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A posteriori error bounds for truncated Markov chain linear systems arising from first transition analysis 第一次过渡分析产生的截断马尔可夫链线性系统的后验误差边界
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-03-12 DOI: 10.1016/j.orl.2024.107106
Alex Infanger , Peter W. Glynn
{"title":"A posteriori error bounds for truncated Markov chain linear systems arising from first transition analysis","authors":"Alex Infanger ,&nbsp;Peter W. Glynn","doi":"10.1016/j.orl.2024.107106","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107106","url":null,"abstract":"<div><p>Many Markov chain expectations and probabilities can be computed as solutions to systems of linear equations, by applying “first transition analysis” (FTA). When the state space is infinite or very large, these linear systems become too large for exact computation. In such settings, one must truncate the FTA linear system. This paper is the first to discuss such FTA truncation issues, and to provide computable a posteriori error bounds.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107106"},"PeriodicalIF":1.1,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140180059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On semidefinite descriptions for convex hulls of quadratic programs 关于二次方程程凸壳的半无限描述
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-03-07 DOI: 10.1016/j.orl.2024.107108
Alex L. Wang , Fatma Kılınç-Karzan
{"title":"On semidefinite descriptions for convex hulls of quadratic programs","authors":"Alex L. Wang ,&nbsp;Fatma Kılınç-Karzan","doi":"10.1016/j.orl.2024.107108","DOIUrl":"10.1016/j.orl.2024.107108","url":null,"abstract":"<div><p>Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural convex relaxation via the standard semidefinite program (SDP) relaxation. In this paper we study when the convex hull of the epigraph of a QCQP coincides with the projected epigraph of the SDP relaxation. We present a sufficient condition for convex hull exactness and show that this condition is further necessary under an additional geometric assumption. The sufficient condition is based on geometric properties of Γ, the cone of convex Lagrange multipliers, and its relatives <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msup><mrow><mi>Γ</mi></mrow><mrow><mo>∘</mo></mrow></msup></math></span>.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107108"},"PeriodicalIF":1.1,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140091876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
How many clues to give? A bilevel formulation for the minimum Sudoku clue problem 给出多少条线索？最小数独线索问题的双层表述
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-03-07 DOI: 10.1016/j.orl.2024.107105
Gennesaret Tjusila , Mathieu Besançon , Mark Turner , Thorsten Koch
{"title":"How many clues to give? A bilevel formulation for the minimum Sudoku clue problem","authors":"Gennesaret Tjusila ,&nbsp;Mathieu Besançon ,&nbsp;Mark Turner ,&nbsp;Thorsten Koch","doi":"10.1016/j.orl.2024.107105","DOIUrl":"10.1016/j.orl.2024.107105","url":null,"abstract":"<div><p>It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107105"},"PeriodicalIF":1.1,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724000415/pdfft?md5=a5f0dd1602511f160c2a05654f329856&pid=1-s2.0-S0167637724000415-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140107134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On upper bounds for the multiple knapsack assignment problem 论多重可纳包分配问题的上界
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-03-06 DOI: 10.1016/j.orl.2024.107104
Laura Galli , Adam N. Letchford
{"title":"On upper bounds for the multiple knapsack assignment problem","authors":"Laura Galli ,&nbsp;Adam N. Letchford","doi":"10.1016/j.orl.2024.107104","DOIUrl":"10.1016/j.orl.2024.107104","url":null,"abstract":"<div><p>The <em>Multiple Knapsack Assignment Problem</em> is a strongly <span><math><mi>NP</mi></math></span>-hard combinatorial optimisation problem, with several applications. We show that an <em>upper bound</em> for the problem, due to Kataoka and Yamada, can be computed in linear time. We then show that some bounds due to Martello and Monaci dominate the Kataoka-Yamada bound. Finally, we define an even stronger bound, which turns out to be particularly effective when the number of knapsacks is not a multiple of the number of item classes.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107104"},"PeriodicalIF":1.1,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724000403/pdfft?md5=8b202ac03ed56140ad2cbd151c395934&pid=1-s2.0-S0167637724000403-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140085983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Faster algorithm and sharper analysis for constrained Markov decision process 约束马尔可夫决策过程的更快算法和更清晰分析
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-03-06 DOI: 10.1016/j.orl.2024.107107
Tianjiao Li , Ziwei Guan , Shaofeng Zou , Tengyu Xu , Yingbin Liang , Guanghui Lan
{"title":"Faster algorithm and sharper analysis for constrained Markov decision process","authors":"Tianjiao Li ,&nbsp;Ziwei Guan ,&nbsp;Shaofeng Zou ,&nbsp;Tengyu Xu ,&nbsp;Yingbin Liang ,&nbsp;Guanghui Lan","doi":"10.1016/j.orl.2024.107107","DOIUrl":"10.1016/j.orl.2024.107107","url":null,"abstract":"<div><p>The problem of constrained Markov decision process <span>(CMDP)</span> is investigated, where an agent aims to maximize the expected accumulated reward subject to constraints on its utilities/costs. We propose a new primal-dual approach with a novel integration of entropy regularization and Nesterov's accelerated gradient method. The proposed approach is shown to converge to the global optimum with a complexity of <span><math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mn>1</mn><mo>/</mo><mi>ϵ</mi><mo>)</mo></math></span> in terms of the optimality gap and the constraint violation, which improves the complexity of the existing primal-dual approaches by a factor of <span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>/</mo><mi>ϵ</mi><mo>)</mo></math></span>.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107107"},"PeriodicalIF":1.1,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140107118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Redesign policy for a system with uncertain failure rates 故障率不确定系统的再设计政策
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-03-04 DOI: 10.1016/j.orl.2024.107093
