Juan A. Mesa

A review of extensive facility location in networks

Abstract A facility is called ‘extensive’ if, for purposes of location, it is too large in relation to its environment regarding the activities of interest for it to be considered as a point. The literature on location on a network of ordinary and obnoxious extensive facilities is reviewed. Suggestions are made for possible directions of future research.

Locating stations on rapid transit lines

When the alignment of a new line or section of a line of a rapid transit system has already been designed, the problem of locating stations arises. One of the measures used to predict the future utilization of the line is the coverage provided by the stations. In this paper the problem of locating a prefixed number of stations so that the weighted coverage will be maximized is considered. To evaluate the coverage of each station an estimation of the street network metric and the triangulations of the census tracts are used. Finally, a longest path type algorithm over an acyclic graph is devised in order to maximize the objective function, in which it was necessary to approximately determine the catchment area for each station.

Continuous location of dimensional structures

Abstract A natural extension of point facility location problems are those problems in which facilities are extensive, i.e. those that cannot be represented by isolated points but as some dimensional structures, such as straight lines, line-segments, polygonal curves, or circles. In this paper a review of the existing work on the location of extensive facilities in continuous spaces is given. Gaps in the knowledge are identified and suggestions for further research are made.

Maximizing Trip Coverage in the Location of a Single Rapid Transit Alignment

This article describes several heuristics for the construction of a rapid transit alignment. The objective is the maximization of the total origin-destination demand covered by the alignment. Computational results show that the best results are provided by a simple greedy extension heuristic. This conclusion is confirmed on the Sevilla data for scenarios when the upper bound for inter-station distance is greater than 1250 m. Otherwise, when those upper bounds are smaller (750 m and 1000 m), an insertion heuristic followed by a post-optimization phase yields the best results. Computational times are always insignificant.

An integrated methodology for the rapid transit network design problem

The Rapid Transit System Network Design Problem consists of two intertwined location problems: the determination of alignments and that of the stations. The underlying space, a network or a region of the plane, mainly depends on the place in which the system is being constructed, at grade or elevated, or underground, respectively. For solving the problem some relevant criteria, among them cost and future utilisation, are applied. Urban planners and engineering consulting usually select a small number of corridors to be combined and then analysed. The way of selecting and comparing these alternatives is performed by the application of the four-stage transit planning model. Due to the complexity of the overall problem, during last ten years some efforts have been dedicated to modelling some aspects as optimisation problems and to provide Operations Research methods for solving them. This approach leads to the consideration of a higher number of candidates than that of the classic corridor analysis. The main aim of this paper is to integrate the steps of the transit planning model (trip attraction and generation, trip distribution, mode choice and traffic equilibrium) into an optimisation process.

Optimization methods for the planning of rapid transit systems

Abstract A central question when planning rapid transit systems is the determination of alignments and stations. Operational research methods can help solve these problems and they are also useful for the assessment of the network characteristics. This survey article reviews the main available methods.

Fitting rectilinear polygonal curves to a set of points in the plane

Abstract In this paper two problems of fitting rectilinear polygonal curves to a set of points in the plane according to the minimax approximation are considered. The constraints are, respectively, on the number of vertices and length of the polygonal curve. In both cases efficient algorithms are developed.

Improved algorithms for several network location problems with equality measures

We consider single facility location problems with equity measures, defined on networks. The models discussed are, the variance, the sum of weighted absolute deviations, the maximum weighted absolute deviation, the sum of absolute weighted differences, the range, and the Lorenz measure. We review the known algorithmic results and present improved algorithms for some of these models.

Multiobjective Routing Problems

SummaryMany network routing problems, particularly where the transportation of hazardous materials is involved, are multiobjective in nature; that is, it is desired to optimise not only physical path length but other features as well. Several such problems are defined here and a general framework for multiobjective routing problems is proposed. The notion of “efficient solution” is defined and it is demonstrated, by means of an example, that a problem may have very many solutions which are efficient. Next, potentially useful solution methods for multiobjective routing problems are discussed with emphasis being placed on the use of shortest/k-shortest path techniques. Finally, some directions for possible further research are indicated.

Conditional location of path and tree shaped facilities on trees

In this paper we deal with the location of extensive facilities on trees, both discrete and continuous, under the condition that existing facilities are already located. We require that the selected new server is a subtree, although we also specialize to the case of paths. We study the problem with the two most widely used criteria in Location Analysis: center and median. Our main results under the center criterion are nestedness properties of the solution and subquadratic algorithms for the location of paths and subtrees. For the case of the median criterion we prove that unlike the case where there is no existing facility, the continuous conditional median subtree problem is NP-hard and we develop a corresponding fully polynomial approximation algorithm. We also present subquadratic algorithms for almost all other models.