Technical Note—A Further Note on One-Dimensional Space Allocation

Simmons, Donald M.

doi:10.1287/opre.19.1.249

Cited by 18 publications

(8 citation statements)

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“…Simmons [32] mentioned the possibility of extending the dynamic programming algorithm of Karp and Held [22] to the SRFLP, which was done by Picard and Queyranne [29]. Different mixed integer linear programming models were also proposed [1,3,21,26], however they have very high computational time and memory requirements, and are unlikely to be effective for problems with more than about 20 facilities.…”

Section: Introductionmentioning

confidence: 99%

Provably near-optimal solutions for very large single-row facility layout problems

Anjos

Yen

2009

Optimization Methods and Software

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The facility layout problem is a global optimization problem that seeks to arrange a given number of rectangular facilities so as to minimize the total cost associated with the (known or projected) interactions between them. This paper is concerned with the single-row facility layout problem (SRFLP), the one-dimensional version of facility layout that is also known as the one-dimensional space allocation problem. It was recently shown that the combination of a semidefinite programming (SDP) relaxation with cutting planes is able to compute globally optimal layouts for SRFLPs with up to 30 facilities. This paper further explores the application of SDP to this problem. First, we revisit the recently proposed quadratic formulation of this problem that underlies the SDP relaxation and provide an independent proof that the feasible set of the formulation is a precise representation of the set of all permutations on n objects. This fact follows from earlier work of Murata et al., but a proof in terms of the variables and structure of the SDP construction provides interesting insights on our approach. Second, we propose a new matrix-based formulation that yields a new SDP relaxation with fewer linear constraints but still yielding high-quality global lower bounds. Using this new relaxation, we are able to compute nearly-optimal solutions for instances with up to 100 facilities.

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Section: Introductionmentioning

confidence: 99%

Provably near-optimal solutions for very large single-row facility layout problems

Anjos

Yen

2009

Optimization Methods and Software

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“…It need not be pressure that matters as a realist account would suggest, however, but norm diffusion within regions sharing similar political cultures and histories can take place without any form of coercion involved. 20 Such regional policy contagion dynamics working via communication, learning, imitation and altered reputational payoffs are well established in the literature on the diffusion of economic policies 21 and have been documented for the ratification of human rights treaties 22 and the acceptance of the authority of the international criminal court 23 .…”

Section: Death Penalty Abolition and The Second Protocolmentioning

confidence: 99%

Death Penalty Abolition and the Ratification of the Second Optional Protocol

Neumayer

2004

SSRN Journal

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LSE has developed LSE Research Online so that users may access research output of the School. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LSE Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. You may freely distribute the URL (http://eprints.lse.ac.uk) of the LSE Research Online website. This document is the author's final manuscript accepted version of the journal article, incorporating any revisions agreed during the peer review process. Some differences between this version and the published version may remain. You are advised to consult the publisher's version if you wish to cite from it.Electronic copy available at: http://ssrn.com/abstract=502104 This article is structured as follows: The next section clarifies the relationship between domestic death penalty abolition and ratification of the Second Optional Protocol, arguing that ratification is the more far-reaching decision. We then discuss which factors are suggested by theory as determinants of ratifying this Protocol, focusing on political factors, which we argue to be more important than cultural, legal or social factors. This is followed by a presentation of the research design and the results of the empirical estimations, the implications of which are discussed in the final, concluding section. DEATH PENALTY ABOLITION AND THE SECOND PROTOCOL POLITICAL FOUNDATIONS OF SECOND PROTOCOL RATIFICATIONIn this section, we look at which political factors theory would suggest as likely determinants of Second Protocol ratification. We start with international relations theories that focus on how external factors persuade or pressure countries to ratify. We then move on to theories that focus on internal or domestic factors, particularly theories of regime type (democracy vs.autocracy and the type and length of democratic regime) and partisan theories. 6From a (neo-)realist perspective, powerful countries ratify international treaties and pressure less powerful countries into doing the same if this is in their perceived interest.Power is often approximated by population size and per capita income 10 and much evidence suggests that more populous and more developed countries are more active members of the world system in that they negotiate, sign and ratify more international treaties in many areas of international co-operation than smaller and/or poorer countries, for example, in the area of environment 11 , monetary affairs 12 and women's rights 13 . However, the question is whether more powerful countries regard an international protocol aimed at the abolition of the death penalty to be in their own interest. With respect to the Second Protocol, the problem is that the United States (US), the most powerful country in the world, is divided into states that are ...

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“…Simmons [36] first studied (SRFLP) and suggested a branch-and-bound algorithm. Later on Simmons [37] pointed out the possibility of extending the dynamic programming algorithm of Karp and Held [27] to (SRFLP). This was later on implemented by Picard and Queyranne [31].…”

Section: Introductionmentioning

confidence: 99%

A computational study and survey of methods for the single-row facility layout problem

Hungerländer

Rendl

2012

Comput Optim Appl

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Abstract. The single-row facility layout problem (SRFLP) is an NP-hard combinatorial optimization problem that is concerned with the arrangement of n departments of given lengths on a line so as to minimize the weighted sum of the distances between department pairs. (SRFLP) is the one-dimensional version of the facility layout problem that seeks to arrange rectangular facilities so as to minimize the overall interaction cost. This paper compares the different modelling approaches for (SRFLP) and applies a recent SDP approach for general quadratic ordering problems from Hungerländer and Rendl to (SRFLP). In particular, we report optimal solutions for several (SRFLP) instances from the literature with up to 42 departments that remained unsolved so far. Secondly we significantly reduce the best known gaps and running times for large instances with up to 100 departments.

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Technical Note—A Further Note on One-Dimensional Space Allocation

Cited by 18 publications

References 0 publications

Provably near-optimal solutions for very large single-row facility layout problems

Provably near-optimal solutions for very large single-row facility layout problems

Death Penalty Abolition and the Ratification of the Second Optional Protocol

A computational study and survey of methods for the single-row facility layout problem

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