (congestion). When all traffic and all congestion are generated by travel to a duopolist, both the Nash–Bertrand equilibrium prices and the Nash–Cournot equilibrium prices exceed the sum of the marginal production cost and the marginal external travel cost. However, when the road is shared by travelers to the duopolists' facilities and travelers in competitive markets, the Nash–Bertrand duopoly price equals the competitive price and the Nash–Cournot price contains a markup.     

DEREGULATING THE DISTRIBUTION OF ELECTRICITY: PRICE AND WELFARE CONSEQUENCES OF SPATIAL OLIGOPOLY WITH UNIFORM DELIVERED PRICES*

ABSTRACT. Theoretical, spatial oligopoly models are developed and calibrated to simulate the price and welfare consequences of deregulating the retail price of electricity (the distribution function), assuming competing sources of generation supply are available. Two types of distribution competition are considered, retaining the currently used uniform delivered pricing structure: competition for customers at neighboring utilities’ borders and franchise competition. Because duplicate facilities are required for borderline competition, short-run price increases ranging between 14 and 37 percent over existing regulated prices are estimated for upstate New York, largely because deregulated prices reflect replacement, not historic, costs of facilities.     

The Optimal Nodal Location of Public Facilities With Price-Sensitive Demand

The purpose of this paper is to present some models for the location of public facilities in nodal networks that explicitly maximize social welfare by accounting for price-elastic demand functions. The models presented here are general; yet they are mathematically equivalent to the plant location problem and are therefore amenable to solution procedures developed for the plant location problem. The models presented here distinguish between two institutional environments that reflect the degree of power of the consumer to choose which facility to patronize. If consumers can be assigned arbitrarily to facilities and can be denied service, then the environment is one of public fiat. If consumers must be served at the facility of their choice, then a “serve-allcomers” environment exists. Separate models for each environment are specified, and the relationship between optimal assignments and pricing policies is developed.     

Spatial Pricing Policies Reconsidered: Monopoly Performance and Location

This paper reexamines the welfare implications of three pricing regimes (mill, uniform, and discriminatory) for a monopoly. Assuming linear demand and constant marginal costs, I show that with the introduction of endogenous location choice, uniform delivered pricing may provide the highest social welfare when demands in different markets are sufficiently heterogeneous; whereas discriminatory pricing always dominates uniform pricing when demands in different markets are similar.     

Hannover after the World Exhibition EXPO 2000--An Attempt to Establish an ICT-cluster

The Hannover Region is extremely interested in the development of an innovative information and communication technology (ICT) cluster through the continued use of the EXPO 2000 site. This article looks into the question of whether the potential for the successful development of an ICT cluster exists. The location factors considered by the ICT firms to be poor, such as cooperation with consulting and transfer facilities, the administration and educational facilities, the missing critical mass of related and supporting industries and R&D facilities, all indicate serious weaknesses in the ICT sector. But, the development of the Hannover EXPO Park into a nucleus of the regional ICT cluster, which was begun after the end of EXPO 2000, is counteracting these deficits     

OPTIMAL REGIONAL GROWTH MODELS: MULTIPLE OBJECTIVES, SINGULAR CONTROLS, AND SUFFICIENCY CONDITIONS

ABSTRACT We develop a generalized Harrod-Domar type of model for optimal regional growth which allows determination of the optimal allocation of regional public investments and which considers multiple growth objectives, as well as both normal and singular fiscal instruments. This general model is shown to include most of the previous optimal regional growth models as special cases. Necessary conditions for some special cases of the general model are analyzed in detail, and decision rules associated with derived optimal regional growth policies are articulated. These special cases verify that singular controls do exist in certain instances, and that they must be considered for the complete specification of optimal regional growth policies; this is significant because singular controls have not been previously analyzed in the literature. We conclude the paper with a discussion of sufficiency conditions for optimal regional growth models which is more general than that given by previous authors.     

THE OPTIMAL LOCATIONS OF BRANCH FACILITIES AND MAIN FACILITIES WITH CONSUMER SEARCH*

ABSTRACT. This paper examines the socially optimal locations of branch facilities (or small stores) and main facilities (or large stores) on a finite linear market that is uniformly populated from position 0 to position 1. Each consumer has a probability w of finding the desired service (or product) at a branch facility, and a probability 1 of finding the desired service (or product) at a main facility. Two types of consumer search are considered: phone search and visit search. Different assumptions are made about the numbers of branch facilities and main facilities (each involving one or two facilities of each type). Under visit search, the socially optimal locations of branch facilities tend to be closer to main facilities than under phone search, and this tendency is more pronounced for smaller values of w.     

