Pub Date : 2025-05-30DOI: 10.1016/j.orl.2025.107311
Jingyang Zhao, Mingyu Xiao
The Traveling Tournament Problem (TTP-k) is a well-known benchmark problem in sports scheduling, which asks us to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue, no pair of teams plays each other on two consecutive days, each team plays at most k consecutive home games or away games, and the total traveling distance of all the n teams is minimized. TTP-k allows a polynomial-time approximation scheme when and becomes APX-hard when . In this paper, we reduce the gap by showing that TTP-k is APX-hard for any fixed .
{"title":"The APX-hardness of the Traveling Tournament Problem","authors":"Jingyang Zhao, Mingyu Xiao","doi":"10.1016/j.orl.2025.107311","DOIUrl":"10.1016/j.orl.2025.107311","url":null,"abstract":"<div><div>The Traveling Tournament Problem (TTP-<em>k</em>) is a well-known benchmark problem in sports scheduling, which asks us to design a double round-robin schedule such that each pair of teams plays one game in each other's home venue, no pair of teams plays each other on two consecutive days, each team plays at most <em>k</em> consecutive home games or away games, and the total traveling distance of all the <em>n</em> teams is minimized. TTP-<em>k</em> allows a polynomial-time approximation scheme when <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span> and becomes APX-hard when <span><math><mi>k</mi><mo>≥</mo><mi>n</mi><mo>−</mo><mn>1</mn></math></span>. In this paper, we reduce the gap by showing that TTP-<em>k</em> is APX-hard for any fixed <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span>.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"62 ","pages":"Article 107311"},"PeriodicalIF":0.8,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144195869","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 : 2025-05-27DOI: 10.1016/j.orl.2025.107307
Yang Yang , Mikhail Y. Kovalyov , Yong Zhang
The budgeted laminar matroid independent set problem seeks to maximize the total profit of a cardinality constrained independent set within a laminar matroid, subject to a budget on total cost. A pseudo-polynomial DP algorithm and an FPTAS were recently proposed for this problem. We extract properties of these algorithms and reduce the running time of the FPTAS from to , where S is the ground set and ε is the relative error.
{"title":"An improved FPTAS for budgeted laminar matroid independent set","authors":"Yang Yang , Mikhail Y. Kovalyov , Yong Zhang","doi":"10.1016/j.orl.2025.107307","DOIUrl":"10.1016/j.orl.2025.107307","url":null,"abstract":"<div><div>The budgeted laminar matroid independent set problem seeks to maximize the total profit of a cardinality constrained independent set within a laminar matroid, subject to a budget on total cost. A pseudo-polynomial DP algorithm and an FPTAS were recently proposed for this problem. We extract properties of these algorithms and reduce the running time of the FPTAS from <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mo>|</mo><mi>S</mi><mo>|</mo></mrow><mrow><mn>7</mn></mrow></msup><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></math></span> to <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mo>|</mo><mi>S</mi><mo>|</mo></mrow><mrow><mn>5</mn></mrow></msup><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mo>|</mo><mi>S</mi><mo>|</mo></mrow><mrow><mn>5</mn></mrow></msup><msub><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msub><mo></mo><mrow><mo>|</mo><mi>S</mi><mo>|</mo></mrow><mo>)</mo></mrow></math></span>, where <em>S</em> is the ground set and <em>ε</em> is the relative error.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"62 ","pages":"Article 107307"},"PeriodicalIF":0.8,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147776","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 : 2025-05-23DOI: 10.1016/j.orl.2025.107309
K. Lakshmanan
Recent work on clean runtime algorithms for the submodular function maximization problem suggests that the dependence of the seed set size for Influence Maximization (IM) algorithms may not be necessary. This also has practical significance if the seed set is of moderate size. We propose a simple modification to Reverse Influence Sampling (RIS) algorithm of Borgs et al. to make its runtime independent of the seed set size while giving the same -approximation guarantee.
{"title":"Influence maximization independent of seed set size","authors":"K. Lakshmanan","doi":"10.1016/j.orl.2025.107309","DOIUrl":"10.1016/j.orl.2025.107309","url":null,"abstract":"<div><div>Recent work on clean runtime algorithms for the submodular function maximization problem suggests that the dependence of the seed set size for Influence Maximization (IM) algorithms may not be necessary. This also has practical significance if the seed set is of moderate size. We propose a simple modification to Reverse Influence Sampling (RIS) algorithm of Borgs et al. to make its runtime independent of the seed set size while giving the same <span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>e</mi><mo>−</mo><mi>ϵ</mi><mo>)</mo></math></span>-approximation guarantee.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"62 ","pages":"Article 107309"},"PeriodicalIF":0.8,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144137927","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 : 2025-05-19DOI: 10.1016/j.orl.2025.107308
Olli Herrala, Topias Terho, Fabricio Oliveira
This paper presents how a mixed-integer programming (MIP) formulation for influence diagrams that is based on their gradual rooted junction tree representation can be extended to incorporate more general modelling features, such as risk considerations and problem-specific constraints. We propose two algorithms that enable our reformulations by performing targeted modifications either to the underlying influence diagram or to the associated gradual rooted junction tree representation. We present computational experiments highlighting the superior computational performance of our reformulation against an alternative state-of-the-art MIP formulation for influence diagrams that, by default, can accommodate those modelling features.
