Pub Date : 2025-01-15DOI: 10.1016/j.orl.2025.107244
Lars Rohwedder , Ashkan Safari , Tjark Vredeveld
In this paper, we address the problem of scheduling a set of n jobs on m identical parallel machines with the objective of makespan minimization, by considering a local search neighborhood, called k-swap. In our previous study, we provided an exponential lower bound of for . In this study, we show that the smoothed number of iterations in finding a local optimum with respect to the k-swap neighborhood is , where is the perturbation parameter.
{"title":"Smoothed analysis of the k-swap neighborhood for makespan scheduling","authors":"Lars Rohwedder , Ashkan Safari , Tjark Vredeveld","doi":"10.1016/j.orl.2025.107244","DOIUrl":"10.1016/j.orl.2025.107244","url":null,"abstract":"<div><div>In this paper, we address the problem of scheduling a set of <em>n</em> jobs on <em>m</em> identical parallel machines with the objective of makespan minimization, by considering a local search neighborhood, called <em>k</em>-swap. In our previous study, we provided an exponential lower bound of <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>Ω</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup></math></span> for <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span>. In this study, we show that the smoothed number of iterations in finding a local optimum with respect to the <em>k</em>-swap neighborhood is <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>⋅</mo><mi>log</mi><mo></mo><mi>m</mi><mo>⋅</mo><mi>ϕ</mi><mo>)</mo></math></span>, where <span><math><mi>ϕ</mi><mo>≥</mo><mn>1</mn></math></span> is the perturbation parameter.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"59 ","pages":"Article 107244"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164392","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 : 2025-01-14DOI: 10.1016/j.orl.2025.107241
Zhigang Cao , Zhibin Tan , Jinchuan Zhou
Neyman (1997) proves in a classical paper that, under certain mild regularity conditions, any strategic game with a smooth strictly concave potential function has a unique correlated equilibrium. We generalize this result by relaxing the smoothness condition, allowing the potential function to include a second part that is not necessarily smoothly concave but separably concave.
{"title":"Correlated equilibrium of games with concave potential functions","authors":"Zhigang Cao , Zhibin Tan , Jinchuan Zhou","doi":"10.1016/j.orl.2025.107241","DOIUrl":"10.1016/j.orl.2025.107241","url":null,"abstract":"<div><div>Neyman (1997) proves in a classical paper that, under certain mild regularity conditions, any strategic game with a smooth strictly concave potential function has a unique correlated equilibrium. We generalize this result by relaxing the smoothness condition, allowing the potential function to include a second part that is not necessarily smoothly concave but separably concave.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"60 ","pages":"Article 107241"},"PeriodicalIF":0.8,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143172986","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 : 2025-01-14DOI: 10.1016/j.orl.2025.107243
Martina Kuchlbauer
We consider mixed-integer nonlinear robust optimization problems with nonconvexities. In detail, the functions can be nonsmooth and generalized convex, i.e., -quasiconvex or -pseudoconvex. We propose a robust optimization method that requires no certain structure of the adversarial problem, but only approximate worst-case evaluations. The method integrates a bundle method, for continuous subproblems, into an outer approximation approach. We prove that our algorithm converges and finds an approximately robust optimal solution and propose robust gas transport as a suitable application.
{"title":"Outer approximation for generalized convex mixed-integer nonlinear robust optimization problems","authors":"Martina Kuchlbauer","doi":"10.1016/j.orl.2025.107243","DOIUrl":"10.1016/j.orl.2025.107243","url":null,"abstract":"<div><div>We consider mixed-integer nonlinear robust optimization problems with nonconvexities. In detail, the functions can be nonsmooth and generalized convex, i.e., <span><math><msup><mrow><mi>f</mi></mrow><mrow><mo>∘</mo></mrow></msup></math></span>-quasiconvex or <span><math><msup><mrow><mi>f</mi></mrow><mrow><mo>∘</mo></mrow></msup></math></span>-pseudoconvex. We propose a robust optimization method that requires no certain structure of the adversarial problem, but only approximate worst-case evaluations. The method integrates a bundle method, for continuous subproblems, into an outer approximation approach. We prove that our algorithm converges and finds an approximately robust optimal solution and propose robust gas transport as a suitable application.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"60 ","pages":"Article 107243"},"PeriodicalIF":0.8,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143172985","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 : 2025-01-09DOI: 10.1016/j.orl.2025.107240
John R. Birge, Levi DeValve
We consider the problem of placing inventory on a network in advance of uncertain demand, in order to minimize the sum of inventory placement costs and expected fulfillment and shortage costs. Complexity results (in terms of inapproximability lower bounds) are derived under different assumptions. Then we develop two approximation guarantees: one is asymptotically optimal as demand grows large, and the other provides a constant guarantee with metric fulfillment costs.