Housing Choice in a Regulated Market: A Nested Multinomial Logit Analysis

The paper integrates several important elements of the institutionalized and regulated nature of the housing market and analyzes the relationship between household type and housing choice in Vienna within a nested multinomial logit framework. In particular, the concept of household specific choice sets is used to account for institutional, informational and income-based constraints of the choice process. Government subsidies (such as housing and rent allowances, non-interest-bearing state loans) are explicitly taken into account in the definition of variables. Housing choice is considered in three stages: the choice of a dwelling unit given dwelling type and residential zone, the choice of a dwelling type given residential zone, and the marginal choice of a residential zone. The coefficients are derived by means of a sequential ML-procedure. The empirical results clearly indicate that demographic variables have significant impacts on housing choice behavior. Income as a single explanatory variable as well as its interacting with size measures and the quality of the house are found to be important criteria for dwelling unit choice, as housing cost variables for dwelling type choice behavior. The dwelling unit and dwelling type choice submodels fit reasonably well, whereas the residential zone model is less successful.     

Order Distance in Regular Point Patterns

This article examines the k th nearest neighbor distance for three regular point patterns: square, triangular, and hexagonal lattices. The probability density functions of the k th nearest distance and the average k th nearest distances are theoretically derived for k =1, 2, …, 7. As an application of the k th nearest distance, we consider a facility location problem with closing of facilities. The problem is to find the optimal regular pattern that minimizes the average distance to the nearest open facility. Assuming that facilities are closed independently and at random, we show that the triangular lattice is optimal if at least 68% of facilities are open by comparing the upper and lower bounds of the average distances.     

UNIFORM SPATIAL PRICING

ABSTRACT Uniform spatial pricing means that a firm delivers its product to any customer at a fixed price, independent of location. Economic theory explains the use of uniform pricing by the added profit generated by absorbing freight charges of distant customers. I extend this insight by demonstrating that when demand elasticity and transportation cost are positively enough correlated, uniform pricing generates higher profits than mill pricing. I show that this result can better explain observed patterns of price policy choice by mail order and web firms. A second result is application of this idea to firms with many shipping facilities.     

THE SPATIAL MONOPSONY: A THEORETICAL ANALYSIS*

ABSTRACT. In this paper some of the most important properties of the behavior of a spatial monopsonist are derived. Many results are mirror images of corresponding results for the spatial monopolist. A few results are, however, genuinely new. A lot of effort is spent in comparing the properties of the profit function under three different pricing policies, f.o.b. (mill)-pricing, uniform delivered pricing, and spatial price discrimination. It is shown, for example, how the profitability and welfare consequences of the different policies are related to the shapes of the supply and demand functions. It is argued that the theory may have important applications in economic analyses of renewable natural resources such as forests, where total transportation costs are nonnegligible.     

LÖSCHIAN COMPETITION VERSUS SPATIAL COLLUSION: PRICE AND WELFARE COMPARISONS*

ABSTRACT. Löschian duopoly under heterogeneous cost conditions is examined to show that it is not equivalent, contra past findings, to spatial collusion. Moreover, within the confines of the assumed demand and cost conditions spatial collusion is shown to be superior to Loschian competition in terms of both (aggregate) consumer surplus and producer surplus, which implies a possible welfare gain from collusion. A general, if not the general, prices-and-welfare comparison of alternative pricing schema including collusive, Löschian, and optimal pricing is summarily presented in a table.     

Facility Location Under Zone Pricing

Zone pricing consists in determining simultaneously several delivered prices together with the zones where these prices apply. A model and algorithm are proposed to determine optimal facility locations, prices, tariff-zones, and market areas in order to maximize the firm's profit under zone pricing. The resulting nonlinear mixed-integer program is tackled by projecting the objective function on the price space, solving repeatedly uncapacitated facility location problems for fixed values of the prices. The implicit profit function so defined is optimized by branch-and-bound. Computational results are reported.     

THE OPTIMAL LOCATIONS OF MULTIPLE BRIDGES,CONNECTING FACILITIES,OR PRODUCT VARIETIES*

ABSTRACT This paper considers the optimal locations of two or more facilities, and the optimal number of facilities, when trips are made in pairs. The results are the same as standard models of spatial competition when there is perfect matching, but not when there is random matching. The first interpretation is bridges across a river, with residential locations on one side matched perfectly or randomly to jobs on the other side. The second interpretation is connecting facilities, such as tennis courts or restaurants where pairs of consumers meet. The third interpretation is product differentiation, with husbands and wives jointly choosing from among varieties.     

The Effect of Public Infrastructure on the Private Productive Sector of Spanish Regions

In this paper we analyze the effect of infrastructure on the cost and productivity performance of the private productive sector of Spanish regions over the period 1980–1993. We use a dual approach based on cost functions that allows us to recover the usual parameters estimated with production functions. In addition, we obtain rates of return and cost elasticities of production factors at the regional level. Our framework explicitly considers that some factors are quasi-fixed and their volume can differ from their optimal endowment levels. Our results indicate that the public sector has contributed significantly to enhance productivity and reduce costs in the private sector of almost every Spanish region. Nevertheless, there is still scope for the government to continue its investment efforts, given that there remains an appreciable gap between observed and optimal public capital, and we find that in the long run, public capital promotes private investment.