{"title":"Risk-averse decision strategies for influence diagrams using rooted junction trees","authors":"Olli Herrala, Topias Terho, Fabricio Oliveira","doi":"10.1016/j.orl.2025.107308","DOIUrl":"10.1016/j.orl.2025.107308","url":null,"abstract":"<div><div>This paper presents how a mixed-integer programming (MIP) formulation for influence diagrams that is based on their gradual rooted junction tree representation can be extended to incorporate more general modelling features, such as risk considerations and problem-specific constraints. We propose two algorithms that enable our reformulations by performing targeted modifications either to the underlying influence diagram or to the associated gradual rooted junction tree representation. We present computational experiments highlighting the superior computational performance of our reformulation against an alternative state-of-the-art MIP formulation for influence diagrams that, by default, can accommodate those modelling features.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"61 ","pages":"Article 107308"},"PeriodicalIF":0.8,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105511","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 : 2025-05-16DOI: 10.1016/j.orl.2025.107305
Paolo Zappalà , Amal Benhamiche , Matthieu Chardy , Francesco De Pellegrini , Rosa Figueiredo
Extensive-form games with perfect information admit at least one Nash equilibrium. The backward induction algorithm identifies in linear time a Nash equilibrium of the game, called subgame perfect. We introduce an extension of the backward induction algorithm which is the first to identify all the outcomes of pure Nash equilibria of the game in linear time with respect to the size of the game.
{"title":"Extension of backward induction for the enumeration of pure Nash equilibria outcomes","authors":"Paolo Zappalà , Amal Benhamiche , Matthieu Chardy , Francesco De Pellegrini , Rosa Figueiredo","doi":"10.1016/j.orl.2025.107305","DOIUrl":"10.1016/j.orl.2025.107305","url":null,"abstract":"<div><div>Extensive-form games with perfect information admit at least one Nash equilibrium. The backward induction algorithm identifies in linear time a Nash equilibrium of the game, called subgame perfect. We introduce an extension of the backward induction algorithm which is the first to identify all the outcomes of pure Nash equilibria of the game in linear time with respect to the size of the game.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"61 ","pages":"Article 107305"},"PeriodicalIF":0.8,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105471","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 : 2025-05-15DOI: 10.1016/j.orl.2025.107304
Tan Yu, Xiang Zhong, Yongpei Guan
In this study, we explore a unique deterministic uncapacitated lot-sizing problem with two products of distinct quality and production cycles. Either product can fulfill the demand, necessitating concurrent inventory tracking, and adding model complexity. We target cost reduction and maintain an average quality level by optimizing ordering strategies. Incorporating multiple ordering properties into backward dynamic programming and the shortest path algorithm, we demonstrate finite value space enumeration and present an optimal algorithm with complexity, where N denotes the number of planning horizon periods. The code is available at Github.
{"title":"Polynomial-time algorithms for deterministic uncapacitated lot-sizing problem with heterogeneous production cycles","authors":"Tan Yu, Xiang Zhong, Yongpei Guan","doi":"10.1016/j.orl.2025.107304","DOIUrl":"10.1016/j.orl.2025.107304","url":null,"abstract":"<div><div>In this study, we explore a unique deterministic uncapacitated lot-sizing problem with two products of distinct quality and production cycles. Either product can fulfill the demand, necessitating concurrent inventory tracking, and adding model complexity. We target cost reduction and maintain an average quality level by optimizing ordering strategies. Incorporating multiple ordering properties into backward dynamic programming and the shortest path algorithm, we demonstrate finite value space enumeration and present an optimal algorithm with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo></math></span> complexity, where <em>N</em> denotes the number of planning horizon periods. The code is available at <span><span>Github</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"61 ","pages":"Article 107304"},"PeriodicalIF":0.8,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144088838","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 : 2025-05-14DOI: 10.1016/j.orl.2025.107306
André Berger, Arman Rouhani, Marc Schröder
This paper studies a scheduling problem where machines must follow a predetermined fixed order for processing jobs. Given n jobs, each with processing times and deadlines, we aim to minimize the number of machines used while meeting deadlines and maintaining the order. We show that the first-fit algorithm is a 2-approximation when the order aligns with non-increasing slacks, non-decreasing slacks, or non-increasing deadlines. In general, we provide an -approximation.
