Pub Date : 2025-11-12DOI: 10.1016/j.orl.2025.107387
Deeparnab Chakrabarty, Luc Coté
In this paper we design and analyze a new approximation algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint. Our algorithm is based on the primal-dual schema and achieves the optimal factor of . While greedy algorithms have been known to achieve this approximation factor, our algorithms also provide a dual certificate which upper bounds the optimum value of any instance. This certificate can be used to certify instance-wise guarantees potentially much better than the worst-case approximation factor.
{"title":"A primal-dual algorithm for monotone submodular maximization","authors":"Deeparnab Chakrabarty, Luc Coté","doi":"10.1016/j.orl.2025.107387","DOIUrl":"10.1016/j.orl.2025.107387","url":null,"abstract":"<div><div>In this paper we design and analyze a new approximation algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint. Our algorithm is based on the primal-dual schema and achieves the optimal factor of <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>e</mi><mo>)</mo></math></span>. While greedy algorithms have been known to achieve this approximation factor, our algorithms also provide a dual certificate which upper bounds the optimum value of any instance. This certificate can be used to certify instance-wise guarantees potentially much better than the worst-case <span><math><mo>(</mo><mn>1</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>e</mi><mo>)</mo></math></span> approximation factor.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"65 ","pages":"Article 107387"},"PeriodicalIF":0.9,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532482","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}
We propose an accelerated algorithm with a Frank-Wolfe method as an oracle for solving strongly monotone variational inequality problems. While standard solution approaches, such as projected gradient descent (aka value iteration), involve projecting onto the desired set at each iteration, a distinctive feature of our proposed method is the use of a linear minimization oracle in each iteration. This difference potentially reduces the projection cost, a factor that can become significant for certain sets or in high-dimensional problems. We validate the performance of the proposed algorithm on the traffic assignment problem, motivated by the fact that the projection complexity per iteration increases exponentially with respect to the number of links.
{"title":"A Frank-Wolfe algorithm for strongly monotone variational inequalities","authors":"Reza Rahimi Baghbadorani , Peyman Mohajerin Esfahani , Sergio Grammatico","doi":"10.1016/j.orl.2025.107388","DOIUrl":"10.1016/j.orl.2025.107388","url":null,"abstract":"<div><div>We propose an accelerated algorithm with a Frank-Wolfe method as an oracle for solving strongly monotone variational inequality problems. While standard solution approaches, such as projected gradient descent (aka value iteration), involve projecting onto the desired set at each iteration, a distinctive feature of our proposed method is the use of a linear minimization oracle in each iteration. This difference potentially reduces the projection cost, a factor that can become significant for certain sets or in high-dimensional problems. We validate the performance of the proposed algorithm on the traffic assignment problem, motivated by the fact that the projection complexity per iteration increases exponentially with respect to the number of links.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"65 ","pages":"Article 107388"},"PeriodicalIF":0.9,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532481","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 : 2025-10-30DOI: 10.1016/j.orl.2025.107386
Waleed Najy , Khaled Elbassioni , Ali Diabat
We consider a distribution network design problem where decisions on location, assignment and inventory management must be made concurrently. The model must simultaneously determine which from among a set of candidate warehouses to set up, which retailers to assign to each open warehouse for stock replenishment, and what the replenishment policy of each facility must be in order to minimize an infinite-horizon two-echelon inventory cost function. This last decision component is based on a one-warehouse multiretailer (OWMR) problem with stochastic demand: retailers replenish stocks from the central warehouse they are assigned to, which in turn replenishes from an outside supplier. Retailer demand is independent and normally distributed with given (non-identical) means and variances. Safety stock must be kept both at retailer sites and at the warehouse in order to maintain certain required Type-I service levels. We consider power-of-two (POT) periodic ordering policies. The goal is to minimize long-term average fixed and holding costs. We design a set-partitioning reformulation for the overall network design problem whose linear relaxation is solved via column generation. In doing so, we leverage tools for the OWMR problem to design an algorithm for the pricing problem used to generate columns for the set-partitioning formulation. Computational experiments show that the formulation exhibits strong tightness properties, and that the proposed method returns good solutions for moderately-sized systems within reasonable computational times.
