P. Liguori, A. Mahjoub, G. Marquès, R. Sadykov, Eduardo Uchoa
“Nonrobust Strong Knapsack Cuts for Capacitated Location Routing and Related Problems,” by Liguori et al., presents a novel BCP algorithm for the CLRP and for other problems that share a nested knapsack structure. It outperforms existing exact algorithms in the literature, making it a powerful tool for solving instances with a large number of depot locations. A key methodological contribution is the introduction of RLKCs, a family of nonrobust cuts derived from the “outer” knapsack constraints. These cuts are strong in the sense that they contain all facets of the master knapsack polytope, dominating the cover cuts by Dabia et al. (2019) . By exploring their monotonicity and superadditivity properties, it is possible to adapt the labeling algorithm for handling RLKCs efficiently. The overall positive impact of RLKCs on the BCP performance varies depending on the problem and instance characteristics, but they have proven particularly effective for CLRP instances with tight depot capacities, making the final BCP algorithm more reliable.
{"title":"Nonrobust Strong Knapsack Cuts for Capacitated Location Routing and Related Problems","authors":"P. Liguori, A. Mahjoub, G. Marquès, R. Sadykov, Eduardo Uchoa","doi":"10.1287/opre.2023.2458","DOIUrl":"https://doi.org/10.1287/opre.2023.2458","url":null,"abstract":"“Nonrobust Strong Knapsack Cuts for Capacitated Location Routing and Related Problems,” by Liguori et al., presents a novel BCP algorithm for the CLRP and for other problems that share a nested knapsack structure. It outperforms existing exact algorithms in the literature, making it a powerful tool for solving instances with a large number of depot locations. A key methodological contribution is the introduction of RLKCs, a family of nonrobust cuts derived from the “outer” knapsack constraints. These cuts are strong in the sense that they contain all facets of the master knapsack polytope, dominating the cover cuts by Dabia et al. (2019) . By exploring their monotonicity and superadditivity properties, it is possible to adapt the labeling algorithm for handling RLKCs efficiently. The overall positive impact of RLKCs on the BCP performance varies depending on the problem and instance characteristics, but they have proven particularly effective for CLRP instances with tight depot capacities, making the final BCP algorithm more reliable.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"19 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79330406","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}
Dangers of Ignoring Market Friction When Leveraging Financial Portfolios Portfolio leveraging is a standard industry practice to target higher fund returns, for example, in risk parity asset allocation. However, the existing models of optimal bet sizing fail to integrate analytically the impact on leveraged portfolio selection resulting from market liquidity issues. The paper “Optimal Leveraged Portfolio Selection Under Quasi-Elastic Market Impact” considers a market in which both temporary and permanent impact on trading prices are present with the former impact being sufficiently large relative to the latter. Our analytical conclusions, supported by a case study that uses even relatively more liquid U.S. exchange-traded fund assets, demonstrate that fund managers are ill advised to ignore market friction when leveraging to achieve target higher returns. Not only risk-adjusted returns significantly deteriorate, but also those losses become steeper when setting higher targets requiring increased levels of leverage. Moreover, leverage-constrained and less risk-averse investors ignoring liquidity costs ex ante face the most losses in expected utility ex post.
{"title":"Optimal Leveraged Portfolio Selection Under Quasi-Elastic Market Impact","authors":"Chanaka Edirisinghe, Jingnan Chen, Jaehwan Jeong","doi":"10.1287/opre.2023.2462","DOIUrl":"https://doi.org/10.1287/opre.2023.2462","url":null,"abstract":"Dangers of Ignoring Market Friction When Leveraging Financial Portfolios Portfolio leveraging is a standard industry practice to target higher fund returns, for example, in risk parity asset allocation. However, the existing models of optimal bet sizing fail to integrate analytically the impact on leveraged portfolio selection resulting from market liquidity issues. The paper “Optimal Leveraged Portfolio Selection Under Quasi-Elastic Market Impact” considers a market in which both temporary and permanent impact on trading prices are present with the former impact being sufficiently large relative to the latter. Our analytical conclusions, supported by a case study that uses even relatively more liquid U.S. exchange-traded fund assets, demonstrate that fund managers are ill advised to ignore market friction when leveraging to achieve target higher returns. Not only risk-adjusted returns significantly deteriorate, but also those losses become steeper when setting higher targets requiring increased levels of leverage. Moreover, leverage-constrained and less risk-averse investors ignoring liquidity costs ex ante face the most losses in expected utility ex post.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"107 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83427212","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}
When applying decision models, we often estimate input parameters using data. In healthcare and some other applications, data are collected from a population of different entities, such as patients. Thus, one faces a modeling question of whether to estimate different models for subpopulations (called stratifying). The potential benefit of stratifying comes from the heterogeneity of subpopulations. For example, patients who progress faster than others require a separate model and a tailored treatment plan. In “Is Separately Modeling Subpopulations Beneficial for Sequential Decision-Making?,” Lee provides theoretical results and empirical methods for deciding whether to stratify subpopulations. The article also presents how to use its results to select the best stratification among many. Improving medical decisions by tailoring to each subpopulation is a building block of precision medicine, and thus, this work aligns closely with the precision medicine paradigm.