{"title":"Fixed order scheduling with deadlines","authors":"André Berger, Arman Rouhani, Marc Schröder","doi":"10.1016/j.orl.2025.107306","DOIUrl":"10.1016/j.orl.2025.107306","url":null,"abstract":"<div><div>This paper studies a scheduling problem where machines must follow a predetermined fixed order for processing jobs. Given <em>n</em> jobs, each with processing times and deadlines, we aim to minimize the number of machines used while meeting deadlines and maintaining the order. We show that the first-fit algorithm is a 2-approximation when the order aligns with non-increasing slacks, non-decreasing slacks, or non-increasing deadlines. In general, we provide an <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span>-approximation.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"61 ","pages":"Article 107306"},"PeriodicalIF":0.8,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068375","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 : 2025-05-07DOI: 10.1016/j.orl.2025.107303
Sylvie Chaddad , Yezekael Hayel , Vineeth S. Varma
Crowdfunding is popular among entrepreneurs who aim to bypass classical funding channels and directly address the crowd via Internet-based Crowdfunding platforms. This work introduces a model to enhance crowdfunding by strategically managing friends and family (F&F) investments. It studies the impact of timely F&F funds on total raised amounts, employing offline and online policy strategies. The offline method aims at maximizing expected investment, while the online uses Markov Decision Processes (MDPs) to improve success probability.
{"title":"A stochastic model for optimizing crowdfunding campaign success","authors":"Sylvie Chaddad , Yezekael Hayel , Vineeth S. Varma","doi":"10.1016/j.orl.2025.107303","DOIUrl":"10.1016/j.orl.2025.107303","url":null,"abstract":"<div><div>Crowdfunding is popular among entrepreneurs who aim to bypass classical funding channels and directly address the crowd via Internet-based Crowdfunding platforms. This work introduces a model to enhance crowdfunding by strategically managing friends and family (F&F) investments. It studies the impact of timely F&F funds on total raised amounts, employing offline and online policy strategies. The offline method aims at maximizing expected investment, while the online uses Markov Decision Processes (MDPs) to improve success probability.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"61 ","pages":"Article 107303"},"PeriodicalIF":0.8,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143921170","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 : 2025-05-06DOI: 10.1016/j.orl.2025.107302
José Rui Figueira , Kathrin Klamroth , Michael Stiglmayr , Julia Sudhoff Santos
Multi-objective unconstrained combinatorial optimization problems (MUCO) are in general hard to solve, i.e., the corresponding decision problem is NP-hard and the outcome set is intractable. In this paper we explore special cases of MUCO problems that are actually easy, i.e., solvable in polynomial time. More precisely, we show that MUCO problems with up to two ordinal objective functions plus one real-valued objective function are tractable, and that their complete nondominated set can be computed in polynomial time. For MUCO problems with one ordinal and a second ordinal or real-valued objective function we present an even more efficient algorithm that applies a greedy strategy multiple times.
{"title":"On the computational complexity of ordinal multi-objective unconstrained combinatorial optimization","authors":"José Rui Figueira , Kathrin Klamroth , Michael Stiglmayr , Julia Sudhoff Santos","doi":"10.1016/j.orl.2025.107302","DOIUrl":"10.1016/j.orl.2025.107302","url":null,"abstract":"<div><div>Multi-objective unconstrained combinatorial optimization problems (MUCO) are in general hard to solve, i.e., the corresponding decision problem is NP-hard and the outcome set is intractable. In this paper we explore special cases of MUCO problems that are actually easy, i.e., solvable in polynomial time. More precisely, we show that MUCO problems with up to two ordinal objective functions plus one real-valued objective function are tractable, and that their complete nondominated set can be computed in polynomial time. For MUCO problems with one ordinal and a second ordinal or real-valued objective function we present an even more efficient algorithm that applies a greedy strategy multiple times.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"61 ","pages":"Article 107302"},"PeriodicalIF":0.8,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923379","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 : 2025-04-28DOI: 10.1016/j.orl.2025.107301
Youngjoo Roh , Junyoung Kim , Kyungsik Lee
Robust cover inequalities are well-known valid inequalities for the robust knapsack problem (RKP). To strengthen them, we use lifting, which involves solving lifting problems—special cases of the RKP. We propose a novel lifting method that leverages upper bounds for lifting problems. First, we introduce a strong, efficiently computable, and quality-guaranteed upper bound for the RKP based on the decomposition property of its solution set. We then devise an efficient lifting method by applying the proposed upper bound to lifting problems.
{"title":"Lifting cover inequalities for the robust knapsack problem","authors":"Youngjoo Roh , Junyoung Kim , Kyungsik Lee","doi":"10.1016/j.orl.2025.107301","DOIUrl":"10.1016/j.orl.2025.107301","url":null,"abstract":"<div><div>Robust cover inequalities are well-known valid inequalities for the robust knapsack problem (RKP). To strengthen them, we use lifting, which involves solving lifting problems—special cases of the RKP. We propose a novel lifting method that leverages upper bounds for lifting problems. First, we introduce a strong, efficiently computable, and quality-guaranteed upper bound for the RKP based on the decomposition property of its solution set. We then devise an efficient lifting method by applying the proposed upper bound to lifting problems.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"61 ","pages":"Article 107301"},"PeriodicalIF":0.8,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895549","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号