A Threshold-Satisfying Competitive Location Model

In this paper we consider a location model based on the threshold concept. We find the best location such that the probability of revenue falling short of the threshold is minimized. This objective is appropriate when a firm will not survive if its revenue falls below a known threshold. A new store is to be located. Demand is not deterministic but rather has a statistical distribution. We seek the location at which the probability that the revenue (expressed as market share attracted by the new store) is below a given threshold is minimized. The model is formulated and solved, and computational results are given.     

A Family of Location Models for Multiple-Type Discrete Dispersion

One of the defining objectives in location science is to maximize dispersion. Facilities can be dispersed for a wide variety of purposes, including attempts to optimize competitive market advantage, disperse negative impacts, and optimize security. With one exception, all of the extant dispersion models consider only one type of facility, and ignore problems where multiple types of facilities must be located. We provide examples where multiple-type dispersion is appropriate and based on this develop a general class of facility location problems that optimize multiple-type dispersion. This family of models expands on the previously formulated definitions of dispersion for single types of facilities, by allowing the interactions among different types of facilities to determine the extent to which they will be spatially dispersed. We provide a set of integer-linear programming formulations for the principal models of this class and suggest a methodology for intelligent constraint elimination. We also present results of solving a range of multiple-type dispersion problems optimally and demonstrate that only the smallest versions of such problems can be solved in a reasonable amount of computer time using general-purpose optimization software. We conclude that the family of multiple-type dispersion models provides a more comprehensive, flexible, and realistic framework for locating facilities where weighted distances should be maximized, when compared with the special case of locating only a single type of facility.     

The Multi‐level Location Set Covering Model

The classical Location Set Covering Problem involves finding the smallest number of facilities and their locations so that each demand is covered by at least one facility. It was first introduced by Toregas in 1970. This problem can represent several different application settings including the location of emergency services and the selection of conservation sites. The Location Set Covering Problem can be formulated as a 0–1 integer‐programming model. Roth (1969) and Toregas and ReVelle (1973) developed reduction approaches that can systematically eliminate redundant columns and rows as well as identify essential sites. Such approaches can often reduce a problem to a size that is considerably smaller and easily solved by linear programming using branch and bound. Extensions to the Location Set Covering Model have been proposed so that additional levels of coverage are either encouraged or required. This paper focuses on one of the extended model forms called the Multi‐level Location Set Covering Model. The reduction rules of Roth and of Toregas and ReVelle violate properties found in the multi‐level model. This paper proposes a new set of reduction rules that can be used for the multi‐level model as well as the classic single‐level model. A demonstration of these new reduction rules is presented which indicates that such problems may be subject to significant reductions in both the numbers of demands as well as sites.     

Multiple Allocation Hub Location Model with Fixed Arc Costs

This article formulates a model to analyze the role of fixed costs in the design of optimal transportation hub networks. The primary purpose of this article is to better model costs in hub networks, an issue that has attracted considerable attention. This article allows particular versions of hub networks to emerge from the cost structure, rather than by imposing a rigid predefined connectivity protocol. The article integrates modeling approaches from an environmental hub location model with the three‐index formulation of Ernst and Krishnamoorthy to produce a hub location model with fixed and variable costs for all arcs. Our goal is to demonstrate how the inclusion of a richer cost model in transportation hub location can generate a wide range of different network types, depending on the relative magnitudes of the cost elements. While the existence of special case network solutions is well known and has been exploited in optimization, the current research provides added insight to the cost of flow in a more, or less, connected hub network. Eight fundamental prototype networks are derived as special cases, and some additional unanticipated network types also emerge. The results are illustrated with a standard CAB25 data set.     

An Integrated Network Equilibrium Model of Urban Location and Travel Choices

This paper develops a mixed, combined, and stochastic user-equilibrium model for urban location and travel choices with variable origin and destination costs. Different types of travelers will be considered explicitly, including: workers with fixed residences seeking jobs, workers with fixed job locations seeking residences, and workers with both fixed residences and jobs. The costs or benefits of residing or working in a zone are described by appropriate location functions. In order to reflect effects of activity congestion the location function includes variables such as the total number of persons residing in a zone and of persons working in a zone. We prove that the proposed model is equivalent to a convex optimization problem that can be solved by a convergent method of successive averages. A numerical example is presented to demonstrate the application of the model and algorithm.     