{"title":"Is Separately Modeling Subpopulations Beneficial for Sequential Decision-Making?","authors":"Ilbin Lee","doi":"10.1287/opre.2023.2474","DOIUrl":"https://doi.org/10.1287/opre.2023.2474","url":null,"abstract":"When applying decision models, we often estimate input parameters using data. In healthcare and some other applications, data are collected from a population of different entities, such as patients. Thus, one faces a modeling question of whether to estimate different models for subpopulations (called stratifying). The potential benefit of stratifying comes from the heterogeneity of subpopulations. For example, patients who progress faster than others require a separate model and a tailored treatment plan. In “Is Separately Modeling Subpopulations Beneficial for Sequential Decision-Making?,” Lee provides theoretical results and empirical methods for deciding whether to stratify subpopulations. The article also presents how to use its results to select the best stratification among many. Improving medical decisions by tailoring to each subpopulation is a building block of precision medicine, and thus, this work aligns closely with the precision medicine paradigm.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"41 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73886960","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}
Utility Preference Robust Optimization with Moment-Type Information Structure In some decision-making problems, information on the true utility function of the decision maker may be incomplete, which may bring potential modeling risk. In “Utility Preference Robust Optimization with Moment-Type Information Structure,” Guo, Xu, and Zhang propose a maximin utility preference robust optimization model where information about the DM’s preference is constructed by moment-type conditions. The authors propose a piecewise linear approximation approach to tackle the maximin problem, reformulate the approximate problem as a single mixed integer linear program, and derive error bounds for the approximate ambiguity set, the optimal value, and the optimal solutions. To examine the performance of the model and the computational schemes, they carry out extensive numerical tests and demonstrate the effectiveness of the model and efficiency of the computational methods.
{"title":"Utility Preference Robust Optimization with Moment-Type Information Structure","authors":"Shaoyan Guo, Huifu Xu, Sainan Zhang","doi":"10.1287/opre.2023.2464","DOIUrl":"https://doi.org/10.1287/opre.2023.2464","url":null,"abstract":"Utility Preference Robust Optimization with Moment-Type Information Structure In some decision-making problems, information on the true utility function of the decision maker may be incomplete, which may bring potential modeling risk. In “Utility Preference Robust Optimization with Moment-Type Information Structure,” Guo, Xu, and Zhang propose a maximin utility preference robust optimization model where information about the DM’s preference is constructed by moment-type conditions. The authors propose a piecewise linear approximation approach to tackle the maximin problem, reformulate the approximate problem as a single mixed integer linear program, and derive error bounds for the approximate ambiguity set, the optimal value, and the optimal solutions. To examine the performance of the model and the computational schemes, they carry out extensive numerical tests and demonstrate the effectiveness of the model and efficiency of the computational methods.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"66 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82336721","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}
In large-scale simulation optimization, it is impossible to exhaustively simulate every choice. However, there are often inherent similarities between choices: for example, two similar sets of input settings to a simulation model can reasonably be expected to produce similar output. The information gained from simulating one choice can thus be used to infer the values of other similar choices, enabling learning more from a relatively small number of samples. The paper “Sequential Learning with a Similarity Selection Index,” by Zhou, Fu, and Ryzhov, develops a new similarity model to improve the final selection decision after all samples have been collected. The new “similarity indices” are complementary to all existing information collection procedures, which do not focus on the final decision. At the same time, the new model allows a tractable theoretical treatment of an optimal procedure, which can be efficiently approximated.
