Pub Date : 2024-10-15DOI: 10.1016/j.orl.2024.107199
Oliver Hinder
We analyze restarted PDHG on totally unimodular linear programs. In particular, we show that restarted PDHG finds an ϵ-optimal solution in matrix-vector multiplies where is the number of constraints, the number of variables, is the number of nonzeros in the constraint matrix, H is the largest absolute coefficient in the right hand side or objective vector, and ϵ is the distance to optimality of the outputted solution.
{"title":"Worst-case analysis of restarted primal-dual hybrid gradient on totally unimodular linear programs","authors":"Oliver Hinder","doi":"10.1016/j.orl.2024.107199","DOIUrl":"10.1016/j.orl.2024.107199","url":null,"abstract":"<div><div>We analyze restarted PDHG on totally unimodular linear programs. In particular, we show that restarted PDHG finds an <em>ϵ</em>-optimal solution in <span><math><mi>O</mi><mo>(</mo><mi>H</mi><msubsup><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2.5</mn></mrow></msubsup><msqrt><mrow><mtext>nnz</mtext><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msqrt><mi>log</mi><mo></mo><mo>(</mo><mi>H</mi><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>/</mo><mi>ϵ</mi><mo>)</mo><mo>)</mo></math></span> matrix-vector multiplies where <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is the number of constraints, <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> the number of variables, <span><math><mtext>nnz</mtext><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is the number of nonzeros in the constraint matrix, <em>H</em> is the largest absolute coefficient in the right hand side or objective vector, and <em>ϵ</em> is the distance to optimality of the outputted solution.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107199"},"PeriodicalIF":0.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441128","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}
We consider the lost-sales inventory systems with stochastic lead times and establish the asymptotic optimality of base-stock policies for such systems. Specifically, we prove that as the per-unit lost-sales penalty cost becomes large compared to the per-unit holding cost, the ratio of the optimal base-stock policy's cost to the optimal cost converges to one. Our paper provides a theoretical guarantee of the widely adopted base-stock policies in lost-sales inventory systems with stochastic lead times for the first time.
{"title":"Asymptotic optimality of base-stock policies for lost-sales inventory systems with stochastic lead times","authors":"Shilin Yuan , Jiameng Lyu , Jinxing Xie , Yuan Zhou","doi":"10.1016/j.orl.2024.107196","DOIUrl":"10.1016/j.orl.2024.107196","url":null,"abstract":"<div><div>We consider the lost-sales inventory systems with stochastic lead times and establish the asymptotic optimality of base-stock policies for such systems. Specifically, we prove that as the per-unit lost-sales penalty cost becomes large compared to the per-unit holding cost, the ratio of the optimal base-stock policy's cost to the optimal cost converges to one. Our paper provides a theoretical guarantee of the widely adopted base-stock policies in lost-sales inventory systems with stochastic lead times for the first time.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107196"},"PeriodicalIF":0.8,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142437979","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 : 2024-10-10DOI: 10.1016/j.orl.2024.107198
David Lowing
To clean a polluted river, some agents must undertake operations that incur costs. The problem is to determine a fair method to share these expenses among agents. We consider the established methods of Local Responsibility Sharing and Upstream Equal Sharing, based on the responsibility principles of Absolute Territorial Sovereignty and Unlimited Territorial Integrity, respectively. We combine these with Total Solidarity, a method based on a solidarity principle. This yields new cost-sharing methods, which we characterize axiomatically.
{"title":"Responsibility and solidarity principles in sharing the costs of cleaning a polluted river","authors":"David Lowing","doi":"10.1016/j.orl.2024.107198","DOIUrl":"10.1016/j.orl.2024.107198","url":null,"abstract":"<div><div>To clean a polluted river, some agents must undertake operations that incur costs. The problem is to determine a fair method to share these expenses among agents. We consider the established methods of Local Responsibility Sharing and Upstream Equal Sharing, based on the responsibility principles of Absolute Territorial Sovereignty and Unlimited Territorial Integrity, respectively. We combine these with Total Solidarity, a method based on a solidarity principle. This yields new cost-sharing methods, which we characterize axiomatically.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107198"},"PeriodicalIF":0.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433519","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 : 2024-09-30DOI: 10.1016/j.orl.2024.107189
Jaehyuk Choi , Jeonggyu Huh , Nan Su
Using the option delta systematically, we derive tighter lower and upper bounds of the Black–Scholes implied volatility than those in Tehranchi (2016) [11]. As an application, we propose a Newton–Raphson algorithm on the log price that converges rapidly for all price ranges when using a new lower bound as an initial guess. Our new algorithm is a better alternative to the widely used naive Newton–Raphson algorithm, whose convergence is slow for extreme option prices.
