The proliferation of emerging mobility technology has led to a significant increase in demand for ride-hailing services, on-demand deliveries, and micromobility services, transforming curb spaces into valuable public infrastructure for which multimodal transportation competes. However, the increasing utilization of curbs by different traffic modes has substantial societal impacts, further altering travelers’ choices and polluting the urban environment. Integrating the spatiotemporal characteristics of various behaviors related to curb utilization into general dynamic networks and exploring mobility patterns with multisource data remain a challenge. To address this issue, this study proposes a comprehensive framework of modeling curbside usage by multimodal transportation in a general dynamic network. The framework encapsulates route choices, curb space competition, and interactive effects among different curb users, and it embeds the dynamics of curb usage into a mesoscopic dynamic network model. Furthermore, a curb-aware dynamic origin-destination demand estimation framework is proposed to reveal the network-level spatiotemporal mobility patterns associated with curb usage through a physics-informed data-driven approach. The framework integrates emerging real-world curb use data in conjunction with other mobility data represented on computational graphs, which can be solved efficiently using the forward-backward algorithm on large-scale networks. The framework is examined on a small network as well as a large-scale real-world network. The estimation results on both networks are satisfactory and compelling, demonstrating the capability of the framework to estimate the spatiotemporal curb usage by multimodal transportation.History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25.Funding: This material is based upon work supported by the Office of Energy Efficiency and Renewable Energy, U.S. Department of Energy [Award DE-EE0009659].Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0522 .
{"title":"Modeling Multimodal Curbside Usage in Dynamic Networks","authors":"Jiachao Liu, Sean Qian","doi":"10.1287/trsc.2024.0522","DOIUrl":"https://doi.org/10.1287/trsc.2024.0522","url":null,"abstract":"The proliferation of emerging mobility technology has led to a significant increase in demand for ride-hailing services, on-demand deliveries, and micromobility services, transforming curb spaces into valuable public infrastructure for which multimodal transportation competes. However, the increasing utilization of curbs by different traffic modes has substantial societal impacts, further altering travelers’ choices and polluting the urban environment. Integrating the spatiotemporal characteristics of various behaviors related to curb utilization into general dynamic networks and exploring mobility patterns with multisource data remain a challenge. To address this issue, this study proposes a comprehensive framework of modeling curbside usage by multimodal transportation in a general dynamic network. The framework encapsulates route choices, curb space competition, and interactive effects among different curb users, and it embeds the dynamics of curb usage into a mesoscopic dynamic network model. Furthermore, a curb-aware dynamic origin-destination demand estimation framework is proposed to reveal the network-level spatiotemporal mobility patterns associated with curb usage through a physics-informed data-driven approach. The framework integrates emerging real-world curb use data in conjunction with other mobility data represented on computational graphs, which can be solved efficiently using the forward-backward algorithm on large-scale networks. The framework is examined on a small network as well as a large-scale real-world network. The estimation results on both networks are satisfactory and compelling, demonstrating the capability of the framework to estimate the spatiotemporal curb usage by multimodal transportation.History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25.Funding: This material is based upon work supported by the Office of Energy Efficiency and Renewable Energy, U.S. Department of Energy [Award DE-EE0009659].Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0522 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":"51 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141571812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jiayang Li, Qianni Wang, Liyang Feng, Jun Xie, Yu (Marco) Nie
The lack of a unique user equilibrium (UE) route flow in traffic assignment has posed a significant challenge to many transportation applications. The maximum-entropy principle, which advocates for the consistent selection of the most likely solution, is often used to address the challenge. Built on a recently proposed day-to-day discrete-time dynamical model called cumulative logit (CumLog), this study provides a new behavioral underpinning for the maximum-entropy user equilibrium (MEUE) route flow. It has been proven that CumLog can reach a UE state without presuming that travelers are perfectly rational. Here, we further establish that CumLog always converges to the MEUE route flow if (i) travelers have no prior information about routes and thus, are forced to give all routes an equal initial choice probability or if (ii) all travelers gather information from the same source such that the general proportionality condition is satisfied. Thus, CumLog may be used as a practical solution algorithm for the MEUE problem. To put this idea into practice, we propose to eliminate the route enumeration requirement of the original CumLog model through an iterative route discovery scheme. We also examine the discrete-time versions of four popular continuous-time dynamical models and compare them with CumLog. The analysis shows that the replicator dynamic is the only one that has the potential to reach the MEUE solution with some regularity. The analytical results are confirmed through numerical experiments.History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference.Funding: This research was funded by the United States National Science Foundation’s Division of Civil, Mechanical and Manufacturing Innovation [Grant 2225087]. The work of J. Xie was funded by the National Natural Science Foundation of China [Grant 72371205].Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0525 .
