Pub Date : 2024-05-01DOI: 10.1016/j.orl.2024.107120
Catherine Rainer , Eilon Solan
We study a game where one player selects a random function and the other guesses that function, and show that with high probability the second player can correctly guess most of the random function. We apply this analysis to continuous-time repeated games played with mixed strategies with delay, identify good responses of a player to any strategy profile of her opponents, and show that each player's minmax value coincides with her minmax value in pure strategies of the one-shot game.
{"title":"Guessing a random function and repeated games in continuous time","authors":"Catherine Rainer , Eilon Solan","doi":"10.1016/j.orl.2024.107120","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107120","url":null,"abstract":"<div><p>We study a game where one player selects a random function and the other guesses that function, and show that with high probability the second player can correctly guess most of the random function. We apply this analysis to continuous-time repeated games played with mixed strategies with delay, identify good responses of a player to any strategy profile of her opponents, and show that each player's minmax value coincides with her minmax value in pure strategies of the one-shot game.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107120"},"PeriodicalIF":1.1,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141072942","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}
Pub Date : 2024-05-01DOI: 10.1016/j.orl.2024.107119
Gérard Cornuéjols, Vrishabh Patil
In a classical paper, Chvátal introduced a rounding procedure for strengthening the polyhedral relaxation P of an integer program; applied recursively, the number of iterations needed to obtain the convex hull of the integer solutions in P is known as the Chvátal rank. Chvátal showed that this rank can be exponential in the input size L needed to describe P. We give a compact extended formulation of P, described by introducing binary variables, whose rank is polynomial in L.
在一篇经典论文中,Chvátal 介绍了一种加强整数程序多面体松弛 P 的舍入过程;递归应用时,获得 P 中整数解凸壳所需的迭代次数称为 Chvátal 秩。我们给出了 P 的紧凑扩展表述,通过引入二进制变量进行描述,其秩为 L 的多项式。
{"title":"Reducing the Chvátal rank through binarization","authors":"Gérard Cornuéjols, Vrishabh Patil","doi":"10.1016/j.orl.2024.107119","DOIUrl":"10.1016/j.orl.2024.107119","url":null,"abstract":"<div><p>In a classical paper, Chvátal introduced a rounding procedure for strengthening the polyhedral relaxation <em>P</em> of an integer program; applied recursively, the number of iterations needed to obtain the convex hull of the integer solutions in <em>P</em> is known as the Chvátal rank. Chvátal showed that this rank can be exponential in the input size <em>L</em> needed to describe <em>P</em>. We give a compact extended formulation of <em>P</em>, described by introducing binary variables, whose rank is polynomial in <em>L</em>.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107119"},"PeriodicalIF":1.1,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167637724000555/pdfft?md5=31547e69830dd0795992e92a3c7a822a&pid=1-s2.0-S0167637724000555-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141052446","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}
Pub Date : 2024-05-01DOI: 10.1016/j.orl.2024.107116
Ragavendran Gopalakrishnan , Yueyang Zhong
This paper presents asymptotic properties of the Erlang-C formula in a spectrum of many-server limiting regimes. Specifically, we address an important gap in the literature regarding its limiting value in critically loaded regimes by studying extensions of the well-known square-root safety staffing rule used in the Quality-and-Efficiency-Driven (QED) regime.
{"title":"Some asymptotic properties of the Erlang-C formula in many-server limiting regimes","authors":"Ragavendran Gopalakrishnan , Yueyang Zhong","doi":"10.1016/j.orl.2024.107116","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107116","url":null,"abstract":"<div><p>This paper presents asymptotic properties of the Erlang-C formula in a spectrum of many-server limiting regimes. Specifically, we address an important gap in the literature regarding its limiting value in critically loaded regimes by studying extensions of the well-known square-root safety staffing rule used in the Quality-and-Efficiency-Driven (QED) regime.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107116"},"PeriodicalIF":1.1,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S016763772400052X/pdfft?md5=4eebe7acf63a930d3a0551a1b0e70e7c&pid=1-s2.0-S016763772400052X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140948488","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}
Pub Date : 2024-04-22DOI: 10.1016/j.orl.2024.107115
Matteo Lapucci
We address conditions for global convergence and worst-case complexity bounds of descent algorithms in nonconvex multi-objective optimization. Specifically, we define the concept of steepest-descent-related directions. We consider iterative algorithms taking steps along such directions, selecting the stepsize according to a standard Armijo-type rule. We prove that methods fitting this framework automatically enjoy global convergence properties. Moreover, we show that a slightly stricter property, satisfied by most known algorithms, guarantees the same complexity bound of as the steepest descent method.
