Pub Date : 2025-08-06DOI: 10.1016/j.orl.2025.107353
Zhichao Geng, Yuan Gao
This paper addresses the robust single-machine makespan scheduling problems, in which the processing times of jobs and a set of discrete scenarios are given, and the release dates of jobs are scenario-dependent. For three common criteria (absolute robustness, maximum regret and relative maximum regret) relevant to robust optimization approaches, we show that the corresponding problems are all polynomially solvable.
{"title":"Single-machine makespan scheduling with scenario-dependent release dates","authors":"Zhichao Geng, Yuan Gao","doi":"10.1016/j.orl.2025.107353","DOIUrl":"10.1016/j.orl.2025.107353","url":null,"abstract":"<div><div>This paper addresses the robust single-machine makespan scheduling problems, in which the processing times of jobs and a set of discrete scenarios are given, and the release dates of jobs are scenario-dependent. For three common criteria (absolute robustness, maximum regret and relative maximum regret) relevant to robust optimization approaches, we show that the corresponding problems are all polynomially solvable.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"63 ","pages":"Article 107353"},"PeriodicalIF":0.9,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829644","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 : 2025-07-30DOI: 10.1016/j.orl.2025.107349
Jiayi Guo , Hao Qiu , Zhen Wang , Zizhuo Wang , Xinxin Zhang
We study the moment problem with nonnegative Chebyshev ambiguity set (MPNC), which is foundational to distributionally robust optimization (DRO) and has applications in inventory, pricing, and portfolio selection problems. While univariate MPNC is well-studied, bivariate/multivariate MPNC lacks analytical solutions. We characterize bivariate MPNC's optimal support for piecewise-linear objectives, propose an exact numerical method, and derive closed-form solutions for two instances. We apply our result to a DRO newsvendor problem and derive interesting managerial insights.
{"title":"Exact solving approach to moment problems with nonnegative Chebyshev ambiguity sets","authors":"Jiayi Guo , Hao Qiu , Zhen Wang , Zizhuo Wang , Xinxin Zhang","doi":"10.1016/j.orl.2025.107349","DOIUrl":"10.1016/j.orl.2025.107349","url":null,"abstract":"<div><div>We study the moment problem with nonnegative Chebyshev ambiguity set (MPNC), which is foundational to distributionally robust optimization (DRO) and has applications in inventory, pricing, and portfolio selection problems. While univariate MPNC is well-studied, bivariate/multivariate MPNC lacks analytical solutions. We characterize bivariate MPNC's optimal support for piecewise-linear objectives, propose an exact numerical method, and derive closed-form solutions for two instances. We apply our result to a DRO newsvendor problem and derive interesting managerial insights.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"63 ","pages":"Article 107349"},"PeriodicalIF":0.9,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749731","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 : 2025-07-30DOI: 10.1016/j.orl.2025.107351
Maria Kyropoulou, Alexandros A. Voudouris
We consider a resource allocation problem with agents that have additive ternary valuations for a set of indivisible items, and bound the price of envy-free up to one item (EF1) allocations. For a large number n of agents, we show a lower bound of , implying that the price of EF1 is no better than when the agents have general subadditive valuations. We then focus on instances with few agents and show that the price of EF1 is 12/11 for , and between 1.2 and 1.256 for .
{"title":"The price of EF1 for few agents with additive ternary valuations","authors":"Maria Kyropoulou, Alexandros A. Voudouris","doi":"10.1016/j.orl.2025.107351","DOIUrl":"10.1016/j.orl.2025.107351","url":null,"abstract":"<div><div>We consider a resource allocation problem with agents that have additive ternary valuations for a set of indivisible items, and bound the price of envy-free up to one item (EF1) allocations. For a large number <em>n</em> of agents, we show a lower bound of <span><math><mi>Ω</mi><mo>(</mo><msqrt><mrow><mi>n</mi></mrow></msqrt><mo>)</mo></math></span>, implying that the price of EF1 is no better than when the agents have general subadditive valuations. We then focus on instances with few agents and show that the price of EF1 is 12/11 for <span><math><mi>n</mi><mo>=</mo><mn>2</mn></math></span>, and between 1.2 and 1.256 for <span><math><mi>n</mi><mo>=</mo><mn>3</mn></math></span>.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"63 ","pages":"Article 107351"},"PeriodicalIF":0.9,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144725040","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 : 2025-07-29DOI: 10.1016/j.orl.2025.107350
Ilan Adler , Richard M. Karp , Sheldon M. Ross
Let be events in a sample space. Given the probability of the intersection of each collection of up to of these events, what can we say about the probability that at least r of the events occur? This question dates back to Boole in the 19th century, and it is well known that the odd partial sums of the Inclusion-Exclusion formula provide upper bounds, while the even partial sums provide lower bounds. We give a combinatorial characterization of the error in these bounds and use it to derive a very simple proof of the strongest possible bounds of a certain form, as well as a couple of improved bounds. The new bounds use more information than the classical Bonferroni-type inequalities, and are often sharper.
{"title":"Improved bounds on the probability of a union and on the number of events that occur","authors":"Ilan Adler , Richard M. Karp , Sheldon M. Ross","doi":"10.1016/j.orl.2025.107350","DOIUrl":"10.1016/j.orl.2025.107350","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> be events in a sample space. Given the probability of the intersection of each collection of up to <span><math><mi>k</mi><mo>+</mo><mn>1</mn></math></span> of these events, what can we say about the probability that at least <em>r</em> of the events occur? This question dates back to Boole in the 19th century, and it is well known that the odd partial sums of the Inclusion-Exclusion formula provide upper bounds, while the even partial sums provide lower bounds. We give a combinatorial characterization of the error in these bounds and use it to derive a very simple proof of the strongest possible bounds of a certain form, as well as a couple of improved bounds. The new bounds use more information than the classical Bonferroni-type inequalities, and are often sharper.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"63 ","pages":"Article 107350"},"PeriodicalIF":0.9,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749730","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 : 2025-07-29DOI: 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}
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