Patrick Gemander, Andreas Bärmann, Alexander Martin
We consider a problem from the context of energy-efficient underground railway timetabling, in which an existing timetable draft is improved by slightly changing departure and running times. In practice, synchronization between accelerating and braking trains to utilize regenerative braking plays a major role for the energy efficiency of a timetable. Because deviations from a planned timetable may lead to unnecessarily high energy consumption during actual operation, we include operational uncertainties in our model to create a timetable that remains energy efficient, even if deviations from the nominal timetable occur. To solve the problem, we use a scenario expansion model in conjunction with a Benders decomposition approach. As an alternative to solving the Benders subproblems, we present a heuristic sparse cut that can be computed efficiently. The resulting sparse-cut heuristic produces high-quality solutions on a set of real-world instances stemming from the Nürnberg underground system, outperforming the integrated mixed-integer programming approach as well as the basic Benders approach. Additionally, we evaluate two static recovery strategies—shortening dwell times as well as shortening dwell and running times—to determine the cost and benefit of handling delays using a simple static rule. In our experiments, we are able to reduce the energy consumption by up to 9.4% and confirm that delay recovery via shortening dwell times is an energy-efficient and effective way to increase punctuality at low cost in terms of energy. Funding: This research was supported by the Bavarian Ministry of Economic Affairs, Regional Development and Energy through the Center for Analytics – Data – Applications (ADA-Center) within the framework of “BAYERN DIGITAL II” (20-3410-2-9-8).
本文从节能地铁调度的角度考虑了一个问题，其中现有的时刻表草案通过稍微改变发车时间和运行时间来改进。在实践中，加速和制动列车之间的同步利用再生制动对时间表的能源效率起着重要作用。由于偏离计划的时间表可能会导致在实际操作中不必要的高能耗，因此我们在模型中包含了操作的不确定性，以创建一个保持能源效率的时间表，即使偏离名义时间表发生了。为了解决这个问题，我们将场景展开模型与Benders分解方法结合使用。作为求解Benders子问题的替代方案，我们提出了一种可以高效计算的启发式稀疏切割。由此产生的稀疏切割启发式算法在一组来自n rnberg地下系统的实际实例上产生高质量的解决方案，优于集成的混合整数规划方法以及基本的Benders方法。此外，我们评估了两种静态恢复策略——缩短停留时间以及缩短停留和运行时间——以确定使用简单的静态规则处理延迟的成本和收益。在我们的实验中，我们能够减少高达9.4%的能源消耗，并确认通过缩短停留时间来恢复延迟是一种节能有效的方式，以低成本的能源增加准点率。本研究由巴伐利亚州经济事务、区域发展和能源部通过“BAYERN DIGITAL II”(20-3410-2-9-8)框架内的分析-数据-应用中心(ADA-Center)支持。
{"title":"A Stochastic Optimization Approach to Energy-Efficient Underground Timetabling Under Uncertain Dwell and Running Times","authors":"Patrick Gemander, Andreas Bärmann, Alexander Martin","doi":"10.1287/trsc.2022.0269","DOIUrl":"https://doi.org/10.1287/trsc.2022.0269","url":null,"abstract":"We consider a problem from the context of energy-efficient underground railway timetabling, in which an existing timetable draft is improved by slightly changing departure and running times. In practice, synchronization between accelerating and braking trains to utilize regenerative braking plays a major role for the energy efficiency of a timetable. Because deviations from a planned timetable may lead to unnecessarily high energy consumption during actual operation, we include operational uncertainties in our model to create a timetable that remains energy efficient, even if deviations from the nominal timetable occur. To solve the problem, we use a scenario expansion model in conjunction with a Benders decomposition approach. As an alternative to solving the Benders subproblems, we present a heuristic sparse cut that can be computed efficiently. The resulting sparse-cut heuristic produces high-quality solutions on a set of real-world instances stemming from the Nürnberg underground system, outperforming the integrated mixed-integer programming approach as well as the basic Benders approach. Additionally, we evaluate two static recovery strategies—shortening dwell times as well as shortening dwell and running times—to determine the cost and benefit of handling delays using a simple static rule. In our experiments, we are able to reduce the energy consumption by up to 9.4% and confirm that delay recovery via shortening dwell times is an energy-efficient and effective way to increase punctuality at low cost in terms of energy. Funding: This research was supported by the Bavarian Ministry of Economic Affairs, Regional Development and Energy through the Center for Analytics – Data – Applications (ADA-Center) within the framework of “BAYERN DIGITAL II” (20-3410-2-9-8).","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136309253","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}