{"title":"Convergence and complexity guarantees for a wide class of descent algorithms in nonconvex multi-objective optimization","authors":"Matteo Lapucci","doi":"10.1016/j.orl.2024.107115","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107115","url":null,"abstract":"<div><p>We address conditions for global convergence and worst-case complexity bounds of descent algorithms in nonconvex multi-objective optimization. Specifically, we define the concept of steepest-descent-related directions. We consider iterative algorithms taking steps along such directions, selecting the stepsize according to a standard Armijo-type rule. We prove that methods fitting this framework automatically enjoy global convergence properties. Moreover, we show that a slightly stricter property, satisfied by most known algorithms, guarantees the same complexity bound of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>ϵ</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo></math></span> as the steepest descent method.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107115"},"PeriodicalIF":1.1,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140643913","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}
Pub Date : 2024-04-12DOI: 10.1016/j.orl.2024.107114
Ermo Chen, Lan Wu, Jingyi He
Traditional static capital allocation incurs significant reallocation costs over periods due to drastic fluctuations. We propose a new framework for dynamic capital allocation with time-varying capital constraints that incorporates reallocation costs. We obtain an analytical solution in a recursive form and demonstrate its admirable performance through simulations. The solution compromises between static allocation and expected future risk structure and strikes a balance between addressing current risk profiles and adjustment costs. It successfully provides an effective allocation tool while preserving stability.
{"title":"Dynamic capital allocation with reallocation cost","authors":"Ermo Chen, Lan Wu, Jingyi He","doi":"10.1016/j.orl.2024.107114","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107114","url":null,"abstract":"<div><p>Traditional static capital allocation incurs significant reallocation costs over periods due to drastic fluctuations. We propose a new framework for dynamic capital allocation with time-varying capital constraints that incorporates reallocation costs. We obtain an analytical solution in a recursive form and demonstrate its admirable performance through simulations. The solution compromises between static allocation and expected future risk structure and strikes a balance between addressing current risk profiles and adjustment costs. It successfully provides an effective allocation tool while preserving stability.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107114"},"PeriodicalIF":1.1,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140555651","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}
Pub Date : 2024-04-02DOI: 10.1016/j.orl.2024.107113
Arnab Bhabak , Subhamay Saha
In this paper, we investigate partially observable zero sum games where the state process is a discrete time Markov chain. We consider a general utility function in the optimization criterion. We show the existence of value for both finite and infinite horizon games and also establish the existence of optimal polices. The main step involves converting the partially observable game into a completely observable game which also keeps track of the total discounted accumulated reward/cost.
{"title":"Partially observable discrete-time discounted Markov games with general utility","authors":"Arnab Bhabak , Subhamay Saha","doi":"10.1016/j.orl.2024.107113","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107113","url":null,"abstract":"<div><p>In this paper, we investigate partially observable zero sum games where the state process is a discrete time Markov chain. We consider a general utility function in the optimization criterion. We show the existence of value for both finite and infinite horizon games and also establish the existence of optimal polices. The main step involves converting the partially observable game into a completely observable game which also keeps track of the total discounted accumulated reward/cost.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107113"},"PeriodicalIF":1.1,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140350457","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}
Pub Date : 2024-03-28DOI: 10.1016/j.orl.2024.107110
Sébastien Deschamps , Frédéric Meunier
In a simple model of assigning workers to tasks, every solution that minimizes the load difference between the most loaded worker and the least loaded one actually minimizes the maximal load and maximizes the minimal load. This can be seen as a consequence of standard results of optimization over polymatroids. We show that similar phenomena still occur in close models, simple to state, and that do not enjoy any polymatroid structure.