在大规模仿真优化中，不可能详尽地模拟每一个选择。然而，选择之间通常存在固有的相似性:例如，模拟模型的两组相似的输入设置可以合理地预期产生相似的输出。因此，从模拟一个选择中获得的信息可以用来推断其他类似选择的值，从而从相对较少的样本中学习更多。Zhou、Fu和Ryzhov的论文《具有相似度选择指数的顺序学习》(Sequential Learning with a Similarity Selection Index)开发了一种新的相似度模型，以改进所有样本收集后的最终选择决策。新的“相似度指数”是对所有现有信息收集程序的补充，这些程序不关注最终决定。同时，新模型允许对最优过程进行易于处理的理论处理，可以有效地逼近。
{"title":"Sequential Learning with a Similarity Selection Index","authors":"Yi Zhou, M. Fu, I. Ryzhov","doi":"10.1287/opre.2023.2478","DOIUrl":"https://doi.org/10.1287/opre.2023.2478","url":null,"abstract":"In large-scale simulation optimization, it is impossible to exhaustively simulate every choice. However, there are often inherent similarities between choices: for example, two similar sets of input settings to a simulation model can reasonably be expected to produce similar output. The information gained from simulating one choice can thus be used to infer the values of other similar choices, enabling learning more from a relatively small number of samples. The paper “Sequential Learning with a Similarity Selection Index,” by Zhou, Fu, and Ryzhov, develops a new similarity model to improve the final selection decision after all samples have been collected. The new “similarity indices” are complementary to all existing information collection procedures, which do not focus on the final decision. At the same time, the new model allows a tractable theoretical treatment of an optimal procedure, which can be efficiently approximated.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"24 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74040312","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}
Zhenghua Long, Hailun Zhang, Jiheng Zhang, Z. Zhang
Dynamic Routing of Queues with Heterogeneous Server Pools In “The Generalized c/μ Rule for Queues with Heterogeneous Server Pools,” Long, Zhang, Zhang, and Zhang study the optimal control of queueing systems with heterogeneous server pools and a single customer class. The goal is to balance the holding cost of the queue with the operating costs of the server pools. They introduce the target-allocation policy, the Gc/μ rule, and the fixed priority policy for systems with general, convex, and concave cost functions, respectively. They also consider an extension to minimize operating costs and maintain a service-level target for customers waiting in the queue. Moreover, they show that their asymptotically optimal routing policies coincide with several classic policies in the literature in special cases.
{"title":"The Generalized c/μ Rule for Queues with Heterogeneous Server Pools","authors":"Zhenghua Long, Hailun Zhang, Jiheng Zhang, Z. Zhang","doi":"10.1287/opre.2023.2472","DOIUrl":"https://doi.org/10.1287/opre.2023.2472","url":null,"abstract":"Dynamic Routing of Queues with Heterogeneous Server Pools In “The Generalized c/μ Rule for Queues with Heterogeneous Server Pools,” Long, Zhang, Zhang, and Zhang study the optimal control of queueing systems with heterogeneous server pools and a single customer class. The goal is to balance the holding cost of the queue with the operating costs of the server pools. They introduce the target-allocation policy, the Gc/μ rule, and the fixed priority policy for systems with general, convex, and concave cost functions, respectively. They also consider an extension to minimize operating costs and maintain a service-level target for customers waiting in the queue. Moreover, they show that their asymptotically optimal routing policies coincide with several classic policies in the literature in special cases.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"154 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90418257","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}
In “An Exponential Cone programming Approach for Managing Electric Vehicle Charging,” Chen, He, and Zhou propose a novel ECP approach to solving large-scale optimization of electric vehicle charging in public stations such as EVgo. Other than the stochastic arrivals of customers with different arrival/departure times and charging requirements, charging stations routinely incur high demand charges, costs related to the highest per-period total electricity used in a billing cycle, which can be as high as 70% of the total electricity bill. For the case with unlimited chargers, the authors characterize the theoretical performances of the ECP approach. For the case with limited chargers, the authors construct an ECP leveraging the idea from distributionally robust optimization and show in a data-calibrated numerical study that it performs better than common approaches, considering many practical implementation issues. The authors’ method of constructing ECPs can be potentially applicable to approximate more general two-stage stochastic programs.