Many warehouses involved in e-commerce order fulfillment use robotic mobile fulfillment systems. Because demand and variability can be high, scheduling orders, robots, and storage pods in interaction with manual workstations are critical to obtaining high performance. Simultaneously, the scheduling problem is extremely complicated because of interactions between decisions, many of which must be taken timely because of short planning horizons and a constantly changing environment. This paper models all such scheduling decisions in combination to minimize order fulfillment time. We propose two decision methods for the above scheduling problem. The models batch the orders using different batching methods and assign orders and batches to pods and workstations in sequence and robots to jobs. Order picking and stock replenishment operations are included in the models. We conduct numerical experiments based on a real-world case to validate the efficacy and efficiency of the model and algorithm. Instances with 14 workstations, 400 orders, 300 stock-keeping units (SKUs), 160 pods, and 160 robots can be solved to near optimality within four minutes. Our methods can be applied to large instances, for example, using a rolling horizon. Because our model can be solved relatively fast, it can be used to take managerial decisions and obtain executive insights. Our results show that making integrated decisions, even when done heuristically, is more beneficial than sequential, isolated optimization. We also find that positioning pick stations close together along one of the system’s long sides is efficient. The replenishment stations can be grouped along another side. Another finding is that SKU diversity per pod and SKU dispersion over pods have strong and positive impacts on the total completion time of handling order batches. Funding: This work was supported by National Natural Science Foundation of China [72025103, 72361137001, 71831008, 72071173] and the Research Grants Council of the Hong Kong Special Administrative Region, China [HKSAR RGC TRS T32-707/22-N]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0265 .
{"title":"How to Deploy Robotic Mobile Fulfillment Systems","authors":"Lu Zhen, Zheyi Tan, René de Koster, Shuaian Wang","doi":"10.1287/trsc.2022.0265","DOIUrl":"https://doi.org/10.1287/trsc.2022.0265","url":null,"abstract":"Many warehouses involved in e-commerce order fulfillment use robotic mobile fulfillment systems. Because demand and variability can be high, scheduling orders, robots, and storage pods in interaction with manual workstations are critical to obtaining high performance. Simultaneously, the scheduling problem is extremely complicated because of interactions between decisions, many of which must be taken timely because of short planning horizons and a constantly changing environment. This paper models all such scheduling decisions in combination to minimize order fulfillment time. We propose two decision methods for the above scheduling problem. The models batch the orders using different batching methods and assign orders and batches to pods and workstations in sequence and robots to jobs. Order picking and stock replenishment operations are included in the models. We conduct numerical experiments based on a real-world case to validate the efficacy and efficiency of the model and algorithm. Instances with 14 workstations, 400 orders, 300 stock-keeping units (SKUs), 160 pods, and 160 robots can be solved to near optimality within four minutes. Our methods can be applied to large instances, for example, using a rolling horizon. Because our model can be solved relatively fast, it can be used to take managerial decisions and obtain executive insights. Our results show that making integrated decisions, even when done heuristically, is more beneficial than sequential, isolated optimization. We also find that positioning pick stations close together along one of the system’s long sides is efficient. The replenishment stations can be grouped along another side. Another finding is that SKU diversity per pod and SKU dispersion over pods have strong and positive impacts on the total completion time of handling order batches. Funding: This work was supported by National Natural Science Foundation of China [72025103, 72361137001, 71831008, 72071173] and the Research Grants Council of the Hong Kong Special Administrative Region, China [HKSAR RGC TRS T32-707/22-N]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0265 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":" ","pages":""},"PeriodicalIF":4.6,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41627310","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 studies a variant of the traveling salesman problem, called the pickup-and-delivery traveling salesman problem with neighborhoods, that combines traditional pickup and delivery requirements with the flexibility of visiting the customers at locations within compact neighborhoods of arbitrary shape. We derive two optimality conditions for the problem, a local condition that verifies whether a given tour is locally optimal at the visiting points and a global condition that can be used to cut off suboptimal regions of the neighborhoods. We model the problem as a mixed-integer nonlinear program and propose a generalized Benders decomposition to solve instances of the problem with convex and nonconvex neighborhoods. Finally, we conduct extensive computational experiments to demonstrate the efficacy of our solution framework. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0138 .