{"title":"A Day-to-Day Dynamical Approach to the Most Likely User Equilibrium Problem","authors":"Jiayang Li, Qianni Wang, Liyang Feng, Jun Xie, Yu (Marco) Nie","doi":"10.1287/trsc.2024.0525","DOIUrl":"https://doi.org/10.1287/trsc.2024.0525","url":null,"abstract":"The lack of a unique user equilibrium (UE) route flow in traffic assignment has posed a significant challenge to many transportation applications. The maximum-entropy principle, which advocates for the consistent selection of the most likely solution, is often used to address the challenge. Built on a recently proposed day-to-day discrete-time dynamical model called cumulative logit (CumLog), this study provides a new behavioral underpinning for the maximum-entropy user equilibrium (MEUE) route flow. It has been proven that CumLog can reach a UE state without presuming that travelers are perfectly rational. Here, we further establish that CumLog always converges to the MEUE route flow if (i) travelers have no prior information about routes and thus, are forced to give all routes an equal initial choice probability or if (ii) all travelers gather information from the same source such that the general proportionality condition is satisfied. Thus, CumLog may be used as a practical solution algorithm for the MEUE problem. To put this idea into practice, we propose to eliminate the route enumeration requirement of the original CumLog model through an iterative route discovery scheme. We also examine the discrete-time versions of four popular continuous-time dynamical models and compare them with CumLog. The analysis shows that the replicator dynamic is the only one that has the potential to reach the MEUE solution with some regularity. The analytical results are confirmed through numerical experiments.History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference.Funding: This research was funded by the United States National Science Foundation’s Division of Civil, Mechanical and Manufacturing Innovation [Grant 2225087]. The work of J. Xie was funded by the National Natural Science Foundation of China [Grant 72371205].Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0525 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":"54 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141571808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper describes an exact branch-and-cut (B&C) algorithm for the split delivery vehicle routing problem. The underlying model is based on a previously proposed two-index vehicle flow formulation that models a relaxation of the problem. We dynamically separate two well-known classes of valid inequalities, namely capacity and connectivity cuts, and use an in-out algorithm to improve the convergence of the cutting phase. We generate no-good cuts from feasible integer solutions to the relaxation using a recently proposed single-commodity flow formulation in the literature. The exact methodology is complemented by a very effective adaptive large neighborhood search (ALNS) heuristic that provides high-quality upper bounds to initiate the B&C algorithm. Key ingredients in the design of the heuristic include the use of a tailored construction algorithm, which can exploit the situation in which the ratio of the number of customers to the minimum number of vehicles needed is low, and the use of a route-based formulation to improve the solutions found before, during, and after the ALNS procedure. An earlier version of this work was submitted to the DIMACS (Center for Discrete Mathematics and Theoretical Computer Science) implementation challenge, where it placed third. On sets of well-known benchmark instances for limited and unlimited fleet variants of the problem, we demonstrate that the heuristic provides very competitive solutions, with respective average gaps of 0.19% and 0.18% from best-known values. Furthermore, the exact B&C framework is also highly competitive with state-of-the-art methods, providing solutions with an average optimality gap of 1.82%.History: This paper has been accepted for the Transportation Science Special Section on DIMACS Implementation Challenge: Vehicle Routing Problems.Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.0353 .
