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.     

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.     

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.     

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.     

LOCATING A SINGLE NEW FACILITY AMONG EXISTING,UNEQUALLY ATTRACTIVE FACILITIES*

ABSTRACT. The location of a new facility in a competitive environment is investigated. It is assumed that customers patronize the facility with the highest utility value rather than the closest facility. Simulations show that the new approach yields a superior location in terms of market size captured. Sensitivity analyses of the problem parameters illustrate the sensitivity of the location and the sensitivity of the market size captured to the facility's quality.     

THE LOCATION OF THE TREASURY OF ATREUS

Summary.   The Treasury of Atreus, the largest and most impressive of the nine tholos tombs found at Mycenae, stands by itself at the southern edge of a bowl in the east slope of the Panagia ridge. This paper argues that the tomb was constructed on this particular spot so that it would be seen from the trackways/roads that led to Mycenae from the east, south-east and south-west and from the main pathway to the palace. The view of the acropolis hill and Mt. Profitis Ilias from the space occupied by the earthen mound above the tholos also appears to have influenced the choice of location. It is suggested that the position of the Treasury of Atreus was, like the tomb itself, a political statement, calculated to show that the ruler who built the tomb succeeded in extending the territory of Mycenae across the central Argolid.     

THE LOCATION THEORY OF THE PLANTATION*

ABSTRACT This paper develops a method for studying noninfinitesimal operational units, with the Thünen location and land use model. With constant returns to scale and perfect divisibility of nonland inputs, all operational units would occupy only a point on the landscape. The present model uses increasing returns to scale to generate large operational units, called “plantations” and studies the comparative statics. The setting of the model is an agricultural operation in which some processing of raw crop must be conducted prior to shipment to market. The processing is assumed to have increasing returns to scale.     

旅游流距离衰减现象演绎研究

以旅游系统空间结构模型为依托,通过绘制旅游流距离衰减曲线,对旅游流距离衰减现象进行演绎研究。结果发现,高斯分布型和指数分布型是旅游流距离衰减曲线的基本类型,旅游系统中客源地结点的空间分布格局是旅游流距离衰减曲线类型的决定性因素,到访率距离衰减速率是曲线形状的修饰性因素,距离衰减曲线的绘制方法不同,距离衰减曲线的类型也不同。最后,以井冈山和庐山为案例进行了实证分析。