{"title":"An Exponential Cone Programming Approach for Managing Electric Vehicle Charging","authors":"Li Chen, Long He, Y. Zhou","doi":"10.1287/opre.2023.2460","DOIUrl":"https://doi.org/10.1287/opre.2023.2460","url":null,"abstract":"In “An Exponential Cone programming Approach for Managing Electric Vehicle Charging,” Chen, He, and Zhou propose a novel ECP approach to solving large-scale optimization of electric vehicle charging in public stations such as EVgo. Other than the stochastic arrivals of customers with different arrival/departure times and charging requirements, charging stations routinely incur high demand charges, costs related to the highest per-period total electricity used in a billing cycle, which can be as high as 70% of the total electricity bill. For the case with unlimited chargers, the authors characterize the theoretical performances of the ECP approach. For the case with limited chargers, the authors construct an ECP leveraging the idea from distributionally robust optimization and show in a data-calibrated numerical study that it performs better than common approaches, considering many practical implementation issues. The authors’ method of constructing ECPs can be potentially applicable to approximate more general two-stage stochastic programs.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87131234","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}
In “Estimating Large-Scale Tree Logit Models,” S. Jagabathula, P. Rusmevichientong, A. Venkataraman, and X. Zhao tackle the demand estimation problem under the tree logit model, also known as the nested logit or d-level nested logit model. The model is ideal for scenarios in which products can be grouped naturally based on their attributes into a hierarchy or taxonomy, such as flight itineraries grouped by departure time (morning or evening) and number of stops (nonstop or one stop). The current estimation methods are not practical for real-world applications that can involve hundreds or even thousands of products. The authors develop a fast, iterative method that computes a sequence of parameter estimates using simple closed-form updates by exploiting the structure of the negative log-likelihood objective. Numerical results on both synthetic and real data show that their proposed algorithm outperforms state-of-the-art optimization methods, especially for large-scale tree logit models with thousands of products.
S. Jagabathula, P. Rusmevichientong, A. Venkataraman和X. Zhao在“估计大规模树Logit模型”中解决了树Logit模型下的需求估计问题，也称为嵌套Logit或d级嵌套Logit模型。该模型非常适合这样的场景，在这些场景中，产品可以根据其属性自然地分组到层次结构或分类法中，例如按起飞时间(早晨或晚上)和停靠次数(直飞或一站)分组的航班行程。当前的估计方法对于可能涉及数百甚至数千个产品的实际应用并不实用。作者开发了一种快速迭代的方法，通过利用负对数似然目标的结构，使用简单的封闭形式更新来计算参数估计序列。合成数据和实际数据的数值结果表明，该算法优于当前最先进的优化方法，特别是对于具有数千个产品的大型树logit模型。
{"title":"Estimating Large-Scale Tree Logit Models","authors":"Srikanth Jagabathula, Paat Rusmevichientong, Ashwin Venkataraman, Xinyi Zhao","doi":"10.1287/opre.2023.2479","DOIUrl":"https://doi.org/10.1287/opre.2023.2479","url":null,"abstract":"In “Estimating Large-Scale Tree Logit Models,” S. Jagabathula, P. Rusmevichientong, A. Venkataraman, and X. Zhao tackle the demand estimation problem under the tree logit model, also known as the nested logit or d-level nested logit model. The model is ideal for scenarios in which products can be grouped naturally based on their attributes into a hierarchy or taxonomy, such as flight itineraries grouped by departure time (morning or evening) and number of stops (nonstop or one stop). The current estimation methods are not practical for real-world applications that can involve hundreds or even thousands of products. The authors develop a fast, iterative method that computes a sequence of parameter estimates using simple closed-form updates by exploiting the structure of the negative log-likelihood objective. Numerical results on both synthetic and real data show that their proposed algorithm outperforms state-of-the-art optimization methods, especially for large-scale tree logit models with thousands of products.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"462 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82987979","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}
Novel Optimality Cuts for Two-Stage Stochastic Mixed-Integer Programs The applicability and use of two-stage stochastic mixed-integer programs is well-established, thus calling for efficient decomposition algorithms to solve them. Such algorithms typically rely on optimality cuts to approximate the expected second stage cost function from below. In “A Converging Benders’ Decomposition Algorithm for Mixed-Integer Recourse Models,” van der Laan and Romeijnders derive a new family of optimality cuts that is sufficiently rich to identify the optimal solution of two-stage stochastic mixed-integer programs in general. That is, general mixed-integer decision variables are allowed in both stages, and all data elements are allowed to be random. Moreover, these new optimality cuts require computations that decompose by scenario, and thus, they can be computed efficiently. Van der Laan and Romeijnders demonstrate the potential of their approach on a range of problem instances, including the DCAP instances from SIPLIB.