{"title":"Exact and Heuristic Methods for the Split Delivery Vehicle Routing Problem","authors":"Mette Gamst, Richard Martin Lusby, Stefan Ropke","doi":"10.1287/trsc.2022.0353","DOIUrl":"https://doi.org/10.1287/trsc.2022.0353","url":null,"abstract":"This paper describes an exact branch-and-cut (B&C) algorithm for the split delivery vehicle routing problem. The underlying model is based on a previously proposed two-index vehicle flow formulation that models a relaxation of the problem. We dynamically separate two well-known classes of valid inequalities, namely capacity and connectivity cuts, and use an in-out algorithm to improve the convergence of the cutting phase. We generate no-good cuts from feasible integer solutions to the relaxation using a recently proposed single-commodity flow formulation in the literature. The exact methodology is complemented by a very effective adaptive large neighborhood search (ALNS) heuristic that provides high-quality upper bounds to initiate the B&C algorithm. Key ingredients in the design of the heuristic include the use of a tailored construction algorithm, which can exploit the situation in which the ratio of the number of customers to the minimum number of vehicles needed is low, and the use of a route-based formulation to improve the solutions found before, during, and after the ALNS procedure. An earlier version of this work was submitted to the DIMACS (Center for Discrete Mathematics and Theoretical Computer Science) implementation challenge, where it placed third. On sets of well-known benchmark instances for limited and unlimited fleet variants of the problem, we demonstrate that the heuristic provides very competitive solutions, with respective average gaps of 0.19% and 0.18% from best-known values. Furthermore, the exact B&C framework is also highly competitive with state-of-the-art methods, providing solutions with an average optimality gap of 1.82%.History: This paper has been accepted for the Transportation Science Special Section on DIMACS Implementation Challenge: Vehicle Routing Problems.Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.0353 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":"145 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141571710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Urban logistic applications that involve pickup and distribution of goods require making routing and allocation decisions with respect to a set of sites. In cases where the supply quantities and the time in which they become available are unknown in advance, these decisions must be determined in real time based on information that arrives gradually. Furthermore, in many applications that satisfy the described setting, fair allocation is desired in addition to system effectiveness. In this paper, we consider the problem of determining a vehicle route that visits two types of sites in any order: pickup points (PPs), from which the vehicle collects supplies, and demand points (DPs), to which these supplies are delivered. The supply quantities offered by each PP are uncertain, and the information on their value arrives gradually over time. We model this problem as a stochastic dynamic routing and resource allocation problem, with the aim of delivering as many goods as possible while obtaining equitable allocations to DPs. We present a Markov decision process formulation for the problem; however, it suffers from the curse of dimensionality. Therefore, we develop a heuristic framework that presents a novel combination of operations research and machine learning and is applicable for many dynamic stochastic combinatorial optimization problems. Specifically, we use a large neighborhood search (LNS) to explore possible decisions combined with a neural network (NN) model that approximates the future value given any state and action. We present a new reinforcement learning method to train the NN when the decision space is too large to enumerate. A numerical experiment with 38 to 180 site instances, based on data from the Berlin Foodbank and randomly generated data sets, confirms that the heuristic obtains solutions that are on average approximately 28.2%, 41.6%, and 57.9% better than three benchmark solutions.Funding: This research was partially supported by the Israel Science Foundation [Grant 463/15], by the Shlomo Shmeltzer Institute for Smart Transportation at Tel Aviv University, by the Israeli Smart Transportation Research Center (ISTRC), and by the Council for Higher Education in Israel (VATAT).Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0228 .