{"title":"A column generation algorithm for a stochastic location-inventory network design problem","authors":"Waleed Najy , Khaled Elbassioni , Ali Diabat","doi":"10.1016/j.orl.2025.107386","DOIUrl":"10.1016/j.orl.2025.107386","url":null,"abstract":"<div><div>We consider a distribution network design problem where decisions on location, assignment and inventory management must be made concurrently. The model must simultaneously determine which from among a set of candidate warehouses to set up, which retailers to assign to each open warehouse for stock replenishment, and what the replenishment policy of each facility must be in order to minimize an infinite-horizon two-echelon inventory cost function. This last decision component is based on a one-warehouse multiretailer (OWMR) problem with stochastic demand: retailers replenish stocks from the central warehouse they are assigned to, which in turn replenishes from an outside supplier. Retailer demand is independent and normally distributed with given (non-identical) means and variances. Safety stock must be kept both at retailer sites and at the warehouse in order to maintain certain required Type-I service levels. We consider power-of-two (POT) periodic ordering policies. The goal is to minimize long-term average fixed and holding costs. We design a set-partitioning reformulation for the overall network design problem whose linear relaxation is solved via column generation. In doing so, we leverage tools for the OWMR problem to design an algorithm for the pricing problem used to generate columns for the set-partitioning formulation. Computational experiments show that the formulation exhibits strong tightness properties, and that the proposed method returns good solutions for moderately-sized systems within reasonable computational times.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"64 ","pages":"Article 107386"},"PeriodicalIF":0.9,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145467077","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 : 2025-10-28DOI: 10.1016/j.orl.2025.107385
Yuanhao Gao , Guangwu Liu , Stephen Shum
Current literature often overlooks link fragility in supply chain flexibility design. We analyze flexibility designs under link disruptions using a model that reveals critical differences from existing findings. In contrast to previous conclusions, long chain structures fail to maintain their incremental benefits and exhibit a 15% performance loss compared to full flexibility when disrupted. Our results demonstrate that long chain offers insufficient disruption protection, suggesting enhanced chaining designs with additional links may be necessary for robust supply chain networks.
{"title":"Supply chain flexibility with link disruptions","authors":"Yuanhao Gao , Guangwu Liu , Stephen Shum","doi":"10.1016/j.orl.2025.107385","DOIUrl":"10.1016/j.orl.2025.107385","url":null,"abstract":"<div><div>Current literature often overlooks link fragility in supply chain flexibility design. We analyze flexibility designs under link disruptions using a model that reveals critical differences from existing findings. In contrast to previous conclusions, long chain structures fail to maintain their incremental benefits and exhibit a 15% performance loss compared to full flexibility when disrupted. Our results demonstrate that long chain offers insufficient disruption protection, suggesting enhanced chaining designs with additional links may be necessary for robust supply chain networks.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"64 ","pages":"Article 107385"},"PeriodicalIF":0.9,"publicationDate":"2025-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145467078","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 : 2025-10-24DOI: 10.1016/j.orl.2025.107383
Lena Silbermayr, Emel Arıkan
We investigate altruistic behavior in an inventory transshipment system of two independent newsvendor retailers. We prove concavity of the objective function and existence and uniqueness of Nash equilibrium. Retailers' orders are increasing (decreasing) in altruism for low (high) transshipment prices and the coordinating transshipment price is not affected by altruism. Unlike self-interested retailers, altruistic retailers may decide in a way such that transshipments lead to lower expected profits than without transshipment. We find that increasing (counter-) altruism (harms) benefits supply chain performance.