{"title":"An Exact Approach for Solving Pickup-and-Delivery Traveling Salesman Problems with Neighborhoods","authors":"C. Gao, Ningji Wei, J. Walteros","doi":"10.1287/trsc.2022.0138","DOIUrl":"https://doi.org/10.1287/trsc.2022.0138","url":null,"abstract":"This paper studies a variant of the traveling salesman problem, called the pickup-and-delivery traveling salesman problem with neighborhoods, that combines traditional pickup and delivery requirements with the flexibility of visiting the customers at locations within compact neighborhoods of arbitrary shape. We derive two optimality conditions for the problem, a local condition that verifies whether a given tour is locally optimal at the visiting points and a global condition that can be used to cut off suboptimal regions of the neighborhoods. We model the problem as a mixed-integer nonlinear program and propose a generalized Benders decomposition to solve instances of the problem with convex and nonconvex neighborhoods. Finally, we conduct extensive computational experiments to demonstrate the efficacy of our solution framework. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0138 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":" ","pages":""},"PeriodicalIF":4.6,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44838008","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}
M. Baum, V. Buchhold, J. Sauer, D. Wagner, T. Zündorf
We study a multimodal journey planning scenario consisting of a public transit network and a transfer graph that represents a secondary transportation mode (e.g., walking, cycling, e-scooter). The objective is to compute Pareto-optimal journeys with respect to arrival time and the number of used public transit trips. Whereas various existing algorithms can efficiently compute optimal journeys in either a pure public transit network or a pure transfer graph, combining the two increases running times significantly. Existing approaches, therefore, typically only support limited walking between stops by either imposing a maximum transfer distance or requiring the transfer graph to be transitively closed. To overcome these shortcomings, we propose a novel preprocessing technique called unlimited transfers (ULTRA): given an unlimited transfer graph, which may represent any non–schedule based transportation mode, ULTRA computes a small number of transfer shortcuts that are provably sufficient for computing a Pareto set of optimal journeys. These transfer shortcuts can be integrated into a variety of state-of-the-art public transit algorithms, establishing the ULTRA-query algorithm family. Our extensive experimental evaluation shows that ULTRA improves these algorithms from limited to unlimited transfers without sacrificing query speed. This is true not just for walking, but also for faster transfer modes, such as bicycle or car. Compared with the state of the art for multimodal journey planning, the fastest ULTRA-based algorithm achieves a speedup of an order of magnitude. Funding: This work was supported by Deutsche Forschungsgemeinschaft [Grant WA 654/23-2]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0198 .
我们研究了一个由公共交通网络和代表第二交通方式(如步行、骑自行车、电动滑板车)的换乘图组成的多模式旅行规划场景。目标是计算关于到达时间和使用公共交通的次数的帕累托最优行程。虽然现有的各种算法可以有效地计算纯公共交通网络或纯换乘图的最优行程，但将两者结合起来会显著增加运行时间。因此，现有的方法通常只能通过施加最大换乘距离或要求换乘图传递封闭来支持站点之间的有限步行。为了克服这些缺点，我们提出了一种新的预处理技术，称为无限传输(ULTRA):给定一个无限传输图，它可以表示任何非基于时间表的运输模式，ULTRA计算少量传输捷径，这些捷径可以证明足以计算帕累托最优行程集。这些换乘捷径可以集成到各种最先进的公共交通算法中，建立ULTRA-query算法家族。我们广泛的实验评估表明，ULTRA在不牺牲查询速度的情况下将这些算法从有限传输提高到无限传输。这不仅适用于步行，也适用于更快的交通方式，如自行车或汽车。与目前最先进的多模式出行规划相比，最快的基于ultra的算法实现了一个数量级的加速。本研究由Deutsche Forschungsgemeinschaft [Grant WA 654/23-2]资助。补充材料:在线附录可在https://doi.org/10.1287/trsc.2022.0198上获得。
{"title":"ULTRA: Unlimited Transfers for Efficient Multimodal Journey Planning","authors":"M. Baum, V. Buchhold, J. Sauer, D. Wagner, T. Zündorf","doi":"10.1287/trsc.2022.0198","DOIUrl":"https://doi.org/10.1287/trsc.2022.0198","url":null,"abstract":"We study a multimodal journey planning scenario consisting of a public transit network and a transfer graph that represents a secondary transportation mode (e.g., walking, cycling, e-scooter). The objective is to compute Pareto-optimal journeys with respect to arrival time and the number of used public transit trips. Whereas various existing algorithms can efficiently compute optimal journeys in either a pure public transit network or a pure transfer graph, combining the two increases running times significantly. Existing approaches, therefore, typically only support limited walking between stops by either imposing a maximum transfer distance or requiring the transfer graph to be transitively closed. To overcome these shortcomings, we propose a novel preprocessing technique called unlimited transfers (ULTRA): given an unlimited transfer graph, which may represent any non–schedule based transportation mode, ULTRA computes a small number of transfer shortcuts that are provably sufficient for computing a Pareto set of optimal journeys. These transfer shortcuts can be integrated into a variety of state-of-the-art public transit algorithms, establishing the ULTRA-query algorithm family. Our extensive experimental evaluation shows that ULTRA improves these algorithms from limited to unlimited transfers without sacrificing query speed. This is true not just for walking, but also for faster transfer modes, such as bicycle or car. Compared with the state of the art for multimodal journey planning, the fastest ULTRA-based algorithm achieves a speedup of an order of magnitude. Funding: This work was supported by Deutsche Forschungsgemeinschaft [Grant WA 654/23-2]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0198 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":" ","pages":""},"PeriodicalIF":4.6,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43397720","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}