{"title":"The Dynamic Pickup and Allocation with Fairness Problem","authors":"Gal Neria, Michal Tzur","doi":"10.1287/trsc.2023.0228","DOIUrl":"https://doi.org/10.1287/trsc.2023.0228","url":null,"abstract":"Urban logistic applications that involve pickup and distribution of goods require making routing and allocation decisions with respect to a set of sites. In cases where the supply quantities and the time in which they become available are unknown in advance, these decisions must be determined in real time based on information that arrives gradually. Furthermore, in many applications that satisfy the described setting, fair allocation is desired in addition to system effectiveness. In this paper, we consider the problem of determining a vehicle route that visits two types of sites in any order: pickup points (PPs), from which the vehicle collects supplies, and demand points (DPs), to which these supplies are delivered. The supply quantities offered by each PP are uncertain, and the information on their value arrives gradually over time. We model this problem as a stochastic dynamic routing and resource allocation problem, with the aim of delivering as many goods as possible while obtaining equitable allocations to DPs. We present a Markov decision process formulation for the problem; however, it suffers from the curse of dimensionality. Therefore, we develop a heuristic framework that presents a novel combination of operations research and machine learning and is applicable for many dynamic stochastic combinatorial optimization problems. Specifically, we use a large neighborhood search (LNS) to explore possible decisions combined with a neural network (NN) model that approximates the future value given any state and action. We present a new reinforcement learning method to train the NN when the decision space is too large to enumerate. A numerical experiment with 38 to 180 site instances, based on data from the Berlin Foodbank and randomly generated data sets, confirms that the heuristic obtains solutions that are on average approximately 28.2%, 41.6%, and 57.9% better than three benchmark solutions.Funding: This research was partially supported by the Israel Science Foundation [Grant 463/15], by the Shlomo Shmeltzer Institute for Smart Transportation at Tel Aviv University, by the Israeli Smart Transportation Research Center (ISTRC), and by the Council for Higher Education in Israel (VATAT).Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0228 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":"90 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Danial Khorasanian, Jonathan Patrick, Antoine Sauré
Despite the rapid growth of the home care industry, research on the scheduling and routing of home care visits in the presence of uncertainty is still limited. This paper investigates a dynamic version of this problem in which the number of referrals and their required number of visits are uncertain. We develop a Markov decision process (MDP) model for the single-nurse problem to minimize the expected weighted sum of the rejection, diversion, overtime, and travel time costs. Because optimally solving the MDP is intractable, we employ an approximate linear program (ALP) to obtain a feasible policy. The typical ALP approach can only solve very small-scale instances of the problem. We derive an intuitively explainable closed-form solution for the optimal ALP parameters in a special case of the problem. Inspired by this form, we provide two heuristic reduction techniques for the ALP model in the general problem to solve large-scale instances in an acceptable time. Numerical results show that the ALP policy outperforms a myopic policy that reflects current practice, and is better than a scenario-based policy in most instances considered.Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2018-05225 and RGPIN-2020-210524] and by the Telfer School of Management SMRG Postdoctoral Research Fellowship Support [Grant 2020].Supplemental Material: The electronic companion is available at https://doi.org/10.1287/trsc.2023.0120 .
尽管家庭护理行业发展迅速，但对存在不确定性的家庭护理访问安排和路由的研究仍然有限。本文研究了这一问题的动态版本，其中转介人数及其所需的访问次数是不确定的。我们为单护士问题开发了一个马尔可夫决策过程（MDP）模型，以最小化拒绝、分流、加班和旅行时间成本的预期加权和。由于马尔可夫决策过程的优化求解难以实现，我们采用了近似线性程序 (ALP) 来获得可行的策略。典型的 ALP 方法只能解决非常小规模的问题实例。在该问题的一个特例中，我们推导出了一个可直观解释的闭式最优 ALP 参数解。受这种形式的启发，我们为一般问题中的 ALP 模型提供了两种启发式简化技术，以在可接受的时间内解决大规模实例。数值结果表明，ALP 政策优于反映当前实践的近视政策，并且在考虑的大多数实例中优于基于情景的政策：这项工作得到了加拿大自然科学与工程研究理事会 [RGPIN-2018-05225 和 RGPIN-2020-210524] 以及特尔弗管理学院 SMRG 博士后研究奖学金 [2020] 的支持：电子版附录见 https://doi.org/10.1287/trsc.2023.0120 。
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This paper addresses the single crew scheduling and routing problem in the context of road network repair and restoration, which is critical in assisting complex postdisaster decisions in humanitarian logistics settings. We present three novel formulations for this problem, which are the first suitable for column generation and branch-and-price (BP) algorithms. Specifically, our first formulation is based on enumerating crew schedules and routes while explicitly defining the relief paths. The second formulation relies on enumerating the schedules, routes, and relief paths. Finally, the third formulation builds upon the second one by including additional constraints and variables related to relief path decisions. Considering each formulation, we propose BP algorithms that rely on several enhancements, including a new dynamic programming labeling algorithm to efficiently solve the subproblems. Extensive computational results based on 648 benchmark instances reveal that our BP algorithms significantly outperform existing exact approaches, solving 450 instances to optimality, and remarkably 118 instances for the first time. Our framework is also very effective in improving the lower bounds, upper bounds, and optimality gaps that have been reported in the literature.Funding: This work was supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo [Grants 15/26453-7, 16/01860-1, 16/15966-6, and 19/23596-2], the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant 313220/2020-4], and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior.Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2023.0227 .
