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.     

CENTER POINTS, EQUILIBRIUM POSITIONS, AND THE OBNOXIOUS LOCATION PROBLEM

ABSTRACT. Real variable analysis has een used to great benefit in a variety of classical problems in location theory. In this paper we explore basic complex variable techniques in one formulation of the obnoxious location problem. A general definition of center points is first given and used to formulate several alternate versions of the obnoxious location problem. A logarithmic transformation is then used to demonstrate some equivalences between these families of distinct location problems (defined via center points). A prototype logarithmic potential function which results from this formulation is then investigated, and it is demonstrated that the extremal solutions with this objective reside on the boundary of its domain of definition. An application using zero- and one-dimensional centers is discussed, and a generalization to the spatial obnoxious problem is also briefly examined. We define a zero-dimensional center as a critical point of the logarithmic potential function, and it is shown that these centers are equivalent to the solutions of the Complex Moment Problem.     

LEONTIEF TECHNOLOGY AND THE LOCATION OF THE FIRM IN A WEBER TRIANGLE–SPECIFIC LOCALIZATION THEOREMS*

In special cases of the Leontief technology's constant input-output coefficients, the general localization theorem that an interior location is a global optimum if every input or market vertex is not a local optimum [Kusumoto (1984)] is confirmed and strengthened. Sufficient conditions are proposed for the portion of a triangular space in which the firm will locate. Finally, it is shown that, if input substitution is permitted and its effects dominate spatial effects, the firm's total cost function will be monotone, as well as concave, hence the vertex is a global optimum if it is a local optimum.     

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.     

THE MOSES-PREDOHL PULL AND THE LOCATION DECISION OF THE FIRM*

ABSTRACT This paper exploits the two-stage approach and the envelope theorem to examine the role of the Moses-Predhol pull in the cost-minimizing location theory of the firm. It shows that the two-stage approach introduces the Moses-Predohl pull into the first-order conditions. The Moses-Predohl pull is shown to be equal to zero through the envelope theorem. These results show why the assertions of Bossert and Buhl (1986) concerning Kusumoto (1984,1985) are incorrect.     

THE RELATIONSHIP BETWEEN THE LOCATION OF SERVICES AND RURAL SETTLEMENT

Soviet planners are advised to consider the linkage between rural settlement patterns and the provision of services, an issue that is assuming particular significance in connection with the present development program in the Nonchernozem Zone of the RSFSR. The number of service establishments per 1,000 population is not considered a useful indicator because it tends to be high in areas with widely dispersed settlement in small inhabited places, and yet does not reflect a high level of services because of the small size of the establishments. It is desirable to cluster sets of services in central places; the presence of a single kind of service (store, school, etc.) in a small place is found tantamount to having no service whatever. Adequate provision of services is found to reduce, or even reverse, rural out-migration.     

THE LOCATION OF METAL-INTENSIVE AND LABOR-INTENSIVE INDUSTRIES IN THE EASTERN REGIONS

The author argues against the widespread view (stated in several articles in Soviet Geography) that labor-intensive industries should be kept out of Siberia because of the shortage of labor resources in that region. Taking the specific example of labor-intensive machinery industry such as instrument-making, as opposed to steel-intensive industry, he points out that labor-intensive plants, by virtue of their smaller size, usually have smaller labor requirements than large heavy-machinery manufacturing plants. Moreover, he argues, location must not be based on total population or total labor resources of a region, but on the availability of so-called free (nonemployed) labor resources, which consist largely of women and of young people just entering upon a career. This category of labor resources happens to be greater in the eastern regions than in the western regions of the Soviet Union. In fact, one reason for the net out-migration from Siberia, according to the author, is that second and third members of households find it difficult to obtain jobs in a regional economy that is largely oriented toward male employment (in extractive industry, timber felling, etc.). The introduction of labor-intensive industries into existing Siberian industrial complexes would thus help provide employment to other household members and eliminate one reason for out-migration.     

PRODUCTION TECHNOLOGY UNCERTAINTY AND THE OPTIMAL LOCATION OF THE FIRM*

ABSTRACT This paper investigates the implication of production-technology uncertainty for the exclusion theorem. The paper presents the result that the risk-averse firm facing production technology uncertainty prefers an intermediate location to avoid risk under certain conditions. The firm chooses an intermediate location (over a corner location) particularly if its degree of risk aversion overwhelms the inherent convexity of profit with respect to location. The latter depends, in turn, on the structure of production technology characterized by the elasticity of substitution and returns to scale parameters.