{"title":"Inventory placement on a network","authors":"John R. Birge, Levi DeValve","doi":"10.1016/j.orl.2025.107240","DOIUrl":"10.1016/j.orl.2025.107240","url":null,"abstract":"<div><div>We consider the problem of placing inventory on a network in advance of uncertain demand, in order to minimize the sum of inventory placement costs and expected fulfillment and shortage costs. Complexity results (in terms of inapproximability lower bounds) are derived under different assumptions. Then we develop two approximation guarantees: one is asymptotically optimal as demand grows large, and the other provides a constant guarantee with metric fulfillment costs.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"60 ","pages":"Article 107240"},"PeriodicalIF":0.8,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143172984","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 : 2025-01-02DOI: 10.1016/j.orl.2024.107238
Woonghee Tim Huh , Siyue Liu
We consider assortment optimization with product-specific capacities under the multinomial logit (MNL) choice model, wherein each product has a finite capacity, i.e., a limited number of units for sale. The number of customers served by each product is the smaller of its demand and capacity. We assume the demand of each product is deterministic as a function of the assortment offered. We show that this assortment optimization problem is NP-hard. We devise a 1/2-approximation algorithm and a fully polynomial-time approximation scheme (FPTAS) by exploiting its connection to a series of knapsack problems.
{"title":"Assortment optimization under the multinomial logit choice model with product-specific capacities","authors":"Woonghee Tim Huh , Siyue Liu","doi":"10.1016/j.orl.2024.107238","DOIUrl":"10.1016/j.orl.2024.107238","url":null,"abstract":"<div><div>We consider assortment optimization with product-specific capacities under the multinomial logit (MNL) choice model, wherein each product has a finite capacity, i.e., a limited number of units for sale. The number of customers served by each product is the smaller of its demand and capacity. We assume the demand of each product is deterministic as a function of the assortment offered. We show that this assortment optimization problem is NP-hard. We devise a 1/2-approximation algorithm and a fully polynomial-time approximation scheme (FPTAS) by exploiting its connection to a series of knapsack problems.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"59 ","pages":"Article 107238"},"PeriodicalIF":0.8,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164395","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 : 2025-01-01DOI: 10.1016/j.orl.2024.107207
Abdellah Bulaich Mehamdi , Mathieu Lacroix , Sébastien Martin
Column generation is used alongside Dantzig-Wolfe Decomposition, especially for linear programs having a decomposable pricing step requiring to solve numerous independent pricing subproblems. We propose a filtering method to detect which pricing subproblems may have improving columns, and only those subproblems are solved during pricing. This filtering is done by providing light, computable bounds using dual information from previous iterations of the column generation. The experiments show a significant impact on different combinatorial optimization problems.
{"title":"Pricing filtering in Dantzig-Wolfe decomposition","authors":"Abdellah Bulaich Mehamdi , Mathieu Lacroix , Sébastien Martin","doi":"10.1016/j.orl.2024.107207","DOIUrl":"10.1016/j.orl.2024.107207","url":null,"abstract":"<div><div>Column generation is used alongside Dantzig-Wolfe Decomposition, especially for linear programs having a decomposable pricing step requiring to solve numerous independent pricing subproblems. We propose a filtering method to detect which pricing subproblems may have improving columns, and only those subproblems are solved during pricing. This filtering is done by providing light, computable bounds using dual information from previous iterations of the column generation. The experiments show a significant impact on different combinatorial optimization problems.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"58 ","pages":"Article 107207"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166897","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 : 2025-01-01DOI: 10.1016/j.orl.2024.107209
Artur Pessoa, Daniel de Araujo, Eduardo Uchoa
Mixed integer programming formulations for the Split Delivery Vehicle Routing Problem (SDVRP) typically use edge decision variables. It was believed that feasibility couldn't be verified in polynomial time. We show that this recognition problem depends on the formulation's constraints and prove that it's strongly NP-hard for a recent formulation. With subtour elimination constraints, we provide an -time recognition algorithm. This challenges assumptions about edge-based formulations and provides new insights into SDVRP solution verification complexity.