本文以道路网络的修复和恢复为背景，探讨了单个施工人员的调度和路由问题，这对于协助人道主义物流环境中复杂的灾后决策至关重要。我们为这一问题提出了三种新的表述方法，这些方法首次适用于列生成和分支-价格（BP）算法。具体来说，我们的第一种方法是在明确定义救灾路径的同时，枚举机组人员时间表和路线。第二种方法依赖于枚举计划、路线和救援路径。最后，第三种方法在第二种方法的基础上增加了与救援路径决策相关的额外约束和变量。考虑到每种方案，我们都提出了 BP 算法，这些算法依赖于若干改进，包括一种新的动态编程标记算法，以高效解决子问题。基于 648 个基准实例的广泛计算结果显示，我们的 BP 算法明显优于现有的精确算法，其中 450 个实例达到最优解，118 个实例首次达到最优解。我们的框架还能有效改善文献中报道的下限、上限和最优性差距：本研究得到了圣保罗州研究基金[15/26453-7、16/01860-1、16/15966-6 和 19/23596-2 号基金]、国家科学与技术发展委员会[313220/2020-4 号基金]和高级研究人员奖学金委员会的资助：在线附录见 https://doi.org/10.1287/trsc.2023.0227 。
{"title":"Crew Scheduling and Routing Problem in Road Restoration via Branch-and-Price Algorithms","authors":"Alfredo Moreno, Pedro Munari, Douglas Alem","doi":"10.1287/trsc.2023.0227","DOIUrl":"https://doi.org/10.1287/trsc.2023.0227","url":null,"abstract":"This paper addresses the single crew scheduling and routing problem in the context of road network repair and restoration, which is critical in assisting complex postdisaster decisions in humanitarian logistics settings. We present three novel formulations for this problem, which are the first suitable for column generation and branch-and-price (BP) algorithms. Specifically, our first formulation is based on enumerating crew schedules and routes while explicitly defining the relief paths. The second formulation relies on enumerating the schedules, routes, and relief paths. Finally, the third formulation builds upon the second one by including additional constraints and variables related to relief path decisions. Considering each formulation, we propose BP algorithms that rely on several enhancements, including a new dynamic programming labeling algorithm to efficiently solve the subproblems. Extensive computational results based on 648 benchmark instances reveal that our BP algorithms significantly outperform existing exact approaches, solving 450 instances to optimality, and remarkably 118 instances for the first time. Our framework is also very effective in improving the lower bounds, upper bounds, and optimality gaps that have been reported in the literature.Funding: This work was supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo [Grants 15/26453-7, 16/01860-1, 16/15966-6, and 19/23596-2], the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant 313220/2020-4], and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior.Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2023.0227 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":"17 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Network equilibrium models have been extensively used for decades. The rationale for using equilibrium as a predictor is essentially that (i) a unique and globally stable equilibrium point is guaranteed to exist and (ii) the transient period over which a system adapts to a change is sufficiently short in time that it can be neglected. However, we find transport problems without a unique and stable equilibrium in the literature. Even if it exists, it is not certain how long it takes for the system to reach an equilibrium point after an external shock onto the transport system, such as infrastructure improvement and damage by a disaster. The day-to-day adjustment process must be analysed to answer these questions. Among several models, the Markov chain approach has been claimed to be the most general and flexible. It is also advantageous as a unique stationary distribution is guaranteed in mild conditions, even when a unique and stable equilibrium does not exist. In the present paper, we first aim to develop a methodology for estimating the Markov chain mixing time (MCMT), a worst-case assessment of the convergence time of a Markov chain to its stationary distribution. The main tools are coupling and aggregation, which enable us to analyse MCMTs in large-scale transport systems. Our second aim is to conduct a preliminary examination of the relationships between MCMTs and critical properties of the system, such as travellers’ sensitivity to differences in travel cost and the frequency of travellers’ revisions of their choices. Through analytical and numerical analyses, we found key relationships in a few transport problems, including those without a unique and stable equilibrium. We also showed that the proposed method, combined with coupling and aggregation, can be applied to larger transport models.History: This paper has been accepted for the Transportation Science Special Issue on the 25th International Symposium on Transportation and Traffic Theory.Funding: This study was financially supported by the Japan Society for the Promotion of Science [Grant-in-Aid 20H00265].Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2024.0523 .