{"title":"Tighter ‘uniform bounds for Black–Scholes implied volatility’ and the applications to root-finding","authors":"Jaehyuk Choi , Jeonggyu Huh , Nan Su","doi":"10.1016/j.orl.2024.107189","DOIUrl":"10.1016/j.orl.2024.107189","url":null,"abstract":"<div><div>Using the option delta systematically, we derive tighter lower and upper bounds of the Black–Scholes implied volatility than those in Tehranchi (2016) <span><span>[11]</span></span>. As an application, we propose a Newton–Raphson algorithm on the log price that converges rapidly for all price ranges when using a new lower bound as an initial guess. Our new algorithm is a better alternative to the widely used naive Newton–Raphson algorithm, whose convergence is slow for extreme option prices.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107189"},"PeriodicalIF":0.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419780","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 : 2024-09-30DOI: 10.1016/j.orl.2024.107185
N. Yekezare , M. Zohrehbandian , M. Maghasedi , F. Bonomo-Braberman
DSatur is a widely-used heuristic algorithm for graph coloring, proposed by Daniel Brélaz in 1979. It is based on the greedy coloring approach, but selecting the next vertex to be colored from those that maximize the number of colors already used by their neighbors. Though not always optimal, this algorithm is known to be optimal on certain families, like cycles or bipartite graphs. In this paper, we prove the optimality of DSatur on chordal graphs, a superclass of interval graphs.
DSatur 是一种广泛使用的图着色启发式算法，由 Daniel Brélaz 于 1979 年提出。它基于贪婪着色法，但要从那些能最大化其邻居已用颜色数的顶点中选择下一个着色顶点。虽然这种算法并不总是最优的，但已知它在某些族上是最优的，比如循环图或双叉图。在本文中，我们将证明 DSatur 在和弦图（一种超类的区间图）上的最优性。
{"title":"Optimality of DSatur algorithm on chordal graphs","authors":"N. Yekezare , M. Zohrehbandian , M. Maghasedi , F. Bonomo-Braberman","doi":"10.1016/j.orl.2024.107185","DOIUrl":"10.1016/j.orl.2024.107185","url":null,"abstract":"<div><div>DSatur is a widely-used heuristic algorithm for graph coloring, proposed by Daniel Brélaz in 1979. It is based on the greedy coloring approach, but selecting the next vertex to be colored from those that maximize the number of colors already used by their neighbors. Though not always optimal, this algorithm is known to be optimal on certain families, like cycles or bipartite graphs. In this paper, we prove the optimality of DSatur on chordal graphs, a superclass of interval graphs.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107185"},"PeriodicalIF":0.8,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419647","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 : 2024-09-27DOI: 10.1016/j.orl.2024.107192
Billel Zaoui, Djamel Benterki, Samia Khelladi
We generalize Zhang and Xu's (2011) [22] interior point algorithm for linear optimization to semidefinite optimization problems in order to define a new search direction. The symmetrization of the search direction is based on the full Nesterov-Todd scaling scheme. Moreover, we show that the obtained algorithm solves the studied problem in polynomial time and that the short-step algorithm has the best-known iteration bound, namely -iterations. Finally, we report a comparative numerical study to show the efficiency of our proposed algorithm.
{"title":"Complexity analysis and numerical implementation of a new interior-point algorithm for semidefinite optimization","authors":"Billel Zaoui, Djamel Benterki, Samia Khelladi","doi":"10.1016/j.orl.2024.107192","DOIUrl":"10.1016/j.orl.2024.107192","url":null,"abstract":"<div><div>We generalize Zhang and Xu's (2011) <span><span>[22]</span></span> interior point algorithm for linear optimization to semidefinite optimization problems in order to define a new search direction. The symmetrization of the search direction is based on the full Nesterov-Todd scaling scheme. Moreover, we show that the obtained algorithm solves the studied problem in polynomial time and that the short-step algorithm has the best-known iteration bound, namely <span><math><mi>O</mi><mo>(</mo><msqrt><mrow><mi>n</mi></mrow></msqrt><mi>log</mi><mo></mo><mfrac><mrow><mi>n</mi></mrow><mrow><mi>ε</mi></mrow></mfrac><mo>)</mo></math></span>-iterations. Finally, we report a comparative numerical study to show the efficiency of our proposed algorithm.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107192"},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419648","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 : 2024-09-27DOI: 10.1016/j.orl.2024.107187
Xin Wen , Xianping Guo , Li Xia
This paper deals with a risk probability minimization problem for finite horizon partially observable semi-Markov decision processes, which are the fairly most general models for stochastic dynamic systems. In contrast to the expected discounted and average criteria, the optimality investigated in this paper is to minimize the probability that the accumulated rewards do not reach a prescribed profit level at the finite terminal stage. First, the state space is augmented as the joint conditional distribution of the current unobserved state and the remaining profit goal. We introduce a class of policies depending on observable histories and a class of Markov policies including observable process with the joint conditional distribution. Then under mild assumptions, we prove that the value function is the unique solution to the optimality equation for the probability criterion by using iteration techniques. The existence of (ϵ-)optimal Markov policy for this problem is established. Finally, we use a bandit problem with the probability criterion to demonstrate our main results in which an effective algorithm and the corresponding numerical calculation are given for the semi-Markov model. Moreover, for the case of reduction to the discrete-time Markov model, we derive a concise solution.