{"title":"Maximal workload, minimal workload, maximal workload difference: Optimizing all criteria at once","authors":"Sébastien Deschamps , Frédéric Meunier","doi":"10.1016/j.orl.2024.107110","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107110","url":null,"abstract":"<div><p>In a simple model of assigning workers to tasks, every solution that minimizes the load difference between the most loaded worker and the least loaded one actually minimizes the maximal load and maximizes the minimal load. This can be seen as a consequence of standard results of optimization over polymatroids. We show that similar phenomena still occur in close models, simple to state, and that do not enjoy any polymatroid structure.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107110"},"PeriodicalIF":1.1,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140341230","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}
Pub Date : 2024-03-27DOI: 10.1016/j.orl.2024.107111
Niloufar Daemi, Juan S. Borrero, Balabhaskar Balasundaram
We introduce a new variant of the network interdiction problem with a Markovian evader that randomly chooses a neighboring vertex in each step to build their path from designated source(s) to terminal(s). The interdictor's goal is to maximize the evader's minimum expected first passage time. We establish sufficient conditions for the interdiction to not be counter-productive, prove that the problem is NP-hard, and demonstrate the model's usefulness by solving a mixed-integer programming formulation on a test bed of social networks.
{"title":"First passage time interdiction in Markov chains","authors":"Niloufar Daemi, Juan S. Borrero, Balabhaskar Balasundaram","doi":"10.1016/j.orl.2024.107111","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107111","url":null,"abstract":"<div><p>We introduce a new variant of the network interdiction problem with a Markovian evader that randomly chooses a neighboring vertex in each step to build their path from designated source(s) to terminal(s). The interdictor's goal is to maximize the evader's minimum expected <em>first passage time</em>. We establish sufficient conditions for the interdiction to not be counter-productive, prove that the problem is NP-hard, and demonstrate the model's usefulness by solving a mixed-integer programming formulation on a test bed of social networks.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107111"},"PeriodicalIF":1.1,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140350456","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}
Pub Date : 2024-03-27DOI: 10.1016/j.orl.2024.107112
Punit Kumar Yadav, Palpandi Karuppaiah
In this paper, we introduce the concept of column nondegenerate-W property to the set of matrices, and we show that when the involved set of matrices have the column nondegenerate-W property is equivalent to the Extended Horizontal Linear Complementarity Problem have the finiteness property of the solution set.
{"title":"On finiteness of the solution set of extended horizontal linear complementarity problem","authors":"Punit Kumar Yadav, Palpandi Karuppaiah","doi":"10.1016/j.orl.2024.107112","DOIUrl":"10.1016/j.orl.2024.107112","url":null,"abstract":"<div><p>In this paper, we introduce the concept of column nondegenerate-<em>W</em> property to the set of matrices, and we show that when the involved set of matrices have the column nondegenerate-<em>W</em> property is equivalent to the Extended Horizontal Linear Complementarity Problem have the finiteness property of the solution set.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107112"},"PeriodicalIF":1.1,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140403705","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}
Pub Date : 2024-03-20DOI: 10.1016/j.orl.2024.107109
Zhe Yang, Xinyu Yang
In this paper, we consider a class of strategy-form games with both nontransferable and transferable utilities. Inspired by NTU and TU α-core concepts, we first introduce the notion of cooperative equilibria, and prove the existence theorem in this model with finite dimensional strategy spaces. Furthermore, we extend the cooperative equilibrium existence theorem to strategy-form games with infinite dimensional strategy spaces.
在本文中,我们考虑了一类同时具有不可转让和可转让效用的策略形式博弈。受 NTU 和 TU α 核心概念的启发,我们首先引入了合作均衡的概念,并证明了该模型中有限维度策略空间的存在性定理。此外,我们还将合作均衡存在定理扩展到无限维策略空间的策略形式博弈。
{"title":"Cooperative equilibria of strategy-form games with both nontransferable and transferable utilities","authors":"Zhe Yang, Xinyu Yang","doi":"10.1016/j.orl.2024.107109","DOIUrl":"https://doi.org/10.1016/j.orl.2024.107109","url":null,"abstract":"<div><p>In this paper, we consider a class of strategy-form games with both nontransferable and transferable utilities. Inspired by NTU and TU <em>α</em>-core concepts, we first introduce the notion of cooperative equilibria, and prove the existence theorem in this model with finite dimensional strategy spaces. Furthermore, we extend the cooperative equilibrium existence theorem to strategy-form games with infinite dimensional strategy spaces.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"54 ","pages":"Article 107109"},"PeriodicalIF":1.1,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140209425","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}