{"title":"Estimating Markov Chain Mixing Times: Convergence Rate Towards Equilibrium of a Stochastic Process Traffic Assignment Model","authors":"Takamasa Iryo, David Watling, Martin Hazelton","doi":"10.1287/trsc.2024.0523","DOIUrl":"https://doi.org/10.1287/trsc.2024.0523","url":null,"abstract":"Network equilibrium models have been extensively used for decades. The rationale for using equilibrium as a predictor is essentially that (i) a unique and globally stable equilibrium point is guaranteed to exist and (ii) the transient period over which a system adapts to a change is sufficiently short in time that it can be neglected. However, we find transport problems without a unique and stable equilibrium in the literature. Even if it exists, it is not certain how long it takes for the system to reach an equilibrium point after an external shock onto the transport system, such as infrastructure improvement and damage by a disaster. The day-to-day adjustment process must be analysed to answer these questions. Among several models, the Markov chain approach has been claimed to be the most general and flexible. It is also advantageous as a unique stationary distribution is guaranteed in mild conditions, even when a unique and stable equilibrium does not exist. In the present paper, we first aim to develop a methodology for estimating the Markov chain mixing time (MCMT), a worst-case assessment of the convergence time of a Markov chain to its stationary distribution. The main tools are coupling and aggregation, which enable us to analyse MCMTs in large-scale transport systems. Our second aim is to conduct a preliminary examination of the relationships between MCMTs and critical properties of the system, such as travellers’ sensitivity to differences in travel cost and the frequency of travellers’ revisions of their choices. Through analytical and numerical analyses, we found key relationships in a few transport problems, including those without a unique and stable equilibrium. We also showed that the proposed method, combined with coupling and aggregation, can be applied to larger transport models.History: This paper has been accepted for the Transportation Science Special Issue on the 25th International Symposium on Transportation and Traffic Theory.Funding: This study was financially supported by the Japan Society for the Promotion of Science [Grant-in-Aid 20H00265].Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2024.0523 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":"77 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chenhao Zhou, Aloisius Stephen, Kok Choon Tan, Ek Peng Chew, Loo Hay Lee
In recent years, advancements in battery technology have led to increased adoption of electric automated guided vehicles in container terminals. Given how critical these vehicles are to terminal operations, this trend requires efficient recharging scheduling for automated guided vehicles, and the main challenges arise from limited charging station capacity and tight vehicle schedules. Motivated by the dynamic nature of the problem, the recharging scheduling problem for an entire vehicle fleet given capacitated stations is formulated as a Markov decision process model. Then, it is solved using a multiagent Q-learning (MAQL) approach to produce a recharging schedule that minimizes the delay of jobs. Numerical experiments show that under a stochastic environment in terms of vehicle travel time, MAQL enables the exploration of better scheduling by coordinating across the entire vehicle fleet and charging facilities and outperforms various benchmark approaches, with an additional improvement of 18.8% on average over the best rule-based heuristic and 5.4% over the predetermined approach.Funding: This work was supported by the National Natural Science Foundation of China [Grant 72101203], the Shaanxi Provincial Key R&D Program, China [Grant 2022KW-02], and the Singapore Maritime Institute [Grant SMI-2017-SP-002].Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0113 .
