Directional approach to gradual cover: the continuous case

The objective of the cover location models is covering demand by facilities within a given distance. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. In this paper we use a recently proposed rule for calculating the joint cover of a demand point by several facilities termed "directional gradual cover". Contrary to all gradual cover models, the joint cover depends on the facilities' directions. In order to calculate the joint cover, existing models apply the partial cover by each facility disregarding their direction. We develop a genetic algorithm to solve the facilities location problem and also solve the problem for facilities that can be located anywhere in the plane. The proposed modifications were extensively tested on a case study of covering Orange County, California

Locating Base Stations for Mobile Servers

In this paper we review location models, specifically covering location models, which are applicable to modeling the location of base stations for cellular phone users. The definition of cover is revisited, suggesting three new definitions of cover: two gradual cover models, and one sum cover model. A new objective for covering models, the variable radius model, is proposed. The probability that a connection can be made between the cellular phone and a base station at a given distance is defined. The objective is to minimize the probability that users cannot be serviced by at least one base station. These four new approaches are reviewed and once the research is completed four papers will be published in peer reviewed journals

Competitive facility location: Unequally attractive facilities.

Existing competitive facility location models assume that the facilities concerned are equally attractive and therefore distance is the only choice variable among them. When the facilities are not equally attractive, additional variables which differentiate facilities come to bear in customer facility preference. The models developed in this dissertation find the best location for a facility which is not equally attractive to existing ones. Two approaches, which employ different assumptions about customer behavior, are taken in the development of the best location solution. The first approach, based on Hotelling's theory, assumes that customers patronize the most attractive facility. Proximity is one component of attractiveness, and is "traded off" for higher quality facilities. Differences in overall quality are converted to a distance measure and the best location for the facility is found such that the market share it captures is maximized. The second approach, based on Huff's formulation, is based on a formula for predicting market share captured by shopping centers. This formula is based on the area of a shopping center in which a retail establishment is located and the distance from it. The best location for a new shopping center is found. The models are further tested on a set of empirical data in a series of simulations. These simulations provide a comparison of the location solutions between existing models and the models developed in this dissertation. The superiority of the location models presented is reflected in market share captured. The sensitivity of the location solution and the market share captured to changes in attractiveness measures, and the impact on market share captured of changes in facility size are demonstrated. The simulations and procedures developed provide decision makers with important policy instruments for strategic planning. In addition to finding the best location for a new facility, the decision maker can assess the impact on the location and/or the market share of his facility (existing or new) of changes in the quality and/or the location of any other facility.Ph.D.Urban, Technological, and Environmental Planning: Urban and Regional PlanningUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/103393/1/9319515.pdfDescription of 9319515.pdf : Restricted to UM users only

LOCATION OF A FACILITY IN A PLANAR NETWORK

In this paper we investigate the location of a facility inside a planar network. Two equivalent problems are analyzed. In one problem it is assumed that the links of the network create a nuisance or hazard and the objective is to locate a facility where the total nuisance is minimized. An equivalent problem is locating an obnoxious facility where the total nuisance generated by the facility and inflicted on the links of the network is minimized. The model is formulated and analyzed. A heuristic solution method for its solution is proposed and tested on a set of planar networks with up to 50,000 links yielding good results

A Note on Applying the Gravity Rule to the Airline Hub Problem

In this note we propose a new model for the airline hub selection problem. Passengers use a hub on the way to their destination. We apply the objective of minimizing the total miles traveled by passengers. This formulation can be used as the basis for other objectives also. Copyright 2001 BlackwellPublishers

Location of casualty collection points

In this paper I find the best location of casualty collection points (CCPs). CCPs are expected to become operational in case of a human-made or natural disaster with mass casualties, such as a high-magnitude earthquake. Five objective functions are suggested and analyzed: p -median, p -center, p -maxcover, min-variance, and Lorenz curve. Multiobjective models are also analyzed. To illustrate the location problem, the models are applied to a scenario based on a large earthquake hitting Orange County, CA as a case study. The optimal locations for the CCPs using the objective functions are found, analyzed, and compared.

Cannibalization in a Competitive Environment

In this article, cannibalization and its effects on location decisions in a competitive retail environment is investigated. The authors analyze maximizing market share while minimizing cannibalization using the gravity (Huff) model. The efficient frontier according to these two noncompatible objectives is constructed and illustrated on an example problem. An easy to implement analysis that provides insight into management decisions is provided. To illustrate the ease of implementing the model using Excel, a description of the spreadsheet along with the Visual Basic for Applications (VBA) code are provided.competitive location; cannibalization; efficient frontier