Pub Date : 2025-07-29DOI: 10.1016/j.orl.2025.107348
Rayen Tan , Alex Xu , Viswanath Nagarajan
We provide a generic method that transforms a non-adaptive solution for classic sequential testing problems into a solution for the more general batched setting, while incurring only an additive fraction loss in the approximation ratio. Combined with previously-known approximation algorithms in the classic setting, we obtain batched algorithms for AND, k-of-n and score-classification functions with approximation ratios 1.707, 2.618 and 6.371 respectively. Our algorithm is very efficient, running in time for all the aforementioned functions.
{"title":"A general framework for sequential batch-testing","authors":"Rayen Tan , Alex Xu , Viswanath Nagarajan","doi":"10.1016/j.orl.2025.107348","DOIUrl":"10.1016/j.orl.2025.107348","url":null,"abstract":"<div><div>We provide a generic method that transforms a non-adaptive solution for classic sequential testing problems into a solution for the more general batched setting, while incurring only an additive <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mrow><mn>2</mn></mrow></msqrt></mrow></mfrac></math></span> fraction loss in the approximation ratio. Combined with previously-known approximation algorithms in the classic setting, we obtain batched algorithms for AND, <em>k</em>-of-<em>n</em> and score-classification functions with approximation ratios 1.707, 2.618 and 6.371 respectively. Our algorithm is very efficient, running in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> time for all the aforementioned functions.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"63 ","pages":"Article 107348"},"PeriodicalIF":0.9,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144770985","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 : 2025-07-24DOI: 10.1016/j.orl.2025.107347
Dan Pirjol , Lingjiong Zhu
We study the pricing of VIX options in the SABR model where are standard Brownian motions correlated with correlation and . VIX is expressed as a risk-neutral conditional expectation of an integral over the volatility process . We show that is the unique solution to a one-dimensional diffusion process. Using the Feller test, we show that explodes in finite time with non-zero probability. As a consequence, VIX futures and VIX call prices are infinite, and VIX put prices are zero for any maturity. As a remedy, we propose a capped volatility process by capping the drift and diffusion terms in the process such that it becomes non-explosive and well-behaved, and study the short-maturity asymptotics for the pricing of VIX options.
{"title":"VIX options in the SABR model","authors":"Dan Pirjol , Lingjiong Zhu","doi":"10.1016/j.orl.2025.107347","DOIUrl":"10.1016/j.orl.2025.107347","url":null,"abstract":"<div><div>We study the pricing of VIX options in the SABR model <span><math><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>t</mi></mrow></msub><msubsup><mrow><mi>S</mi></mrow><mrow><mi>t</mi></mrow><mrow><mi>β</mi></mrow></msubsup><mi>d</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo><mi>d</mi><msub><mrow><mi>σ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>ω</mi><msub><mrow><mi>σ</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>d</mi><msub><mrow><mi>Z</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> where <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> are standard Brownian motions correlated with correlation <span><math><mi>ρ</mi><mo><</mo><mn>0</mn></math></span> and <span><math><mn>0</mn><mo>≤</mo><mi>β</mi><mo><</mo><mn>1</mn></math></span>. VIX is expressed as a risk-neutral conditional expectation of an integral over the volatility process <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>t</mi></mrow><mrow><mi>β</mi><mo>−</mo><mn>1</mn></mrow></msubsup><msub><mrow><mi>σ</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span>. We show that <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> is the unique solution to a one-dimensional diffusion process. Using the Feller test, we show that <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> explodes in finite time with non-zero probability. As a consequence, VIX futures and VIX call prices are infinite, and VIX put prices are zero for any maturity. As a remedy, we propose a capped volatility process by capping the drift and diffusion terms in the <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> process such that it becomes non-explosive and well-behaved, and study the short-maturity asymptotics for the pricing of VIX options.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"63 ","pages":"Article 107347"},"PeriodicalIF":0.8,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713678","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 : 2025-07-21DOI: 10.1016/j.orl.2025.107344
Tom Bruinink , Lotte Berghman , Twan Dollevoet
Due to a shortage of drivers and a stronger focus on employee well-being, there is an increasing need to take driver satisfaction explicitly into account when solving the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW). We focus on workload balance and region consistency. In a first attempt to assess the consequences of adding driver satisfaction to the original objective of cost minimization, we evaluate both a two-step approach and an integrated approach using real-life instances from two different companies.