{"title":"Multiagent Q-Learning Approach for the Recharging Scheduling of Electric Automated Guided Vehicles in Container Terminals","authors":"Chenhao Zhou, Aloisius Stephen, Kok Choon Tan, Ek Peng Chew, Loo Hay Lee","doi":"10.1287/trsc.2022.0113","DOIUrl":"https://doi.org/10.1287/trsc.2022.0113","url":null,"abstract":"In recent years, advancements in battery technology have led to increased adoption of electric automated guided vehicles in container terminals. Given how critical these vehicles are to terminal operations, this trend requires efficient recharging scheduling for automated guided vehicles, and the main challenges arise from limited charging station capacity and tight vehicle schedules. Motivated by the dynamic nature of the problem, the recharging scheduling problem for an entire vehicle fleet given capacitated stations is formulated as a Markov decision process model. Then, it is solved using a multiagent Q-learning (MAQL) approach to produce a recharging schedule that minimizes the delay of jobs. Numerical experiments show that under a stochastic environment in terms of vehicle travel time, MAQL enables the exploration of better scheduling by coordinating across the entire vehicle fleet and charging facilities and outperforms various benchmark approaches, with an additional improvement of 18.8% on average over the best rule-based heuristic and 5.4% over the predetermined approach.Funding: This work was supported by the National Natural Science Foundation of China [Grant 72101203], the Shaanxi Provincial Key R&D Program, China [Grant 2022KW-02], and the Singapore Maritime Institute [Grant SMI-2017-SP-002].Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0113 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":"46 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140569406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nour ElHouda Tellache, Frédéric Meunier, Axel Parmentier
Some airlines use the preferential bidding system to construct the schedules of their pilots. In this system, the pilots bid on the different activities and the schedules that lexicographically maximize the scores of the pilots according to their seniority are selected. A sequential approach to solve this maximization problem is natural: The problem is first solved with the bids of the most senior pilot, and then it is solved with those of the second most senior without decreasing the score of the most senior, and so on. The literature admits that the structure of the problem somehow imposes such an approach. The problem can be modeled as an integer linear lexicographic program. We propose a new efficient method, which relies on column generation for solving its continuous relaxation and returns proven optimality gaps. To design this column generation, we prove that bounded linear lexicographic programs admit “primal-dual” feasible bases, and we show how to compute such bases efficiently. Another contribution on which our method relies is the extension of standard tools for resource-constrained longest path problems to their lexicographic versions. This is useful in our context because the generation of new columns is modeled as a lexicographic resource-constrained longest path problem. Numerical experiments show that this new method is already able to solve to proven optimality industrial instances provided by Air France, with up to 150 pilots. By adding a last ingredient in the resolution of the longest path problems, which exploits the specificity of the preferential bidding system, the method achieves for these instances computational times that are compatible with operational constraints.Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0372 .
{"title":"Linear Lexicographic Optimization and Preferential Bidding System","authors":"Nour ElHouda Tellache, Frédéric Meunier, Axel Parmentier","doi":"10.1287/trsc.2022.0372","DOIUrl":"https://doi.org/10.1287/trsc.2022.0372","url":null,"abstract":"Some airlines use the preferential bidding system to construct the schedules of their pilots. In this system, the pilots bid on the different activities and the schedules that lexicographically maximize the scores of the pilots according to their seniority are selected. A sequential approach to solve this maximization problem is natural: The problem is first solved with the bids of the most senior pilot, and then it is solved with those of the second most senior without decreasing the score of the most senior, and so on. The literature admits that the structure of the problem somehow imposes such an approach. The problem can be modeled as an integer linear lexicographic program. We propose a new efficient method, which relies on column generation for solving its continuous relaxation and returns proven optimality gaps. To design this column generation, we prove that bounded linear lexicographic programs admit “primal-dual” feasible bases, and we show how to compute such bases efficiently. Another contribution on which our method relies is the extension of standard tools for resource-constrained longest path problems to their lexicographic versions. This is useful in our context because the generation of new columns is modeled as a lexicographic resource-constrained longest path problem. Numerical experiments show that this new method is already able to solve to proven optimality industrial instances provided by Air France, with up to 150 pilots. By adding a last ingredient in the resolution of the longest path problems, which exploits the specificity of the preferential bidding system, the method achieves for these instances computational times that are compatible with operational constraints.Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0372 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":"28 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Leon Lan, Jasper M. H. van Doorn, Niels A. Wouda, Arpan Rijal, Sandjai Bhulai