{"title":"Finite horizon partially observable semi-Markov decision processes under risk probability criteria","authors":"Xin Wen , Xianping Guo , Li Xia","doi":"10.1016/j.orl.2024.107187","DOIUrl":"10.1016/j.orl.2024.107187","url":null,"abstract":"<div><div>This paper deals with a risk probability minimization problem for finite horizon partially observable semi-Markov decision processes, which are the fairly most general models for stochastic dynamic systems. In contrast to the expected discounted and average criteria, the optimality investigated in this paper is to minimize the probability that the accumulated rewards do not reach a prescribed profit level at the finite terminal stage. First, the state space is augmented as the joint conditional distribution of the current unobserved state and the remaining profit goal. We introduce a class of policies depending on observable histories and a class of Markov policies including observable process with the joint conditional distribution. Then under mild assumptions, we prove that the value function is the unique solution to the optimality equation for the probability criterion by using iteration techniques. The existence of (<em>ϵ</em>-)optimal Markov policy for this problem is established. Finally, we use a bandit problem with the probability criterion to demonstrate our main results in which an effective algorithm and the corresponding numerical calculation are given for the semi-Markov model. Moreover, for the case of reduction to the discrete-time Markov model, we derive a concise solution.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107187"},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142359041","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 : 2024-09-27DOI: 10.1016/j.orl.2024.107188
Bar Light
This note studies monotone Markov chains, a subclass of Markov chains with extensive applications in operations research and economics. While the properties that ensure the global stability of these chains are well studied, their establishment often relies on the fulfillment of a certain splitting condition. We address the challenges of verifying the splitting condition by introducing simple, applicable conditions that ensure global stability. The simplicity of these conditions is demonstrated through various examples including autoregressive processes, portfolio allocation problems and resource allocation dynamics.
{"title":"A note on the stability of monotone Markov chains","authors":"Bar Light","doi":"10.1016/j.orl.2024.107188","DOIUrl":"10.1016/j.orl.2024.107188","url":null,"abstract":"<div><div>This note studies monotone Markov chains, a subclass of Markov chains with extensive applications in operations research and economics. While the properties that ensure the global stability of these chains are well studied, their establishment often relies on the fulfillment of a certain splitting condition. We address the challenges of verifying the splitting condition by introducing simple, applicable conditions that ensure global stability. The simplicity of these conditions is demonstrated through various examples including autoregressive processes, portfolio allocation problems and resource allocation dynamics.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107188"},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142359040","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 : 2024-09-27DOI: 10.1016/j.orl.2024.107195
Y. Elboulqe , M. El Maghri
A three-term Polak–Ribière–Polyak conjugate gradient-like method for bicriteria optimization without scalarization is proposed in this paper. Three advantages are to be noted. First, the descent directions are given explicitly and can then be directly computed. Second, the descent property turns out to be sufficient and independent of the line search. Third, without Lipschitzian hypotheses, global convergence towards Pareto stationary points is proved under an Armijo type condition. Numerical experiments including comparisons with other methods are also reported.
{"title":"An explicit three-term Polak–Ribière–Polyak conjugate gradient method for bicriteria optimization","authors":"Y. Elboulqe , M. El Maghri","doi":"10.1016/j.orl.2024.107195","DOIUrl":"10.1016/j.orl.2024.107195","url":null,"abstract":"<div><div>A three-term Polak–Ribière–Polyak conjugate gradient-like method for bicriteria optimization without scalarization is proposed in this paper. Three advantages are to be noted. First, the descent directions are given explicitly and can then be directly computed. Second, the descent property turns out to be sufficient and independent of the line search. Third, without Lipschitzian hypotheses, global convergence towards Pareto stationary points is proved under an Armijo type condition. Numerical experiments including comparisons with other methods are also reported.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107195"},"PeriodicalIF":0.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419779","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 : 2024-09-26DOI: 10.1016/j.orl.2024.107193
Merve Doganbas, Hayong Shin
This paper introduces the Traveling Salesman Problem (TSP) with Backend Information Processing (bTSP), which integrates backend processing times into path planning to minimize the makespan. The study develops a mixed integer linear programming formulation and conducts a theoretical analysis to understand the relationship between the TSP and the bTSP. The results show that an optimal solution for the bTSP can be efficiently derived by leveraging the connection to the standard TSP.
{"title":"Traveling salesman problem with backend information processing","authors":"Merve Doganbas, Hayong Shin","doi":"10.1016/j.orl.2024.107193","DOIUrl":"10.1016/j.orl.2024.107193","url":null,"abstract":"<div><div>This paper introduces the Traveling Salesman Problem (TSP) with Backend Information Processing (bTSP), which integrates backend processing times into path planning to minimize the makespan. The study develops a mixed integer linear programming formulation and conducts a theoretical analysis to understand the relationship between the TSP and the bTSP. The results show that an optimal solution for the bTSP can be efficiently derived by leveraging the connection to the standard TSP.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"57 ","pages":"Article 107193"},"PeriodicalIF":0.8,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142359035","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