{"title":"Beyond efficiency: Exploring the cost effects of prioritizing driver satisfaction in vehicle routing","authors":"Tom Bruinink , Lotte Berghman , Twan Dollevoet","doi":"10.1016/j.orl.2025.107344","DOIUrl":"10.1016/j.orl.2025.107344","url":null,"abstract":"<div><div>Due to a shortage of drivers and a stronger focus on employee well-being, there is an increasing need to take driver satisfaction explicitly into account when solving the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW). We focus on workload balance and region consistency. In a first attempt to assess the consequences of adding driver satisfaction to the original objective of cost minimization, we evaluate both a two-step approach and an integrated approach using real-life instances from two different companies.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"63 ","pages":"Article 107344"},"PeriodicalIF":0.8,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144711863","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 : 2025-07-08DOI: 10.1016/j.orl.2025.107333
Ahmad Abdi, Mahsa Dalirrooyfard, Meike Neuwohner
Given a connected graph and a crossing family over ground set V such that for every , we prove there exists a strong orientation of G for , i.e., an orientation of G such that each set in has at least one outgoing and at least one incoming arc. This implies the main conjecture in Chudnovsky et al. (2016) [3].
{"title":"Strong orientation of a connected graph for a crossing family","authors":"Ahmad Abdi, Mahsa Dalirrooyfard, Meike Neuwohner","doi":"10.1016/j.orl.2025.107333","DOIUrl":"10.1016/j.orl.2025.107333","url":null,"abstract":"<div><div>Given a connected graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> and a crossing family <span><math><mi>C</mi></math></span> over ground set <em>V</em> such that <span><math><mo>|</mo><msub><mrow><mi>δ</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>U</mi><mo>)</mo><mo>|</mo><mo>≥</mo><mn>2</mn></math></span> for every <span><math><mi>U</mi><mo>∈</mo><mi>C</mi></math></span>, we prove there exists a strong orientation of <em>G</em> for <span><math><mi>C</mi></math></span>, i.e., an orientation of <em>G</em> such that each set in <span><math><mi>C</mi></math></span> has at least one outgoing and at least one incoming arc. This implies the main conjecture in Chudnovsky et al. (2016) <span><span>[3]</span></span>.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"62 ","pages":"Article 107333"},"PeriodicalIF":0.8,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579275","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 : 2025-06-27DOI: 10.1016/j.orl.2025.107325
Paul Revenant , Hadrien Cambazard , Nicolas Catusse
The order picking problem involves determining the shortest tour for a picker to collect a set of products in a warehouse. Ratliff and Rosenthal introduced a linear algorithm to solve this problem for warehouses with two cross aisles, allowing for tours that double-cross entire aisles. In this paper, we prove that in rectangular warehouses, a minimum-length tour always exists that avoids double-crossing any aisle. This result simplifies the problem by eliminating redundant configurations.
{"title":"A note about a transition of Ratliff and Rosenthal's order picking algorithm for rectangular warehouses","authors":"Paul Revenant , Hadrien Cambazard , Nicolas Catusse","doi":"10.1016/j.orl.2025.107325","DOIUrl":"10.1016/j.orl.2025.107325","url":null,"abstract":"<div><div>The order picking problem involves determining the shortest tour for a picker to collect a set of products in a warehouse. Ratliff and Rosenthal introduced a linear algorithm to solve this problem for warehouses with two cross aisles, allowing for tours that double-cross entire aisles. In this paper, we prove that in rectangular warehouses, a minimum-length tour always exists that avoids double-crossing any aisle. This result simplifies the problem by eliminating redundant configurations.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"62 ","pages":"Article 107325"},"PeriodicalIF":0.8,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144491979","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 : 2025-06-18DOI: 10.1016/j.orl.2025.107324
Tamanna Yadav, S.K. Gupta, Bishal Biswas
This research delves into the study of a multiobjective non-smooth semi-infinite programming problem with equilibrium constraints. Utilizes the locally Lipschitz property of functions, we develop an approximate sufficient optimality result for the semi-infinite program using the approximate M-stationary point. Additionally, we construct an approximate mixed-type dual problem for the considered semi-infinite model and establish approximate duality relations under the generalized convexity assumptions and using the notion of the approximate M-stationary point.
{"title":"Approximate mixed type duality for semi-infinite programs having equilibrium constraints","authors":"Tamanna Yadav, S.K. Gupta, Bishal Biswas","doi":"10.1016/j.orl.2025.107324","DOIUrl":"10.1016/j.orl.2025.107324","url":null,"abstract":"<div><div>This research delves into the study of a multiobjective non-smooth semi-infinite programming problem with equilibrium constraints. Utilizes the locally Lipschitz property of functions, we develop an approximate sufficient optimality result for the semi-infinite program using the approximate <em>M</em>-stationary point. Additionally, we construct an approximate mixed-type dual problem for the considered semi-infinite model and establish approximate duality relations under the generalized convexity assumptions and using the notion of the approximate <em>M</em>-stationary point.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"62 ","pages":"Article 107324"},"PeriodicalIF":0.8,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144364856","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 : 2025-06-12DOI: 10.1016/j.orl.2025.107323
John Cotrina , Carlos Calderón
In this paper, we focus on the concept of projected solutions in generalized Nash games and examine their relationship with generalized Nash equilibria. We also establish the existence of projected solutions through an elegant reformulation that allows the use of a result by Arrow and Debreu. Finally, abstract economy is considered as an application.