A challenge in same-day delivery operations is that delivery requests are typically not known beforehand, but are instead revealed dynamically during the day. This uncertainty introduces a trade-off between dispatching vehicles to serve requests as soon as they are revealed to ensure timely delivery and delaying the dispatching decision to consolidate routing decisions with future, currently unknown requests. In this paper, we study the dynamic dispatch waves problem, a same-day delivery problem in which vehicles are dispatched at fixed decision moments. At each decision moment, the system operator must decide which of the known requests to dispatch and how to route these dispatched requests. The operator’s goal is to minimize the total routing cost while ensuring that all requests are served on time. We propose iterative conditional dispatch (ICD), an iterative solution construction procedure based on a sample scenario approach. ICD iteratively solves sample scenarios to classify requests to be dispatched, postponed, or undecided. The set of undecided requests shrinks in each iteration until a final dispatching decision is made in the last iteration. We develop two variants of ICD: one variant based on thresholds, and another variant based on similarity. A significant strength of ICD is that it is conceptually simple and easy to implement. This simplicity does not harm performance: through rigorous numerical experiments, we show that both variants efficiently navigate the large state and action spaces of the dynamic dispatch waves problem and quickly converge to a high-quality solution. Finally, we demonstrate that the threshold-based ICD variant achieves excellent results on instances from the EURO Meets NeurIPS 2022 Vehicle Routing Competition, nearly matching the performance of the winning machine learning–based strategy.History: This paper has been accepted for the Transportation Science Special Issue on DIMACS Implementation Challenge: Vehicle Routing Problems.Funding: This work was supported by TKI Dinalog, Topsector Logistics, and the Dutch Ministry of Economic Affairs and Climate Policy.Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0111 .
{"title":"An Iterative Sample Scenario Approach for the Dynamic Dispatch Waves Problem","authors":"Leon Lan, Jasper M. H. van Doorn, Niels A. Wouda, Arpan Rijal, Sandjai Bhulai","doi":"10.1287/trsc.2023.0111","DOIUrl":"https://doi.org/10.1287/trsc.2023.0111","url":null,"abstract":"A challenge in same-day delivery operations is that delivery requests are typically not known beforehand, but are instead revealed dynamically during the day. This uncertainty introduces a trade-off between dispatching vehicles to serve requests as soon as they are revealed to ensure timely delivery and delaying the dispatching decision to consolidate routing decisions with future, currently unknown requests. In this paper, we study the dynamic dispatch waves problem, a same-day delivery problem in which vehicles are dispatched at fixed decision moments. At each decision moment, the system operator must decide which of the known requests to dispatch and how to route these dispatched requests. The operator’s goal is to minimize the total routing cost while ensuring that all requests are served on time. We propose iterative conditional dispatch (ICD), an iterative solution construction procedure based on a sample scenario approach. ICD iteratively solves sample scenarios to classify requests to be dispatched, postponed, or undecided. The set of undecided requests shrinks in each iteration until a final dispatching decision is made in the last iteration. We develop two variants of ICD: one variant based on thresholds, and another variant based on similarity. A significant strength of ICD is that it is conceptually simple and easy to implement. This simplicity does not harm performance: through rigorous numerical experiments, we show that both variants efficiently navigate the large state and action spaces of the dynamic dispatch waves problem and quickly converge to a high-quality solution. Finally, we demonstrate that the threshold-based ICD variant achieves excellent results on instances from the EURO Meets NeurIPS 2022 Vehicle Routing Competition, nearly matching the performance of the winning machine learning–based strategy.History: This paper has been accepted for the Transportation Science Special Issue on DIMACS Implementation Challenge: Vehicle Routing Problems.Funding: This work was supported by TKI Dinalog, Topsector Logistics, and the Dutch Ministry of Economic Affairs and Climate Policy.Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0111 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":"46 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140303277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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