Applications In Location Theory Research Articles

New models for the location of controversial facilities: A bilevel programming approach

Motivated by recent real-life applications in Location Theory in which the location decisions generate controversy, we propose a novel bilevel location model in which, on the one hand, there is a leader that chooses among a number of fixed potential locations which ones to establish. Next, on the second hand, there is one or several followers that, once the leader location facilities have been set, chooses his location points in a continuous framework. The leader’s goal is to maximize some proxy to the weighted distance to the follower’s location points, while the follower(s) aim is to locate his location points as close as possible to the leader ones. We develop the bilevel location model for one follower and for any polyhedral distance, and we extend it for several followers and any ℓp-norm, p∈Q,p≥1. We prove the NP-hardness of the problem and propose different mixed integer linear programming formulations. Moreover, we develop alternative Benders decomposition algorithms for the problem. Finally, we report some computational results comparing the formulations and the Benders decompositions on a set of instances.

A LOCATION MODEL FOR THE ALLOCATION OF THE OFF-STREET PARKING FACILITIES

In this study, an application of the location theory on the allocation of the off-street parking facilities is explored. A multi-objective linear Integer Programming model is developed for this problem. Due to its linearity, the proposed compromise programming method for the model can be solved by the LINDO compute software. Based on the results of the numerical experiment, the proposed model can provide reasonable solution to the problem addressed. The following information can be provided by the proposed solution procedure for the decision makers to determine the locations of the off-street parking facilities: the optimal locations of facilities, the demands served by each facility, and the optimal type for each of the selected parking facilities. With the rapid increase in the car ownership per household and the urban population, in the newly developed industrial country, the mass use of the private car in the metropolitan area results in a serious parking problem with limited land resource. The more the city is urbanized, the more serious the parking situation is for the city. To develop an effective procedure to allocate appropriate space for the parking facility is a crucial task for the urban planner and the associated traffic agencies. With the scarce land resource in the urban area, the use the non-parking public facilities as the potential candidates of the parking facilities is a promising alternative for the metropolitan decision maker. With the relative high land cost in the urban area, it will be a waste for the public investment, if the public facilities do not used for multiple purposes. The use of the existing public facility as a parking facility, it will not only reduce the public resistance for buying their land, but also decrease the additional investment for the land cost. Therefore, the purpose of this study is to develop an efficient procedure to allocate the off-street parking facilities in the existing public facilities as the reference basis for the decision making process. In the current parking practice, the allocation of the off-street parking facilities is often based on the ratio between forecast parking demand and supply. The facility location theory has seldom been applied to this type of problem. In this study, we explore the application of the facility location theory on the off-street parking facility locations. A suitable location model is developed to deal with the allocation of the public off-street parking facilities. In the previous studies dealt with the parking problem, Kanafani (1972) treated the behavior of the parking system as a distribution process. He developed a gravity-type model to forecast the potential parking demand for each parking facility. The allocation of the parking facility is

Concepts of generalized concavity based on triangular norms

Motivated by extensive applications of quasiconcave functions in economics and optimization, we introduce and study generalizations of quasiconcavity of functions that map a finite-dimensional real vector space into the unit interval of real numbers. The generalizations are based on the properties of triangular norms introduced by Schweizer and Sklar in connection with a probabilistic generalization of metric spaces. Also we use triangular norms to generalize the conventional concept of compromise solutions of multiobjective optimization problems. Furthermore we derive elementary properties of the resulting generalizations and discuss applications in location theory.

Multiple objective programming with piecewise linear functions

An approach to generating all efficient solutions of multiple objective programs with piecewise linear objective functions and linear constraints is presented. The approach is based on the decomposition of the feasible set into subsets, referred to as cells, so that the original problem reduces to a series of lenear multiple objective programs over the cells. The concepts of cell-efficiency and complex-efficiency are introduced and their relationship with efficiency is examined. A generic algorithm for finding efficent solutions is proposed. Applications in location theory as well as in worst case analysis are highlighted.

Police Briefing Stations: A Location Problem

Abstract The paper presents a successful application of location theory in the public sector. The problem involved development of a reliable technique to assist the Oklahoma City Police Department in selecting the locations of two police briefing stations to supplement an existing police headquarters. Difficulties encountered in applying "textbook methods" to solve an actual problem and how they were resolved are discussed. Accordingly, data collection, model development, and solution techniques are also presented. Quantitative results of a test application are included. Final site selection was based upon results of this study and other qualitative factors such as zoning requirements, land availability, political considerations, potential growth and environmental impact.

The Minimum Covering Sphere Problem

The minimum covering sphere problem, with applications in location theory, is that of finding the sphere of smallest radius which encloses a set of points in En. For a finite set of points, it is shown that the Wolfe dual is equivalent to a particular quadratic programming problem and that converse duality holds. A finite decomposition algorithm, based on the Simplex method of quadratic programming, is developed for which computer storage requirements are independent of the number of points and computing time is approximately linear in the number of points.