Multiple Facilities Location in the Plane Using the Gravity Model

Two problems are considered in this article. Both problems seek the location of p facilities. The first problem is the p median where the total distance traveled by customers is minimized. The second problem focuses on equalizing demand across facilities by minimizing the variance of total demand attracted to each facility. These models are unique in that the gravity rule is used for the allocation of demand among facilities rather than assuming that each customer selects the closest facility. In addition, we also consider a multiobjective approach, which combines the two objectives. We propose heuristic solution procedures for the problem in the plane. Extensive computational results are presented.     

Microeconomic Formulation and Estimation of a Residential Location Choice Model: Implications for the Value of Time

Abstract We formulate a microeconomic model of residential location choice behavior as an aggregate of the individual behaviors of household members, subject to individual time constraints and a common income budget. A simplified version of the model is estimated from stated preference rank‐order data, yielding a function that may be interpretated as a conditional indirect utility function. We consider Box‐Tukey transformations, segmentation by income class, and a consistent treatment of data at different rank depths using the simultaneous mixed‐estimation method. Measures of the household's willingness‐to‐pay (through rents) for reducing travel times to work and study in the short run, are interpreted as subjective values of time and compared with such values derived from mode choice models. Our results are plausible, and consistent with recent findings showing that the short‐run benefits of transport projects derived by transport models are larger than benefits measured at the land use system.     

A Synthesis of Aggregation Methods for Multifacility Location Problems: Strategies for Containing Error

When solving a location problem using aggregated units to represent demand, it is well known that the process of aggregation introduces error. Research has focussed on individual components of error, with little work on identifying and controlling total error. We provide a focussed review of some of this literature and suggest a strategy for controlling total error. Consideration of alternative criteria for evaluating aggregation schemes shows that the method selected should be compatible with the objectives of the analyses in which it is used. Experiments are described that show that two different measures of error are related in a nonlinear way to the number of aggregate demand points (q), for any value of the number of facilities (p). We focus on the parameter q/p and show that it is critical for determining the expected severity of the error. Many practical implementations of location algorithms operate within the range of q/p where the rate of change of error with respect to q/p is highest.     

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.     

The Strategic Choice of Location and Transport Mode in a Successive Monopoly Model

This work emphasizes the incentives for vertical integration in a spatial model. A downstream monopoly will both strategically increase its transport costs and locate inefficiently relative to its customers. This forces the upstream monopolist to lower its input price rather than permit sales to decline. The excess costs and the inefficient location lower total profit in the vertical stream generating an incentive for vertical integration.     

行为区位论的初步研究

本文论述了行为区位论的产生和发展历程,分析了区位决策行为、空间位移行为和消费行为空间等模式,并对行为区位论在区位理论中的地位和作用进行了评价。     

西吕地望小议

西周时期有两个姜姓吕国,一在南土(今河南南阳市),可称为南吕;一在西土,可称为西吕。西吕即《诗》、《书》所载周文王、武王时期之西戎"旅(莒)国",曾为周人盟友,与周王室、密须国互通婚姻,西周末年则与西申、缯、西戎联合灭周。西吕地望当在今甘肃泾川县东、蒲河入泾的河口地带。     

The Chronology of the Russian Hunting Stations on Svalbard: A Reconsideration

Abstract

There is no agreement on the exact starting point of Russian sea mammal hunting on the Svalbard archipelago, although the question has been discussed for decades among Russian and Norwegian historians and archaeologists. After more than 25 years of archaeological research, the Russian archaeologist Vadim F. Starkov argues that Russian hunting in the Svalbard archipelago was initiated around 1550 (if not earlier), i.e. well in advance of Willem Barentsz’ discovery of Svalbard in 1596. Starkov's chronology is first and foremost based on dendrochronological datings of remnants from Russian hunting stations. This author is critical of Starkov's interpretations, and argues that almost all of his dendro-datings can in one way or another be connected with re-used material such as ship planks or local driftwood. That means there is no direct correspondence between these datings and the period when the hunting stations were in use.