Shadi Sanoubar, Bram de Jonge, L. Maillart, O. Prokopyev
We consider the problem of performing condition-based maintenance on a set of geographically distributed assets via a single maintenance resource that travels between the assets’ locations. That is, we dynamically determine the optimal positioning of the maintenance resource and the optimal timing of condition-based maintenance interventions that the maintenance resource performs. These decisions are made as a function of the conditions of the assets and the current location of the maintenance resource to minimize total expected costs, which include downtime, travel, and maintenance expenses. This holistic approach enables us to study unique trade-offs, namely, maintaining an asset early if the maintenance resource is currently close by, or alternatively, optimally repositioning the maintenance resource or having it idle in key locations in anticipation of asset deterioration. We model the location of the maintenance resource and assets using a graph representation and the assets’ deterioration process as a discrete-time Markov chain. We formulate a Markov decision process to obtain the optimal policy for the maintenance resource (i.e., where to travel, idle, or repair). We explore the properties of the optimal policies (analytically and numerically) and how they are affected by the graph structure. Finally, we develop and analyze some implementation-friendly heuristic policies. Funding: This research was supported by Pitt Momentum Fund Award (3463) and NSF [Grant CMMI-2002681]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2021.0302 .
{"title":"Optimal Condition-Based Maintenance via a Mobile Maintenance Resource","authors":"Shadi Sanoubar, Bram de Jonge, L. Maillart, O. Prokopyev","doi":"10.1287/trsc.2021.0302","DOIUrl":"https://doi.org/10.1287/trsc.2021.0302","url":null,"abstract":"We consider the problem of performing condition-based maintenance on a set of geographically distributed assets via a single maintenance resource that travels between the assets’ locations. That is, we dynamically determine the optimal positioning of the maintenance resource and the optimal timing of condition-based maintenance interventions that the maintenance resource performs. These decisions are made as a function of the conditions of the assets and the current location of the maintenance resource to minimize total expected costs, which include downtime, travel, and maintenance expenses. This holistic approach enables us to study unique trade-offs, namely, maintaining an asset early if the maintenance resource is currently close by, or alternatively, optimally repositioning the maintenance resource or having it idle in key locations in anticipation of asset deterioration. We model the location of the maintenance resource and assets using a graph representation and the assets’ deterioration process as a discrete-time Markov chain. We formulate a Markov decision process to obtain the optimal policy for the maintenance resource (i.e., where to travel, idle, or repair). We explore the properties of the optimal policies (analytically and numerically) and how they are affected by the graph structure. Finally, we develop and analyze some implementation-friendly heuristic policies. Funding: This research was supported by Pitt Momentum Fund Award (3463) and NSF [Grant CMMI-2002681]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2021.0302 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":" ","pages":""},"PeriodicalIF":4.6,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44155310","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}
C. M. Schenekemberg, T. Guimarães, A. A. Chaves, Leandro C. Coelho
Production and inventory routing problems consider a single-product supply chain operating under a vendor-managed inventory system. A plant creates a production plan and vehicle routes over a planning horizon to replenish its customers at minimum cost. In this paper, we present two- and three-index formulations, implement a branch-and-cut algorithm based on each formulation, and introduce a local search matheuristic-based algorithm to solve the problem. In order to combine all benefits of each algorithm, we design a parallel framework to integrate all three fronts, called the three-front parallel branch-and-cut algorithm (3FP-B&C). We assess the performance of our method on well-known benchmark instances of the inventory routing problem (IRP) and the production routing problem (PRP). The results show that our 3FP-B&C outperforms by far other approaches from the literature. For the 956 feasible small-size IRP instances, our method proves optimality for 746, being the first exact algorithm to solve all instances with up to two vehicles. 