{"title":"Transshipments between (counter-) altruistic retailers","authors":"Lena Silbermayr, Emel Arıkan","doi":"10.1016/j.orl.2025.107383","DOIUrl":"10.1016/j.orl.2025.107383","url":null,"abstract":"<div><div>We investigate altruistic behavior in an inventory transshipment system of two independent newsvendor retailers. We prove concavity of the objective function and existence and uniqueness of Nash equilibrium. Retailers' orders are increasing (decreasing) in altruism for low (high) transshipment prices and the coordinating transshipment price is not affected by altruism. Unlike self-interested retailers, altruistic retailers may decide in a way such that transshipments lead to lower expected profits than without transshipment. We find that increasing (counter-) altruism (harms) benefits supply chain performance.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"64 ","pages":"Article 107383"},"PeriodicalIF":0.9,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145417539","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 : 2025-10-16DOI: 10.1016/j.orl.2025.107384
Timothy C.Y. Chan, Jangwon Park , Vahid Sarhangian
We propose a robust optimization approach for constructing confidence bands for stochastic processes using a finite number of simulated sample paths. Our methodology addresses optimization bias within the constraints, avoiding overly narrow confidence bands of existing methods. In our first case study, we show that our approach achieves the desired coverage rates with an order-of-magnitude fewer sample paths than the state-of-the-art baseline approach. In our second case study, we illustrate how our approach can validate stochastic simulation models.
{"title":"Robust confidence bands for stochastic processes using simulation","authors":"Timothy C.Y. Chan, Jangwon Park , Vahid Sarhangian","doi":"10.1016/j.orl.2025.107384","DOIUrl":"10.1016/j.orl.2025.107384","url":null,"abstract":"<div><div>We propose a robust optimization approach for constructing confidence bands for stochastic processes using a finite number of simulated sample paths. Our methodology addresses optimization bias within the constraints, avoiding overly narrow confidence bands of existing methods. In our first case study, we show that our approach achieves the desired coverage rates with an order-of-magnitude fewer sample paths than the state-of-the-art baseline approach. In our second case study, we illustrate how our approach can validate stochastic simulation models.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"64 ","pages":"Article 107384"},"PeriodicalIF":0.9,"publicationDate":"2025-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364080","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 : 2025-10-13DOI: 10.1016/j.orl.2025.107382
Jonathan Chen , Jiawei Zhang
We introduce a composite metric for the ski rental problem, taking the minimum of the Expectation of Ratio (EoR) and the Ratio of Expectations (RoE). While the bound for either metric alone is , our primal-dual analysis proves the combined metric achieves a strictly better bound of approximately 1.458. This significant improvement suggests similar composite metrics could provide stronger guarantees for other online optimization problems, refining our understanding of algorithmic performance under uncertainty.
{"title":"A new performance metric for the ski rental problem","authors":"Jonathan Chen , Jiawei Zhang","doi":"10.1016/j.orl.2025.107382","DOIUrl":"10.1016/j.orl.2025.107382","url":null,"abstract":"<div><div>We introduce a composite metric for the ski rental problem, taking the minimum of the Expectation of Ratio (EoR) and the Ratio of Expectations (RoE). While the bound for either metric alone is <span><math><mfrac><mrow><mi>e</mi></mrow><mrow><mi>e</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>≈</mo><mn>1.582</mn></math></span>, our primal-dual analysis proves the combined metric achieves a strictly better bound of approximately 1.458. This significant improvement suggests similar composite metrics could provide stronger guarantees for other online optimization problems, refining our understanding of algorithmic performance under uncertainty.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"64 ","pages":"Article 107382"},"PeriodicalIF":0.9,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364079","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 : 2025-10-02DOI: 10.1016/j.orl.2025.107381
Britta Peis, Niklas Rieken
We give a simpler analysis of the ascending auction of Bikhchandani, de Vries, Schummer, and Vohra (OR 2011) to sell a welfare-maximizing base of a matroid at Vickrey prices. The new proofs for economic efficiency and the charge of Vickrey prices only require a few matroid folklore lemmas, therefore shortening the analysis of the design goals of the auction significantly.