{"title":"On the feasibility of solutions to the split delivery vehicle routing problem represented as edge variables","authors":"Artur Pessoa, Daniel de Araujo, Eduardo Uchoa","doi":"10.1016/j.orl.2024.107209","DOIUrl":"10.1016/j.orl.2024.107209","url":null,"abstract":"<div><div>Mixed integer programming formulations for the Split Delivery Vehicle Routing Problem (SDVRP) typically use edge decision variables. It was believed that feasibility couldn't be verified in polynomial time. We show that this recognition problem depends on the formulation's constraints and prove that it's strongly NP-hard for a recent formulation. With subtour elimination constraints, we provide an <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span>-time recognition algorithm. This challenges assumptions about edge-based formulations and provides new insights into SDVRP solution verification complexity.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"58 ","pages":"Article 107209"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166898","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 : 2024-12-30DOI: 10.1016/j.orl.2024.107239
Konstantin Pavlikov
Fractional and Rounded capacity inequalities are two important families of valid inequalities known for the homogeneous Capacitated Vehicle Routing Problem (CVRP). Such inequalities impose the minimum number of vehicles required to service each and every subset of customers, be it a fractional or an integer value. In case of the Heterogeneous version of the routing problem (HCVRP), the minimum number of vehicles required for a subset of customers is not defined uniquely: it depends on the vehicle types and fleet composition that was engaged in serving the customers. This paper revises existing literature on the capacity-based valid inequalities for the HCVRP and presents new routines to separate them exactly using mixed integer linear programming (MILP). In addition, this paper proposes a new family of capacity-based valid inequalities for the HCVRP together with an exact routine to separate them. A computational study demonstrates applicability of considered inequalities in solving HCVRP instances using a standard MILP solver.
{"title":"On the capacity inequalities for the heterogeneous vehicle routing problem","authors":"Konstantin Pavlikov","doi":"10.1016/j.orl.2024.107239","DOIUrl":"10.1016/j.orl.2024.107239","url":null,"abstract":"<div><div>Fractional and Rounded capacity inequalities are two important families of valid inequalities known for the homogeneous Capacitated Vehicle Routing Problem (CVRP). Such inequalities impose the minimum number of vehicles required to service each and every subset of customers, be it a fractional or an integer value. In case of the Heterogeneous version of the routing problem (HCVRP), the minimum number of vehicles required for a subset of customers is not defined uniquely: it depends on the vehicle types and fleet composition that was engaged in serving the customers. This paper revises existing literature on the capacity-based valid inequalities for the HCVRP and presents new routines to separate them exactly using mixed integer linear programming (MILP). In addition, this paper proposes a new family of capacity-based valid inequalities for the HCVRP together with an exact routine to separate them. A computational study demonstrates applicability of considered inequalities in solving HCVRP instances using a standard MILP solver.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"59 ","pages":"Article 107239"},"PeriodicalIF":0.8,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164396","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 : 2024-12-27DOI: 10.1016/j.orl.2024.107234
Alexander Shapiro , Yan Li
The main goal of this paper is to discuss construction of distributionally robust counterparts of stochastic optimal control problems. Randomized and non-randomized policies are considered. In particular necessary and sufficient conditions for existence of non-randomized policies are given.
{"title":"Distributionally robust stochastic optimal control","authors":"Alexander Shapiro , Yan Li","doi":"10.1016/j.orl.2024.107234","DOIUrl":"10.1016/j.orl.2024.107234","url":null,"abstract":"<div><div>The main goal of this paper is to discuss construction of distributionally robust counterparts of stochastic optimal control problems. Randomized and non-randomized policies are considered. In particular necessary and sufficient conditions for existence of non-randomized policies are given.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"60 ","pages":"Article 107234"},"PeriodicalIF":0.8,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143172983","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 : 2024-12-20DOI: 10.1016/j.orl.2024.107237
Biplab Hawlader , Pradip Kundu , Amarjit Kundu
This research focuses on determining the optimal allocation of redundancies within a system, strategically placing them to enhance system performance. The paper explores redundancy allocation strategies through stochastic comparisons of resulting system lifetimes in various stochastic orders. While previous studies mainly focused on two or n-component series systems with some specific distributions for component lifetimes, this study extends the investigation with arbitrary distributions or some semiparametric families. It presents some new and extended results, offering novel insights to the topic.
{"title":"Optimal allocation of active and standby redundancies in series systems","authors":"Biplab Hawlader , Pradip Kundu , Amarjit Kundu","doi":"10.1016/j.orl.2024.107237","DOIUrl":"10.1016/j.orl.2024.107237","url":null,"abstract":"<div><div>This research focuses on determining the optimal allocation of redundancies within a system, strategically placing them to enhance system performance. The paper explores redundancy allocation strategies through stochastic comparisons of resulting system lifetimes in various stochastic orders. While previous studies mainly focused on two or <em>n</em>-component series systems with some specific distributions for component lifetimes, this study extends the investigation with arbitrary distributions or some semiparametric families. It presents some new and extended results, offering novel insights to the topic.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"60 ","pages":"Article 107237"},"PeriodicalIF":0.8,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143172982","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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