3FP-B&C finds 949 best known solutions (BKS) with 153 new BKS (NBKS). For the large-size set, our method provides two new optimal solutions (OPT), and finds 82% of BKS, being 70% of NBKS for instances with up to five vehicles. This result is more than twice the number of BKS considering all heuristic methods from the literature combined. Finally, our 3FP-B&C finds the best lower bounds (BLB) for 1,169/1,316 instances, outperforming all previous exact algorithms. On the PRP, our method obtained 278 OPT out of the 336 instances of benchmark set of small- and medium-size instances being 19 new ones in addition to 335 BKS (74 NBKS) and 313 BLB (52 new ones). On another set of PRP with medium- and large-size instances, our algorithm finds 1,105 BKS out of 1,440 instances with 584 NBKS. Besides that, our 3FP-B&C is the first exact algorithm to solve the instances with an unlimited fleet, providing the first lower bounds for this subset with an average optimality gap of 0.61%. We also address a very large-size instance set, the second exact algorithm to address this set, outperforming the previous approach by far. Finally, a comparative analysis of each front shows the gains of the integrated approach. History: This paper has been accepted for the Transportation Science Special Issue: DIMACS Implementation Challenge: Vehicle Routing. Funding: C. M. Schenekemberg was supported by the São Paulo Research Foundation (FAPESP) [Grant 2020/07145-8]. A. A. Chaves was supported by FAPESP [Grants 2018/15417-8 and 2016/01860-1] and Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 312747/2021-7 and 405702/2021-3]. L. C. Coelho was supported by the Canadian Natural Sciences and Engineering Research Council [Grant 2019-00094]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0261 .
{"title":"A Three-Front Parallel Branch-and-Cut Algorithm for Production and Inventory Routing Problems","authors":"C. M. Schenekemberg, T. Guimarães, A. A. Chaves, Leandro C. Coelho","doi":"10.1287/trsc.2022.0261","DOIUrl":"https://doi.org/10.1287/trsc.2022.0261","url":null,"abstract":"Production and inventory routing problems consider a single-product supply chain operating under a vendor-managed inventory system. A plant creates a production plan and vehicle routes over a planning horizon to replenish its customers at minimum cost. In this paper, we present two- and three-index formulations, implement a branch-and-cut algorithm based on each formulation, and introduce a local search matheuristic-based algorithm to solve the problem. In order to combine all benefits of each algorithm, we design a parallel framework to integrate all three fronts, called the three-front parallel branch-and-cut algorithm (3FP-B&C). We assess the performance of our method on well-known benchmark instances of the inventory routing problem (IRP) and the production routing problem (PRP). The results show that our 3FP-B&C outperforms by far other approaches from the literature. For the 956 feasible small-size IRP instances, our method proves optimality for 746, being the first exact algorithm to solve all instances with up to two vehicles. 3FP-B&C finds 949 best known solutions (BKS) with 153 new BKS (NBKS). For the large-size set, our method provides two new optimal solutions (OPT), and finds 82% of BKS, being 70% of NBKS for instances with up to five vehicles. This result is more than twice the number of BKS considering all heuristic methods from the literature combined. Finally, our 3FP-B&C finds the best lower bounds (BLB) for 1,169/1,316 instances, outperforming all previous exact algorithms. On the PRP, our method obtained 278 OPT out of the 336 instances of benchmark set of small- and medium-size instances being 19 new ones in addition to 335 BKS (74 NBKS) and 313 BLB (52 new ones). On another set of PRP with medium- and large-size instances, our algorithm finds 1,105 BKS out of 1,440 instances with 584 NBKS. Besides that, our 3FP-B&C is the first exact algorithm to solve the instances with an unlimited fleet, providing the first lower bounds for this subset with an average optimality gap of 0.61%. We also address a very large-size instance set, the second exact algorithm to address this set, outperforming the previous approach by far. Finally, a comparative analysis of each front shows the gains of the integrated approach. History: This paper has been accepted for the Transportation Science Special Issue: DIMACS Implementation Challenge: Vehicle Routing. Funding: C. M. Schenekemberg was supported by the São Paulo Research Foundation (FAPESP) [Grant 2020/07145-8]. A. A. Chaves was supported by FAPESP [Grants 2018/15417-8 and 2016/01860-1] and Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 312747/2021-7 and 405702/2021-3]. L. C. Coelho was supported by the Canadian Natural Sciences and Engineering Research Council [Grant 2019-00094]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0261 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":" ","pages":""},"PeriodicalIF":4.6,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44304093","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}
Anastasios Kouvelas, M. Saeedmanesh, N. Geroliminis
An alternative approach for real-time network-wide traffic control in cities that has recently gained attention is perimeter flow control. Many studies have shown that this method is more efficient than state-of-the-art adaptive signal control strategies for heterogeneously congested urban networks. The basic concept of such an approach is to partition heterogeneous cities into a small number of homogeneous regions (zones) and apply perimeter control to the interregional flows along the boundaries between regions. The transferring flows are controlled at the traffic intersections located at the borders between regions so as to distribute the congestion in an optimal way and minimize the total delay of the system. The focus of current work is the mathematical formulation of the original nonlinear problem in a linear parameter-varying (LPV) form so that optimal control can be applied in a (rolling horizon) model predictive concept. This work presents the mathematical analysis of the optimal control problem as well as the approximations and simplifications that are assumed in order to derive the formulation of a linear optimization problem. Numerical simulation results for the case of a macroscopic environment (plant) are presented in order to demonstrate the efficiency of the proposed approach. Results for the closed-loop model predictive control scheme are presented for the nonlinear case, which is used as “benchmark,” as well as the linear case. Furthermore, the developed scheme is applied to a large-scale microsimulation of a European city with more than 500 signalized intersections in order to better investigate its applicability to real-life conditions. The simulation experiments demonstrate the effectiveness of the scheme compared with fixed-time control because all of the performance indicators are significantly improved. Funding: This work was supported by Dit4Tram “Distributed Intelligence & Technology for Traffic & Mobility Management” project from the European Union’s Horizon 2020 research and innovation programme under [Grant agreement 953783].