Qianru Ge , Zümbül Atan , Willem van Jaarsveld
{"title":"Redesign policy for a system with uncertain failure rates","authors":"Qianru Ge ,&nbsp;Zümbül Atan ,&nbsp;Willem van Jaarsveld","doi":"10.1016/j.orl.2024.107093","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107093","url":null,"abstract":"<div><p>Consider a newly developed system sold under a performance based contract (PBC), and subject to failures following various failure modes. Redesign may address certain failure modes. To trade-off redesign costs and costs associated with the PBC, we find the optimal failure modes to redesign based on the current beliefs on the failure rate per failure mode, and the amount of time remaining under the PBC. We develop analytic insights into the structure of the optimal policy.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107093"},"PeriodicalIF":1.1,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724000294/pdfft?md5=242d541b6e529813eae13d29b5118db1&pid=1-s2.0-S0167637724000294-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140112767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Envy-free house allocation with minimum subsidy 最低补贴下的无羡住房分配
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-03-02 DOI: 10.1016/j.orl.2024.107103
Davin Choo , Yan Hao Ling , Warut Suksompong , Nicholas Teh , Jian Zhang
{"title":"Envy-free house allocation with minimum subsidy","authors":"Davin Choo ,&nbsp;Yan Hao Ling ,&nbsp;Warut Suksompong ,&nbsp;Nicholas Teh ,&nbsp;Jian Zhang","doi":"10.1016/j.orl.2024.107103","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107103","url":null,"abstract":"<div><p>House allocation refers to the problem where <em>m</em> houses are to be allocated to <em>n</em> agents so that each agent receives one house. Since an envy-free house allocation does not always exist, we consider finding such an allocation in the presence of subsidy. We show that computing an envy-free allocation with minimum subsidy is NP-hard in general, but can be done efficiently if <em>m</em> differs from <em>n</em> by an additive constant or if the agents have identical utilities.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107103"},"PeriodicalIF":1.1,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724000397/pdfft?md5=c6c307f86a7510bbca9b7b354ea2e586&pid=1-s2.0-S0167637724000397-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140042048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Markov decision process design: A framework for integrating strategic and operational decisions 马尔可夫决策过程设计：整合战略和运营决策的框架
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-02-21 DOI: 10.1016/j.orl.2024.107090
Seth Brown, Saumya Sinha, Andrew J. Schaefer
{"title":"Markov decision process design: A framework for integrating strategic and operational decisions","authors":"Seth Brown,&nbsp;Saumya Sinha,&nbsp;Andrew J. Schaefer","doi":"10.1016/j.orl.2024.107090","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107090","url":null,"abstract":"<div><p>We consider the problem of optimally designing a system for repeated use under uncertainty. We develop a modeling framework that integrates the design and operational phases, which are represented by a mixed-integer program and discounted-cost infinite-horizon Markov decision processes, respectively. We seek to simultaneously minimize the design costs and the subsequent expected operational costs. This problem setting arises naturally in several application areas, as we illustrate through examples. We derive a bilevel mixed-integer linear programming formulation for the problem and perform a computational study to demonstrate that realistic instances can be solved numerically.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107090"},"PeriodicalIF":1.1,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140052794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the number of pivots of Dantzig's simplex methods for linear and convex quadratic programs 论线性和凸二次方程程的丹齐格单纯形方法的枢轴数
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-02-20 DOI: 10.1016/j.orl.2024.107091
Shaoning Han, Xinyao Zhang, Jong-Shi Pang
{"title":"On the number of pivots of Dantzig's simplex methods for linear and convex quadratic programs","authors":"Shaoning Han,&nbsp;Xinyao Zhang,&nbsp;Jong-Shi Pang","doi":"10.1016/j.orl.2024.107091","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107091","url":null,"abstract":"<div><p>Refining and extending works by Ye and Kitahara-Mizuno, this paper presents new results on the number of pivots of simplex-type methods for solving linear programs of the Leontief kind, certain linear complementarity problems of the P kind, and nonnegatively constrained convex quadratic programs. Our results contribute to the further understanding of the complexity and efficiency of simplex-type methods for solving these problems. Two applications of the quadratic programming results are presented.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"53 ","pages":"Article 107091"},"PeriodicalIF":1.1,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139936376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterizing the nonemptiness and compactness of weakly efficient solution sets for non-convex multiobjective optimization problems 表征非凸多目标优化问题的弱有效解集的非空旷性和紧凑性
IF 1.1 4区 管理学
Operations Research Letters Pub Date : 2024-02-19 DOI: 10.1016/j.orl.2024.107092
Gang Wang, Yihan Fu
{"title":"Characterizing the nonemptiness and compactness of weakly efficient solution sets for non-convex multiobjective optimization problems","authors":"Gang Wang,&nbsp;Yihan Fu","doi":"10.1016/j.orl.2024.107092","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107092","url":null,"abstract":"<div><p>In this paper, we demonstrate that non-convex multiobjective optimization problems have nonempty and compact weakly efficient solution sets if and only if finite scalar optimization problems have nonempty and compact solution sets under mild conditions, which partially reduces the gap between non-convex and convex multiobjective problems in characterizing the nonemptiness and compactness of weakly efficient solution sets. Two examples are provided to support the findings.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"53 ","pages":"Article 107092"},"PeriodicalIF":1.1,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139915149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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