两阶段随机混合整数规划的适用性和应用已经得到了证实，因此需要有效的分解算法来求解这类规划。这种算法通常依赖于最优切割来从下面近似预期的第二阶段成本函数。在“混合整数追索权模型的收敛弯曲分解算法”中，van der Laan和Romeijnders导出了一个新的最优性切割族，它足够丰富，可以识别一般的两阶段随机混合整数规划的最优解。也就是说，两个阶段都允许使用一般的混合整数决策变量，并且允许所有数据元素都是随机的。此外，这些新的最优性切割需要按场景分解的计算，因此，它们可以有效地计算。Van der Laan和Romeijnders在一系列问题实例(包括SIPLIB中的DCAP实例)上展示了他们的方法的潜力。
{"title":"A Converging Benders’ Decomposition Algorithm for Two-Stage Mixed-Integer Recourse Models","authors":"N. van der Laan, Ward Romeijnders","doi":"10.1287/opre.2021.2223","DOIUrl":"https://doi.org/10.1287/opre.2021.2223","url":null,"abstract":"Novel Optimality Cuts for Two-Stage Stochastic Mixed-Integer Programs The applicability and use of two-stage stochastic mixed-integer programs is well-established, thus calling for efficient decomposition algorithms to solve them. Such algorithms typically rely on optimality cuts to approximate the expected second stage cost function from below. In “A Converging Benders’ Decomposition Algorithm for Mixed-Integer Recourse Models,” van der Laan and Romeijnders derive a new family of optimality cuts that is sufficiently rich to identify the optimal solution of two-stage stochastic mixed-integer programs in general. That is, general mixed-integer decision variables are allowed in both stages, and all data elements are allowed to be random. Moreover, these new optimality cuts require computations that decompose by scenario, and thus, they can be computed efficiently. Van der Laan and Romeijnders demonstrate the potential of their approach on a range of problem instances, including the DCAP instances from SIPLIB.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"12 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78507565","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}
The pricing problem of vehicle routing problems is strongly NP hard. Many algorithms for finding optimal solutions to various vehicle routing problems rely on a subroutine to solve a so-called pricing problem of a set partitioning formulation. Only exponential time algorithms are known for these pricing problems. Therefore, the set partitioning formulation is oftentimes relaxed at the expense of weaker LP bounds, so that the resulting pricing problem can now be solved using a pseudopolynomial or polynomial time algorithm. In “The Complexity of the Pricing Problem of the Set Partitioning Formulation of Vehicle Routing Problems,” it is proven by Remy Spliet that the pricing problem is strongly NP hard for many different vehicle routing problems. This means that, unless P = NP, no pseudopolynomial or polynomial time algorithm exists for the pricing problem, justifying the common use of relaxations.
{"title":"Technical Note—The Complexity of the Pricing Problem of the Set Partitioning Formulation of Vehicle Routing Problems","authors":"R. Spliet","doi":"10.1287/opre.2023.2481","DOIUrl":"https://doi.org/10.1287/opre.2023.2481","url":null,"abstract":"The pricing problem of vehicle routing problems is strongly NP hard. Many algorithms for finding optimal solutions to various vehicle routing problems rely on a subroutine to solve a so-called pricing problem of a set partitioning formulation. Only exponential time algorithms are known for these pricing problems. Therefore, the set partitioning formulation is oftentimes relaxed at the expense of weaker LP bounds, so that the resulting pricing problem can now be solved using a pseudopolynomial or polynomial time algorithm. In “The Complexity of the Pricing Problem of the Set Partitioning Formulation of Vehicle Routing Problems,” it is proven by Remy Spliet that the pricing problem is strongly NP hard for many different vehicle routing problems. This means that, unless P = NP, no pseudopolynomial or polynomial time algorithm exists for the pricing problem, justifying the common use of relaxations.","PeriodicalId":49809,"journal":{"name":"Military Operations Research","volume":"143 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76433218","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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