{"title":"A Linear-Parameter-Varying Formulation for Model Predictive Perimeter Control in Multi-Region MFD Urban Networks","authors":"Anastasios Kouvelas, M. Saeedmanesh, N. Geroliminis","doi":"10.1287/trsc.2022.0103","DOIUrl":"https://doi.org/10.1287/trsc.2022.0103","url":null,"abstract":"An alternative approach for real-time network-wide traffic control in cities that has recently gained attention is perimeter flow control. Many studies have shown that this method is more efficient than state-of-the-art adaptive signal control strategies for heterogeneously congested urban networks. The basic concept of such an approach is to partition heterogeneous cities into a small number of homogeneous regions (zones) and apply perimeter control to the interregional flows along the boundaries between regions. The transferring flows are controlled at the traffic intersections located at the borders between regions so as to distribute the congestion in an optimal way and minimize the total delay of the system. The focus of current work is the mathematical formulation of the original nonlinear problem in a linear parameter-varying (LPV) form so that optimal control can be applied in a (rolling horizon) model predictive concept. This work presents the mathematical analysis of the optimal control problem as well as the approximations and simplifications that are assumed in order to derive the formulation of a linear optimization problem. Numerical simulation results for the case of a macroscopic environment (plant) are presented in order to demonstrate the efficiency of the proposed approach. Results for the closed-loop model predictive control scheme are presented for the nonlinear case, which is used as “benchmark,” as well as the linear case. Furthermore, the developed scheme is applied to a large-scale microsimulation of a European city with more than 500 signalized intersections in order to better investigate its applicability to real-life conditions. The simulation experiments demonstrate the effectiveness of the scheme compared with fixed-time control because all of the performance indicators are significantly improved. Funding: This work was supported by Dit4Tram “Distributed Intelligence & Technology for Traffic & Mobility Management” project from the European Union’s Horizon 2020 research and innovation programme under [Grant agreement 953783].","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":" ","pages":""},"PeriodicalIF":4.6,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47110617","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}
Isaac Balster, Teobaldo Bulhões, P. Munari, A. Pessoa, R. Sadykov
We propose a new family of formulations with route-based variables for the split delivery vehicle routing problem with and without time windows. Each formulation in this family is characterized by the maximum number of different demand quantities that can be delivered to a customer during a vehicle visit. As opposed to previous formulations in the literature, the exact delivery quantities are not always explicitly known in this new family. The validity of these formulations is ensured by an exponential set of nonrobust constraints. Additionally, we explore a property of optimal solutions that enables us to determine a minimum delivery quantity based on customer demand and vehicle capacity, and this number is often greater than one. We use this property to reduce the number of possible delivery quantities in our formulations, improving the solution times of the computationally strongest formulation in the family. Furthermore, we propose new variants of nonrobust cutting planes that strengthen the formulations, namely limited-memory subset-row covering inequalities and limited-memory strong k-path inequalities. Finally, we develop a branch-cut-and-price (BCP) algorithm to solve our formulations enriched with the proposed valid inequalities, which resorts to state-of-the-art algorithmic enhancements. We show how to effectively manage the nonrobust cuts when solving the pricing problem that dynamically generates route variables. Numerical results indicate that our formulations and BCP algorithm establish new state-of-the-art results for the variant with time windows, as many benchmark instances with 50 and 100 customers are solved to optimality for the first time. Several instances of the variant without time windows are solved to proven optimality for the first time. Funding: This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 306033/2019-4, 313220/2020-4, and 314088/2021-0], the Région Nouvelle Aquitaine, France [Grant AAPR2020A-2020-8601810], the Agence Nationale de la Recherche [Grant ANR-20-CE40-0021-01], the Fundação de Amparo à Pesquisa do Estado de São Paulo [Grants 13/07375-0, 16/01860-1, and 19/23596-2], and the Paraíba State Research Foundation [Grants 261/2020 and 041/2023]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0085 .