我们对Bikhchandani， de Vries， Schummer和Vohra （OR 2011）的上升拍卖进行了更简单的分析，以维克瑞价格出售福利最大化的矩阵基础。经济效率的新证明和维克里价格的收费只需要一些矩阵民俗学引理，因此大大缩短了对拍卖设计目标的分析。
{"title":"A simplified analysis of the ascending auction to sell a matroid base","authors":"Britta Peis, Niklas Rieken","doi":"10.1016/j.orl.2025.107381","DOIUrl":"10.1016/j.orl.2025.107381","url":null,"abstract":"<div><div>We give a simpler analysis of the ascending auction of Bikhchandani, de Vries, Schummer, and Vohra (OR 2011) to sell a welfare-maximizing base of a matroid at Vickrey prices. The new proofs for economic efficiency and the charge of Vickrey prices only require a few matroid folklore lemmas, therefore shortening the analysis of the design goals of the auction significantly.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"64 ","pages":"Article 107381"},"PeriodicalIF":0.9,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269253","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 : 2025-10-02DOI: 10.1016/j.orl.2025.107380
Satoru Fujishige , Koji Yokote
As a generalization of ordinal concavity we introduce a new notion of discrete concavity called tandem concavity defined for a function over the subsets of a finite set E endowed with an ordered partition . Every function expressed as a lexicographic composition of two ordinally concave functions satisfies tandem concavity. We apply tandem concavity to the rationalization of choice rules in stable matching problems. We show that tandem concavity rationalizes a wider class of choice rules than ordinal concavity.
{"title":"Tandem concavity with application to matching problems","authors":"Satoru Fujishige , Koji Yokote","doi":"10.1016/j.orl.2025.107380","DOIUrl":"10.1016/j.orl.2025.107380","url":null,"abstract":"<div><div>As a generalization of ordinal concavity we introduce a new notion of discrete concavity called <em>tandem concavity</em> defined for a function over the subsets of a finite set <em>E</em> endowed with an ordered partition <span><math><mo>(</mo><msub><mrow><mi>E</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span>. Every function expressed as a lexicographic composition of two ordinally concave functions satisfies tandem concavity. We apply tandem concavity to the rationalization of choice rules in stable matching problems. We show that tandem concavity rationalizes a wider class of choice rules than ordinal concavity.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"64 ","pages":"Article 107380"},"PeriodicalIF":0.9,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269254","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 : 2025-10-01DOI: 10.1016/j.orl.2025.107379
Jonatha Anselmi, Bruno Gaujal
In this paper, we study the execution of a single task with an unknown size on a server with variable processing speed. Our goal is to analyze structural properties of the optimal energy consumption under the optimal speed profile that minimizes the expected energy consumption while meeting a hard deadline constraint. Specifically, we investigate how the task size probability distribution impacts the overall energy.
Under mild assumptions, our main result shows that the expected energy consumption induced by the optimal speed profile preserves the convex increasing order with respect to the task size distribution. Then, we leverage this property to derive simple bounds and conduct a worst-case analysis. In particular, we derive a simple, general formula for the energy gap induced by the ‘best’ and ‘worst’ task size distributions, expressed in terms of the support and expectation of the task size.
{"title":"Energy-optimal scheduling with variable processing speed: The role of task size variability","authors":"Jonatha Anselmi, Bruno Gaujal","doi":"10.1016/j.orl.2025.107379","DOIUrl":"10.1016/j.orl.2025.107379","url":null,"abstract":"<div><div>In this paper, we study the execution of a single task with an unknown size on a server with variable processing speed. Our goal is to analyze structural properties of the optimal energy consumption under the optimal speed profile that minimizes the expected energy consumption while meeting a hard deadline constraint. Specifically, we investigate how the task size probability distribution impacts the overall energy.</div><div>Under mild assumptions, our main result shows that the expected energy consumption induced by the optimal speed profile preserves the convex increasing order with respect to the task size distribution. Then, we leverage this property to derive simple bounds and conduct a worst-case analysis. In particular, we derive a simple, general formula for the energy gap induced by the ‘best’ and ‘worst’ task size distributions, expressed in terms of the support and expectation of the task size.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"64 ","pages":"Article 107379"},"PeriodicalIF":0.9,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222609","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}
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