Showing papers in "Top in 1998"
TL;DR: In this paper, the many to many location routing problem is introduced and its relationship to various problems in distribution management is emphasised, and useful mathematical formulations which can be easily extended to cater for other related problems are produced.
Abstract: In this paper the many to many location routing problem is introduced, and its relationship to various problems in distribution management is emphasised. Useful mathematical formulations which can be easily extended to cater for other related problems are produced. Techniques for tackling this complex distribution problem are also outlined.
85 citations
TL;DR: It is proved that there always exists a finite set that includes an optimal solution for the Huff and the Pareto-Huff competitive models on networks with the assumption of a concave function of the distance.
Abstract: In this paper we prove that there always exists a finite set that includes an optimal solution for the Huff and the Pareto-Huff competitive models on networks with the assumption of a concave function of the distance. In the Huff model, there is always a vertex of the network that belongs to the solution set. For the Pareto-Huff model, we prove that there is always an optimal solution at, or an e-optimal solution close to, a vertex or an isodistant point, a new concept introduced in this paper.
26 citations
TL;DR: A “multi-local” optimization procedure using inexact line searches is presented, and an application of the method to a semi-infinite programming procedure is included.
Abstract: The development of efficient algorithms that provide all the local minima of a function is crucial to solve certain subproblems in many optimization methods. A “multi-local” optimization procedure using inexact line searches is presented, and numerical experiments are also reported. An application of the method to a semi-infinite programming procedure is included.
20 citations
TL;DR: The stability of these values from a dynamic point of view is examined and a reinteropretation of them from the standpoint of the propernsity to disrupt approach is proposed and an alternative kernel-like formulation of them is provided.
Abstract: In this paper we present some new results concerning the least square family of values for TU games. We first examine the stability of these values from a dynamic point of view and propose a reinteropretation of them from the standpoint of the propernsity to disrupt approach. In the second part the family of individually rational least square (IRLS) values is introduced and an alternative kernel-like formulation of them is provided. Finally we describe a natural and simple algorithm for calculating any IRLS value of a game.
19 citations
TL;DR: In this paper, the authors investigated the properties of these two closely related problems and derived polynomial algorithms to solve them both in case of either (possibly inflated) Euclidean or polyhedral distances.
Abstract: A location is sought within some convex region of the plane for the central site of some public service to a finite number of demand points. The parametric maxcovering problem consists in finding for eachR>0 the point from which the total weight of the demand points within distanceR is maximal. The parametric minimal quantile problem asks for each percentage α the point minimising the distance necessary for covering demand points of total weight at least α. We investigate the properties of these two closely related problems and derive polynomial algorithms to solve them both in case of either (possibly inflated) Euclidean or polyhedral distances.
17 citations
TL;DR: In this paper, the authors investigated the simple uncapacitated plant location problem on a line and showed that under general conditions the special structure of the problem allows the optimal solution to be obtained directly from a linear programming relaxation.
Abstract: This paper investigates the simple uncapacitated plant location problem on a line. We show that under general conditions the special structure of the problem allows the optimal solution to be obtained directly from a linear programming relaxation. This result may be extended to the related p-median problem on a line. Thus, the practitioner is now able to use readily available LP codes in place of specialized algorithms to solve these one-dimensional models. The findings also shed some light on the “integer friendliness” of the general problem.
14 citations
TL;DR: In this paper, a convergent approximation scheme of the optimal solution set of the multi-criteria Weber problem with strict norms is presented, using sequences of optimal solution sets of the same problem with polyhedral norms.
Abstract: In this paper a convergent approximation scheme of the optimal solution set of the multi-criteria Weber problem with strict norms is presented. To this end, we use sequences of optimal solution sets of the same problem with polyhedral norms. In addition, an alternative description of the optimal solution of the single criterion Weber problem with any strict norm is also obtained using polyhedral norms.
12 citations
TL;DR: In this paper, a polynomial time geometric procedure to find a center trajectory subject to the number of bends is presented, and when the polygonal is constrained on the extreme segments a modified algorithm is designed.
Abstract: A rectilinear center trajectory is a polygonal line consisting only of horizontal and vertical segments which minimizes the maximum distance tom given points in the plane. In this paper a polynomial time geometric procedure, to find a center trajectory subject to the number of bends, is presented. When the polygonal is constrained on the extreme segments a modified algorithm is designed.
7 citations
TL;DR: A packing algorithm that includes the formation of units with variable number of pieces is proposed and the value of the percentage variability reduction index is obtained.
Abstract: In this paper we study the variability reduction gain that results from the use of multiweighing proceedings in packing processes with the objective of sales at constant nominal weights. According to this, we have proposed a packing algorithm that includes the formation of units with variable number of pieces and we have obtained the value of the percentage variability reduction index.