{"title":"A New Family of Route Formulations for Split Delivery Vehicle Routing Problems","authors":"Isaac Balster, Teobaldo Bulhões, P. Munari, A. Pessoa, R. Sadykov","doi":"10.1287/trsc.2022.0085","DOIUrl":"https://doi.org/10.1287/trsc.2022.0085","url":null,"abstract":"We propose a new family of formulations with route-based variables for the split delivery vehicle routing problem with and without time windows. Each formulation in this family is characterized by the maximum number of different demand quantities that can be delivered to a customer during a vehicle visit. As opposed to previous formulations in the literature, the exact delivery quantities are not always explicitly known in this new family. The validity of these formulations is ensured by an exponential set of nonrobust constraints. Additionally, we explore a property of optimal solutions that enables us to determine a minimum delivery quantity based on customer demand and vehicle capacity, and this number is often greater than one. We use this property to reduce the number of possible delivery quantities in our formulations, improving the solution times of the computationally strongest formulation in the family. Furthermore, we propose new variants of nonrobust cutting planes that strengthen the formulations, namely limited-memory subset-row covering inequalities and limited-memory strong k-path inequalities. Finally, we develop a branch-cut-and-price (BCP) algorithm to solve our formulations enriched with the proposed valid inequalities, which resorts to state-of-the-art algorithmic enhancements. We show how to effectively manage the nonrobust cuts when solving the pricing problem that dynamically generates route variables. Numerical results indicate that our formulations and BCP algorithm establish new state-of-the-art results for the variant with time windows, as many benchmark instances with 50 and 100 customers are solved to optimality for the first time. Several instances of the variant without time windows are solved to proven optimality for the first time. Funding: This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 306033/2019-4, 313220/2020-4, and 314088/2021-0], the Région Nouvelle Aquitaine, France [Grant AAPR2020A-2020-8601810], the Agence Nationale de la Recherche [Grant ANR-20-CE40-0021-01], the Fundação de Amparo à Pesquisa do Estado de São Paulo [Grants 13/07375-0, 16/01860-1, and 19/23596-2], and the Paraíba State Research Foundation [Grants 261/2020 and 041/2023]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0085 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":" ","pages":""},"PeriodicalIF":4.6,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45418742","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 optimization or network design with an embedded traffic assignment (TA) to model user equilibrium principle, sometimes expressed as bilevel problems or mathematical programs with equilibrium constraints (MPEC), is at the heart of transportation planning and operations. For applications to large-scale multimodal networks with high dimensional decision variables, the problem is nontrivial, to say the least. General-purpose algorithms and problem-specific bilevel formulations have been proposed in the past to solve small problems for demonstration purposes. Research gap, however, exists in developing efficient solution methods for large-scale problems in both static and dynamic contexts. This paper proposes an efficient gradient estimation method called Iterative Backpropagation (IB) for network optimization problems with an embedded static TA model. IB exploits the iterative structure of the TA solution procedure and simultaneously calculates the gradients while the TA process converges. IB does not require any additional function evaluation and consequently scales very well with higher dimensions. We apply the proposed approach to origin-destination (OD) estimation, an MPEC problem, of the Hong Kong multimodal network with 49,806 decision variables, 8,797 nodes, 18,207 links, 2,684 transit routes, and 165,509 OD pairs. The calibrated model performs well in matching the link counts. Specifically, the IB-gradient based optimization technique reduces the link volume squared error by 98%, mean absolute percentage error (MAPE) from 95.29% to 21.23%, and the average GEH statistics from 24.18 to 6.09 compared with the noncalibrated case. The framework, even though applied to OD estimation in this paper, is applicable to a wide variety of optimization problems with an embedded TA model, opening up an efficient way to solve large-scale MPEC or bilevel problems. Funding: The study is supported by IVADO Postdoctoral Fellowship scheme 2021, HSBC 150th Anniversary Charity Programme HKBF17RG01, National Science Foundation of China (No. 71890970, No. 71890974), General Research Fund (No. 16212819, No. 16207920) of the HKSAR Government, and the Hong Kong PhD Fellowship.