{"title":"Remarks on projected solutions in generalized Nash games","authors":"John Cotrina , Carlos Calderón","doi":"10.1016/j.orl.2025.107323","DOIUrl":"10.1016/j.orl.2025.107323","url":null,"abstract":"<div><div>In this paper, we focus on the concept of projected solutions in generalized Nash games and examine their relationship with generalized Nash equilibria. We also establish the existence of projected solutions through an elegant reformulation that allows the use of a result by Arrow and Debreu. Finally, abstract economy is considered as an application.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"62 ","pages":"Article 107323"},"PeriodicalIF":0.8,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144298175","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 : 2025-06-10DOI: 10.1016/j.orl.2025.107321
Guillaume Massonnet , Gautier Stauffer
In this work, it is demonstrated that the technique developed by Gayon et al. (2017) [11] for designing 2-approximation algorithms for the one-warehouse multi-retailer (OWMR) problem is highly versatile and can be applied to stochastic variants of the original OWMR problem. The mechanics of this approach are illustrated on two (static) stochastic variants of the Joint Replenishment Problem (JRP). Additionally, the simplicity and versatility of this technique suggest its potential for broader applications in the stochastic setting.
{"title":"2-approximation algorithms for two variants of the static stochastic joint replenishment problem","authors":"Guillaume Massonnet , Gautier Stauffer","doi":"10.1016/j.orl.2025.107321","DOIUrl":"10.1016/j.orl.2025.107321","url":null,"abstract":"<div><div>In this work, it is demonstrated that the technique developed by Gayon et al. (2017) <span><span>[11]</span></span> for designing 2-approximation algorithms for the one-warehouse multi-retailer (OWMR) problem is highly versatile and can be applied to stochastic variants of the original OWMR problem. The mechanics of this approach are illustrated on two (static) stochastic variants of the Joint Replenishment Problem (JRP). Additionally, the simplicity and versatility of this technique suggest its potential for broader applications in the stochastic setting.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"62 ","pages":"Article 107321"},"PeriodicalIF":0.8,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263863","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 : 2025-06-06DOI: 10.1016/j.orl.2025.107322
Shutian Liu , Quanyan Zhu
Preferences might be affected by exogenous inputs, such as information generated by advanced technologies. This paper proposes a thought experiment called risk preference design to investigate this influence within a class of principal-agent problems. Risk preference design has potential to mitigate moral hazard in insurance contracting. A quantitative approach is introduced to study the effects. We use a linear contract case study to demonstrate the role of risk preference design in strengthening financial security.
{"title":"Mitigating moral hazard in insurance contracts using risk preference design","authors":"Shutian Liu , Quanyan Zhu","doi":"10.1016/j.orl.2025.107322","DOIUrl":"10.1016/j.orl.2025.107322","url":null,"abstract":"<div><div>Preferences might be affected by exogenous inputs, such as information generated by advanced technologies. This paper proposes a thought experiment called risk preference design to investigate this influence within a class of principal-agent problems. Risk preference design has potential to mitigate moral hazard in insurance contracting. A quantitative approach is introduced to study the effects. We use a linear contract case study to demonstrate the role of risk preference design in strengthening financial security.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"62 ","pages":"Article 107322"},"PeriodicalIF":0.8,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144243076","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 : 2025-05-30DOI: 10.1016/j.orl.2025.107310
Immanuel M. Bomze , Daniel de Vicente
The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many relevant real-life applications ranging from portfolio optimization to pairwise clustering and replicator dynamics.
Sometimes, the data matrix is uncertain. We investigate models where the distribution of the data matrix is known but where both the StQP after realization of the data matrix and the here-and-now problem are indefinite.
{"title":"Uncertain standard quadratic optimization under distributional assumptions: A chance-constrained epigraphic approach","authors":"Immanuel M. Bomze , Daniel de Vicente","doi":"10.1016/j.orl.2025.107310","DOIUrl":"10.1016/j.orl.2025.107310","url":null,"abstract":"<div><div>The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many relevant real-life applications ranging from portfolio optimization to pairwise clustering and replicator dynamics.</div><div>Sometimes, the data matrix is uncertain. We investigate models where the distribution of the data matrix is known but where both the StQP after realization of the data matrix and the here-and-now problem are indefinite.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"62 ","pages":"Article 107310"},"PeriodicalIF":0.8,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144195870","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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