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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
G. Tilg, Lukas Ambühl, S. Batista, M. Menéndez, L. Leclercq, F. Busch
The design of network-wide traffic management schemes or transport policies for urban areas requires computationally efficient traffic models. The macroscopic fundamental diagram (MFD) is a promising tool for such applications. Unfortunately, empirical MFDs are not always available, and semi-analytical estimation methods require a reduction of the network to a corridor that introduces substantial inaccuracies. We propose a semi-analytical methodology to estimate the MFD for realistic urban networks without the information loss induced by the reduction of networks to corridors. The methodology is based on the method of cuts but applies to networks with irregular topologies, accounts for different spatial demand patterns, and determines the upper bound of network flow. Therefore, we consider both flow conservation and the effects of spillbacks at the network level. Our framework decomposes a given network into a set of corridors, creates a hypernetwork, including the impacts of source terms, and then treats the dependencies across corridors (e.g., because of turning flows and spillbacks). Based on this hypernetwork, we derive the free-flow and capacity branch of the MFD. The congested branch is estimated by considering gridlock characteristics and utilizing recent advancements in MFD research. We showcase the applicability of the proposed methodology in a case study with a realistic setting based on the Sioux Falls network. We then compare the results to the original method of cuts and a ground truth derived from the cell transmission model. This comparison reveals that our method is more than five times more accurate than the state of the art in estimating the network-wide capacity and jam density. Moreover, the results clearly indicate the MFD’s dependency on spatial demand patterns. Compared with simulation-based MFD estimation approaches, the potential of the proposed framework lies in the modeling flexibility, explanatory value, and reduced computational cost. Funding: G. Tilg acknowledges support from the German Federal Ministry for Digital and Transport (BMDV) for the funding of the project LSS (capacity increase of urban networks). S. F. A. Batista and M. Menéndez acknowledge support from the NYUAD Center for Interacting Urban Networks (CITIES), funded by Tamkeen under the NYUAD Research Institute Award [CG001]. L. Ambühl acknowledges support from the ETH Research Grant [ETH-27 16-1] under the project name SPEED. L. Leclercq acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program Grant [646592 - MAGnUMproject]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0402 .
为城市地区设计全网交通管理方案或交通政策需要计算效率高的交通模型。宏观基本图(MFD)是一种很有前途的工具。不幸的是，经验mfd并不总是可用的，半分析估计方法需要将网络减少到一个引入大量不准确性的走廊。我们提出了一种半解析的方法来估计现实城市网络的MFD，而不考虑网络减少到廊道所导致的信息损失。该方法基于切割方法，但适用于不规则拓扑的网络，考虑了不同的空间需求模式，并确定了网络流量的上限。因此，我们在网络层面同时考虑流量守恒和溢出效应。我们的框架将给定的网络分解为一组走廊，创建一个超网络，包括源项的影响，然后处理跨走廊的依赖关系(例如，由于转向流和溢出)。在此基础上，导出了MFD的自由流分支和容量分支。通过考虑交通阻塞特征和利用MFD研究的最新进展，对拥堵路段进行了估计。我们在一个基于苏福尔斯网络的现实设置的案例研究中展示了所提出方法的适用性。然后，我们将结果与原始切割方法和从细胞传输模型中导出的基础真值进行比较。这一比较表明，我们的方法在估计网络容量和堵塞密度方面比目前的技术水平精确五倍以上。此外，研究结果还清楚地表明，土地利用对空间需求格局的依赖性。与基于仿真的MFD估计方法相比，该框架的潜力在于建模灵活性、解释性和计算成本的降低。资金:G. Tilg感谢德国联邦数字和运输部(BMDV)对LSS(城市网络容量增加)项目的资金支持。S. F. A. Batista和M. menzendz感谢纽约大学城市网络互动中心的支持，该中心由塔姆肯根据纽约大学研究机构奖[CG001]资助。L. amb感谢联邦理工学院研究基金[ETH-27 16-1]在项目名称SPEED下的支持。L. Leclercq承认欧洲研究委员会(ERC)在欧盟地平线2020研究和创新计划拨款[646592 - MAGnUMproject]下的资助。补充材料:电子伴侣可在https://doi.org/10.1287/trsc.2022.0402上获得。
{"title":"From Corridor to Network Macroscopic Fundamental Diagrams: A Semi-Analytical Approximation Approach","authors":"G. Tilg, Lukas Ambühl, S. Batista, M. Menéndez, L. Leclercq, F. Busch","doi":"10.1287/trsc.2022.0402","DOIUrl":"https://doi.org/10.1287/trsc.2022.0402","url":null,"abstract":"The design of network-wide traffic management schemes or transport policies for urban areas requires computationally efficient traffic models. The macroscopic fundamental diagram (MFD) is a promising tool for such applications. Unfortunately, empirical MFDs are not always available, and semi-analytical estimation methods require a reduction of the network to a corridor that introduces substantial inaccuracies. We propose a semi-analytical methodology to estimate the MFD for realistic urban networks without the information loss induced by the reduction of networks to corridors. The methodology is based on the method of cuts but applies to networks with irregular topologies, accounts for different spatial demand patterns, and determines the upper bound of network flow. Therefore, we consider both flow conservation and the effects of spillbacks at the network level. Our framework decomposes a given network into a set of corridors, creates a hypernetwork, including the impacts of source terms, and then treats the dependencies across corridors (e.g., because of turning flows and spillbacks). Based on this hypernetwork, we derive the free-flow and capacity branch of the MFD. The congested branch is estimated by considering gridlock characteristics and utilizing recent advancements in MFD research. We showcase the applicability of the proposed methodology in a case study with a realistic setting based on the Sioux Falls network. We then compare the results to the original method of cuts and a ground truth derived from the cell transmission model. This comparison reveals that our method is more than five times more accurate than the state of the art in estimating the network-wide capacity and jam density. Moreover, the results clearly indicate the MFD’s dependency on spatial demand patterns. Compared with simulation-based MFD estimation approaches, the potential of the proposed framework lies in the modeling flexibility, explanatory value, and reduced computational cost. Funding: G. Tilg acknowledges support from the German Federal Ministry for Digital and Transport (BMDV) for the funding of the project LSS (capacity increase of urban networks). S. F. A. Batista and M. Menéndez acknowledge support from the NYUAD Center for Interacting Urban Networks (CITIES), funded by Tamkeen under the NYUAD Research Institute Award [CG001]. L. Ambühl acknowledges support from the ETH Research Grant [ETH-27 16-1] under the project name SPEED. L. Leclercq acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program Grant [646592 - MAGnUMproject]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0402 .","PeriodicalId":51202,"journal":{"name":"Transportation Science","volume":null,"pages":null},"PeriodicalIF":4.6,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42076122","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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