THE MAXIMUM CAPTURE OR “SPHERE OF INFLUENCE” LOCATION PROBLEM: HOTELLING REVISITED ON A NETWORK*

ABSTRACT. The problem of the ice cream vendor on the beach is extended to the siting of multiple entering servers into the midst of existing servers which are already in place at multiple sites on a network. The network of population nodes, joining arcs, and eligible sites for servers provides the underlying matrix of the problem. The goal of the single firm which is siting the multiple entering servers is the capture of the maximum population from existing servers. This combinatorial problem can be described as a linear integer program for which solutions can easily be derived. Computational experience and insights derived therefrom are reported.     

MARKET CAPTURE BY TWO COMPETITORS: THE PREEMPTIVE LOCATION PROBLEM*

ABSTRACT. We consider a location and allocation game for two competitor firms, A and B, that each seek to locate p facilities in a network. A market is captured by a particular firm if that market's closest facility belongs to that firm rather than a competitor. The question is as follows: Firm A wants to locate its p facilities so that B, which enters also with p facilities after Firm A has located its facilities, will capture the minimum market value possible. That is, Firm A wishes to preempt Firm B in its bid to capture market share to the maximum extent possible. A model is presented that addresses this issue, together with solution methods and computing times.     

AN ALGORITHM FOR THE SPATIAL PRICE EQUILIBRIUM PROBLEM ON A GENERAL NETWORK IN THE SPACE OF THE PATH FLOWS*

ABSTRACT. The spatial price equilibrium on a general network may be formulated as a nonlinear-cost mathematical programming problem with simple constraints, when the decision variables are the path flows. The solution of this problem is difficult due to the very large number of variables (paths) and the impracticality of generating all the paths from all the origins to all the destinations. In this paper, we develop a Gauss-Seidel-Newton Projection algorithm and combine it with a restriction strategy. That makes it unnecessary to generate a priori all the paths. This algorithm may be further improved by exploiting the equivalence between the spatial price equilibrium on a general network and the network equilibrium. Computational results that we present in this paper demonstrate the efficiency of the proposed solution algorithms.     

OBNOXIOUS FACILITY LOCATION IN THE INTERIOR OF A PLANAR NETWORK*

ABSTRACT. The problem of locating a point that is as far as possible from arcs and nodes of a network is investigated. Each arc or node may have a different multiplicative factor (weight) for its distance. A graphical solution approach, as well as a computational algorithm, is presented.     

THE MINIMAX-MIN LOCATION PROBLEM*

We consider a new objective function for the placement of a public facility with reference to variations in accessibility : the minimization of the range between the maximal and the minimal distances to users. Some properties of the solution are given; algorithms for the Euclidean and rectilinear distance cases are presented.     

THE LOGISTICS-COST LOCATION-PRODUCTION PROBLEM*

ABSTRACT. The paper applies an inventory model to the standard Weber-Moses location-production problem. By setting the problem within a time framework, costs are seen to be incurred by both the holding of goods and the shipment of goods. The optimum location of the firm is seen to depend not only on transportation costs and the nature of the firm's production function, but also on the value of the materials being shipped. Under these conditions there is no homogeneous solution to the Weber-Moses problem. Furthermore, it is shown that the value added at the point of production is the primary factor which governs the optimum location of the firm.     

NETWORK LOADING VERSUS EQUILIBRIUM ESTIMATION OF THE STOCHASTIC ROUTE CHOICE MODEL MAXIMUM LIKELIHOOD AND LEAST SQUARES REVISITED*

Daganzo (1977, 1979), Daganzo and Sheffi (1977), Sheffi (1985), and Sheffi and Daganzo (1980) have used one assumption about traveler behavior in developing estimation techniques for the stochastic route-choice problem and another assumption in predicting flows on networks by using the same model. In estimation, they calculate the congested travel costs of the network links from observed flows on the network, and the network is loaded based on these costs. In prediction, they follow their stochastic user-equilibrium assumption by which travelers evaluate costs using the mean of the observed flows (or equilibrium flows). The travel-cost coefficient obtained from the loading method systematically overestimates the true travel-cost coefficient from which the observed flow data (which must be used in loading) is generated. The estimates of the same coefficient, obtained in this paper, by constraining the estimation results to conform to the equilibrium conditions are unbiased, and only marginally less efficient (have larger standard deviations). The average percentage error and inefficiency of the link flow predictions based on the loading method increases as the level of congestion on the network rises. In contrast, the average percentage error of link flow predictions based on the equilibrium estimation method declines and their efficiency remains very high as the level of congestion on the network rises.     

THE LAW OF ONE PRICE IN A NETWORK: ARBITRAGE AND PRICE DYNAMICS IN NATURAL GAS CITY GATE MARKETS*

ABSTRACT. In this paper we develop a model of the law of one price in a network where many markets are linked with a structure of paths. We show that arbitrage-free prices depend on the structure of the network and so do price dynamics. Our estimates indicate that local bypass and open access pipeline transportation were instrumental in opening arbitrage paths to natural gas city markets and causing their prices to converge. Spot markets in the city gates, pipeline hubs, and production fields, that are scattered over distant points in the vast pipeline network in the United States, now form a single market.     

MANDATING AS A POLICY ISSUE – THE DEFINITIONAL PROBLEM*

Mandating of state policies by agencies of the federal government and of local government policies by both state and federal agencies has emerged in recent years as an important policy issue. This conceptualization of mandating behavior offers a typology based upon (1) substantive aspects of the mandate; (2) the method by which a mandate is imposed; and (3) the mode of application. Problems associated with different types of mandates suggest multidimensional effects of intergovernmental relations on state and local policy formulation and Implementation.     

AN ECONOMIC INTERPRETATION OF KUHN'S DUAL FOR THE STEINER-WEBER PROBLEM A NOTE*

In this paper, we given an economic interpretation of Kuhn's dual of the Steiner-Weber problem. It depends essentially on the notion that different transportation systems arerelevant for the primal and the dual. Moreover, the Euclidean metric underlies the interpretation of the primal, the block one that of the dual.