Queueing-location problems on the plane

Drezner, Zvi; Schaible, Siegfried; Simchi‐Levi, David

doi:10.1002/1520-6750(199012)37:6<929::aid-nav3220370611>3.0.co;2-8

Cited by 26 publications

(10 citation statements)

References 12 publications

(13 reference statements)

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“…The minimization of the mean response time in queueing location problems gives rise to (1.2) as well, as shown by Drezner et al [21]; see also [59].…”

Section: Applicationsmentioning

confidence: 72%

Fractional programming: The sum-of-ratios case

Schaible

Shi²

2003

Optimization Methods and Software

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140

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One of the most difficult fractional programs encountered so far is the sum-of-ratios problem. Contrary to earlier expectations it is much more removed from convex programming than other multi-ratio problems analyzed before. It really should be viewed in the context of global optimization. It proves to be essentially NP-hard in spite of its special structure under the usual assumptions on numerators and denominators. The article provides a recent survey of applications, theoretical results and various algorithmic approaches for this challenging problem.

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“…The minimization of the mean response time in queueing location problems gives rise to (1.2) as well, as shown by Drezner et al [21]; see also [59].…”

Section: Applicationsmentioning

confidence: 72%

Fractional programming: The sum-of-ratios case

Schaible

Shi²

2003

Optimization Methods and Software

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140

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“…Further variants include Weber problems with possible negative weights (Drezner and Wesolowsky 1991), Weber problems taking queuing into account (Drezner et al 1990), Weber problems within buildings (Arriola et al 2005), competitive location models (Drezner and Drezner 2004), models that include price decisions (Fernández et al (2007), and single facility location-allocation problems (Plastria and Elosmani 2008). In most of these applications, only convergence to a local optimum may be expected.…”

Section: Other Single Facility Location Problemsmentioning

confidence: 99%

Hub Location Problems: The Location of Interacting Facilities

Kara

Taner

2011

International Series in Operations Research &Amp; Management Science

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), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. PrefaceThis book is the final result of a number of incidents that occurred to us while discussing location issues with colleagues at conferences. Frequently we attended presentations, in which the authors quoted the well-known references that helped to make the discipline what it is today. Upon further inquiry, though, it turned out that some of these colleagues had never actually read the original papers. We then discussed among ourselves which contributions could be credited with shaping the field. And, lo and behold, we found that we, too, had neglected to read some of the papers that form the foundation of our science. Whether it was laziness or other things that got in the way, it had become clear that something had to be done. Our first thought was to collect the original contributions (once we could agree on what they were) and reprint them. When discussing this possibility with a publisher, we immediately ran into a roadblock in the form of copyright. While this appeared to have stopped our enthusiastic effort dead in its tracks, we kept on collecting and reading what we considered original contributions.This went on until we met Camille Price, who suggested that, rather than reprinting the original contributions, we should invite some of the leaders in our field and ask them to describe the original contribution, explain and interpret it, and comment on the impact that it had to the field. This was, of course, an excellent idea, and the response by our colleagues to our pertinent requests was equally enthusiastic. What you hold in your hands is the result of this effort.In other words, the purpose of this book is to provide easy access to the main contributions to location theory. The book is organized as follows. The introductory chapter provides an overview of some of the many facets of location analysis. This is followed by contributions in the main three fields of inquiry: minisum, minimax, and covering problems. The next chapters are part of an ever-growing list of nonstandard location models: models including competitive components, those that locate undesirable facilities, those with probabilistic features, and those that allow interactions between facilities. The following chapters discuss solution techniques: after a discussion of exact and heuristic techniques, we devote an entire chapter to Weiszfeld's method, and another to Lagrangean techniques. The last chapters of this book deal with the spheres of influence that the facilities generate and that attract viii customers to them, an...

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“…In general, problem (FP) possesses more local optimal solutions that are not globally optimal [ 3 ], and so problem (FP) owns major theoretical and computational difficulties. From an application point view, this problem has a large deal of applications; for instance, traffic and economic domain [ 4 , 5 ], multistage stochastic shipping problems [ 6 ], data envelopment analysis [ 7 ], and queueing-location problems [ 8 ]. The reader is referred to a survey to find many other applications [ 4 , 5 , 9 – 11 ].…”

Section: Introductionmentioning

confidence: 99%

Regional division and reduction algorithm for minimizing the sum of linear fractional functions

Shen

2018

J Inequal Appl

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This paper presents a practicable regional division and cut algorithm for minimizing the sum of linear fractional functions over a polyhedron. In the algorithm, by using an equivalent problem (P) of the original problem, the proposed division operation generalizes the usual standard bisection, and the deleting and reduction operations can cut away a large part of the current investigated region in which the global optimal solution of (P) does not exist. The main computation involves solving a sequence of univariate equations with strict monotonicity. The proposed algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of univariate equations. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm.

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Queueing-location problems on the plane

Cited by 26 publications

References 12 publications

Fractional programming: The sum-of-ratios case

Fractional programming: The sum-of-ratios case

Hub Location Problems: The Location of Interacting Facilities

Regional division and reduction algorithm for minimizing the sum of linear fractional functions

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