5 citations
TL;DR: A polynomial algorithm which either finds a tour traversing each edge of G exactly two non-consecutive times, one in each direction, or decides that no such tour exists.
Abstract: Given a connected graph G, we present a polynomial algorithm which either finds a tour traversing each edge of G exactly two non-consecutive times, one in each direction, or decides that no such tour exists. The main idea of this algorithm is based on the modification of a proof given by Thomassen related to a problem proposed by Ore in 1951.
4 citations
TL;DR: In this article, the expected distance concept applied to the bias of the road network distance and trajectory deviations is used to separate the set of origin-destination pairs into two samples and also to analyse each sample using regression.
Abstract: Round norms τl
p, p ∈ (1,2] and block norms have been utilised for modelling actual distances in transportation networks. A geometric setting will permit the establishment of a relationship between bias of the road network distance and trajectory deviations, which will be used to separate the set of origin-destination pairs into two samples and also to analyse each sample using regression, thus obtaining several types of estimators. What will be demonstrated in this paper is that these functions can be combined through either a weighted sum, or by means of the introduction of the expected distance concept applied to the bias, to obain distance predicting functions for the region considered.
TL;DR: In this paper, the authors show that if the maximin problem with concave increasing utility functions is solved by inspecting the extreme points of the Voronoi diagram, one may have to inspect an infinite number of candidate points.
Abstract: In this note we show by means of a simple example that, if the maximin problem with (nonlinear) concave increasing utility functions is solved by inspecting the extreme points of the (generalized) Voronoi diagram (as usually proposed), one may have to inspect an infinite number of candidate points.
TL;DR: In this paper, the authors present two equivalent representations of a 0-1 model for the air traffic flow management problem, and show that the LP relaxation of the second representation is tighter than that of the first one.
Abstract: We present two equivalent representations of a 0–1 model for the Air Traffic Flow Management Problem. We show that the LP relaxation of the second representation is tighter than the LP relaxation of the first one. As a direct implication, the Branch-and-Cut effort can be reduced. Computational results are reported on a set of large-scale instances.
TL;DR: In this paper, the optimal location of paths on trees with regard to two objective functions: the eccentricity and the superior section, is considered and an algorithm based on a progressive reduction of the initial tree is proposed to obtain all efficient paths.
Abstract: Network location theory has traditionally been concerned with the optimal location of a single-point facility at either a vertex or along an arc in the network. Recently, some authors have departed from this traditional problem and have considered the location of extensive facilities, such as paths, trees or cycles. In this paper, we consider the optimal location of paths on trees with regard to two objective functions: the eccentricity and the superior section. We first present methods to find paths with minimal eccentricity and minimal superior section on trees with arbitrary positive lengths. Then, we analyse the biobjective optimization problem and propose an algorithm, based on a progressive reduction of the initial tree, to obtain all efficient paths. Modifications of the proposed algorithm to solve the problem when a general objective function is used instead of the eccentricity function are also given.
TL;DR: Previous solution techniques are extended to provide an efficient algorithm for the Indirect Covering Tree problem and the generalization in which demand covered is attenuated by distance.
Abstract: In recent years, interest has been shown in the optimal location of ‘extensive’ facilities in a network. Two such problems—the Maximal Direct and Indirect Covering Tree problems—were introduced by Hutson and ReVelle. Previous solution techniques are extended to provide an efficient algorithm for the Indirect Covering Tree problem and the generalization in which demand covered is attenuated by distance. It is also shown that the corresponding problem is NP-hard when the underlying network is not a tree.
TL;DR: In this article, a general model of dynamic optimization, deterministic, in discrete time, and with infinite time horizon is considered, and conditions for stability of the optimal solution are studied.
Abstract: A general model of dynamic optimization, deterministic, in discrete time, and with infinite time horizon is considered. We assume that there are parameters in the formulation of the model. Conditions for stability of the optimal solution are studied. Analysis of steady state comparative statics and comparative dynamics are presented. In addition we apply these results to a quadratic case and to an economic example: a one sector growth model.
TL;DR: This study extends the Viscolani's results to the non Markovian case and derives some performance measures of the recognition procedure such as the waste time, the queue length of patterns, the classification error probabilities and so on.
Abstract: A recognition procedure is modelled as a queuing problem. We obtain first the steady-state distribution of probabilities of the basic process describing its evolution. Then, we derive some performance measures of the recognition procedure such as the waste time, the queue length of patterns, the classification error probabilities and so on. Stochastic comparisons are also provided. Our study extend the Viscolani's results to the non Markovian case.