{"title":"Iterative Backpropagation Method for Efficient Gradient Estimation in Bilevel Network Equilibrium Optimization Problems","authors":"A. Patwary, Shuling Wang, H. Lo","doi":"10.1287/trsc.2021.0110","DOIUrl":"https://doi.org/10.1287/trsc.2021.0110","url":null,"abstract":"Network optimization or network design with an embedded traffic assignment (TA) to model user equilibrium principle, sometimes expressed as bilevel problems or mathematical programs with equilibrium constraints (MPEC), is at the heart of transportation planning and operations. For applications to large-scale multimodal networks with high dimensional decision variables, the problem is nontrivial, to say the least. General-purpose algorithms and problem-specific bilevel formulations have been proposed in the past to solve small problems for demonstration purposes. Research gap, however, exists in developing efficient solution methods for large-scale problems in both static and dynamic contexts. This paper proposes an efficient gradient estimation method called Iterative Backpropagation (IB) for network optimization problems with an embedded static TA model. IB exploits the iterative structure of the TA solution procedure and simultaneously calculates the gradients while the TA process converges. IB does not require any additional function evaluation and consequently scales very well with higher dimensions. We apply the proposed approach to origin-destination (OD) estimation, an MPEC problem, of the Hong Kong multimodal network with 49,806 decision variables, 8,797 nodes, 18,207 links, 2,684 transit routes, and 165,509 OD pairs. The calibrated model performs well in matching the link counts. Specifically, the IB-gradient based optimization technique reduces the link volume squared error by 98%, mean absolute percentage error (MAPE) from 95.29% to 21.23%, and the average GEH statistics from 24.18 to 6.09 compared with the noncalibrated case. The framework, even though applied to OD estimation in this paper, is applicable to a wide variety of optimization problems with an embedded TA model, opening up an efficient way to solve large-scale MPEC or bilevel problems. Funding: The study is supported by IVADO Postdoctoral Fellowship scheme 2021, HSBC 150th Anniversary Charity Programme HKBF17RG01, National Science Foundation of China (No. 71890970, No. 71890974), General Research Fund (No. 16212819, No. 16207920) of the HKSAR Government, and the Hong Kong PhD Fellowship.","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":" ","pages":""},"PeriodicalIF":4.6,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44205640","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}
We study a server routing-scheduling problem in a distributed queueing system, where the system consists of multiple queues at different locations. In a distributed queueing system, servers are shared among multiple queues, and they travel between queues in response to stochastic and time-varying demands. Although server traveling can improve service levels and shorten queue lengths, server routing and scheduling is complicated. We propose a dynamic programming model to solve this special routing-scheduling problem with time-varying demand, stochastic travel time, and queue-length constraints. In order to tackle large-scale practical instances, we design a dynamic programming-based rollout heuristic algorithm. Experiments on large-scale airports and scenic spots show that our approach reduces the total working periods of servers/employees without violating queue-length constraints. Furthermore, we demonstrate that our algorithm outperforms existing benchmark methods and the practical schedules of a scenic spot. Funding: Financial support from the National Natural Science Foundation of China [Grant 71972133] is gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0099 .
{"title":"Server Routing-Scheduling Problem in Distributed Queueing System with Time-Varying Demand and Queue Length Control","authors":"Zerui Wu, Ran Liu, E. Pan","doi":"10.1287/trsc.2022.0099","DOIUrl":"https://doi.org/10.1287/trsc.2022.0099","url":null,"abstract":"We study a server routing-scheduling problem in a distributed queueing system, where the system consists of multiple queues at different locations. In a distributed queueing system, servers are shared among multiple queues, and they travel between queues in response to stochastic and time-varying demands. Although server traveling can improve service levels and shorten queue lengths, server routing and scheduling is complicated. We propose a dynamic programming model to solve this special routing-scheduling problem with time-varying demand, stochastic travel time, and queue-length constraints. In order to tackle large-scale practical instances, we design a dynamic programming-based rollout heuristic algorithm. Experiments on large-scale airports and scenic spots show that our approach reduces the total working periods of servers/employees without violating queue-length constraints. Furthermore, we demonstrate that our algorithm outperforms existing benchmark methods and the practical schedules of a scenic spot. Funding: Financial support from the National Natural Science Foundation of China [Grant 71972133] is gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0099 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":"1 1","pages":""},"PeriodicalIF":4.6,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41364166","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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