Restaurant meal delivery companies have begun to provide customers with meal arrival time estimations to inform the customers’ selection. Accurate estimations increase customer experience, whereas inaccurate estimations may lead to dissatisfaction. Estimating arrival times is a challenging prediction problem because of uncertainty in both delivery and meal preparation process. To account for both processes, we present an offline and online-offline estimation approaches. Our offline method uses supervised learning to map state features directly to expected arrival times. Our online-offline method pairs online simulations with an offline approximation of the delivery vehicles’ routing policy, again achieved via supervised learning. Our computational study shows that both methods perform comparably to a full near-optimal online simulation at a fraction of the computational time. We present an extensive analysis on how arrival time estimation changes the experience for customers, restaurants, and the platform. Our results indicate that accurate arrival times not only raise service perception but also improve the overall delivery system by guiding customer selections, effectively resulting in faster delivery and fresher food.
{"title":"Supervised Learning for Arrival Time Estimations in Restaurant Meal Delivery","authors":"F. D. Hildebrandt, M. Ulmer","doi":"10.1287/trsc.2021.1095","DOIUrl":"https://doi.org/10.1287/trsc.2021.1095","url":null,"abstract":"Restaurant meal delivery companies have begun to provide customers with meal arrival time estimations to inform the customers’ selection. Accurate estimations increase customer experience, whereas inaccurate estimations may lead to dissatisfaction. Estimating arrival times is a challenging prediction problem because of uncertainty in both delivery and meal preparation process. To account for both processes, we present an offline and online-offline estimation approaches. Our offline method uses supervised learning to map state features directly to expected arrival times. Our online-offline method pairs online simulations with an offline approximation of the delivery vehicles’ routing policy, again achieved via supervised learning. Our computational study shows that both methods perform comparably to a full near-optimal online simulation at a fraction of the computational time. We present an extensive analysis on how arrival time estimation changes the experience for customers, restaurants, and the platform. Our results indicate that accurate arrival times not only raise service perception but also improve the overall delivery system by guiding customer selections, effectively resulting in faster delivery and fresher food.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"30 1","pages":"1058-1084"},"PeriodicalIF":0.0,"publicationDate":"2021-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78677078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hours of service (HOS) regulations are among the conventional safety constraints that are compiled by long-haul truck drivers. These regulations have been considered in models and algorithms of vehicle routing problems to assign safe schedules to drivers. However, the HOS regulations neglect a few crucial fatigue risk factors and, at times, fail to generate fatigue-reducing schedules. In this study, a set of biomathematical fatigue constraints (BFCs) derived from biomathematical models are considered for a long-haul vehicle routing and scheduling problem. A BFC scheduling algorithm and a BFC-HOS scheduling algorithm have been developed and then embedded within a tabu search heuristic to solve the combined vehicle routing and scheduling problem. All the solution methods have been tested on modified Solomon instances and a real-life instance, and the computational results confirm the advantages of employing a sophisticated and fatigue-reducing scheduling procedure when planning long-haul transportation.
{"title":"Long-Haul Vehicle Routing and Scheduling with Biomathematical Fatigue Constraints","authors":"Jiawei Fu, Liang Ma","doi":"10.1287/trsc.2021.1089","DOIUrl":"https://doi.org/10.1287/trsc.2021.1089","url":null,"abstract":"Hours of service (HOS) regulations are among the conventional safety constraints that are compiled by long-haul truck drivers. These regulations have been considered in models and algorithms of vehicle routing problems to assign safe schedules to drivers. However, the HOS regulations neglect a few crucial fatigue risk factors and, at times, fail to generate fatigue-reducing schedules. In this study, a set of biomathematical fatigue constraints (BFCs) derived from biomathematical models are considered for a long-haul vehicle routing and scheduling problem. A BFC scheduling algorithm and a BFC-HOS scheduling algorithm have been developed and then embedded within a tabu search heuristic to solve the combined vehicle routing and scheduling problem. All the solution methods have been tested on modified Solomon instances and a real-life instance, and the computational results confirm the advantages of employing a sophisticated and fatigue-reducing scheduling procedure when planning long-haul transportation.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"6 1","pages":"404-435"},"PeriodicalIF":0.0,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72758733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper develops a bottleneck model in which the capacity of the bottleneck is assumed to be stochastic and follow a general distribution that has a positive upper bound. The user equilibrium principle in terms of mean trip cost is adopted to formulate commuters’ departure time choice in the stochastic bottleneck. We find that there exist five possible equilibrium departure patterns, which depend on both commuters’ unit costs of travel time, schedule delay early and late, and the uncertainty of the stochastic capacity of the bottleneck. All possible equilibrium departure patterns are analytically derived. Both the analytical and numerical results show that increasing the uncertainty of the capacity of the bottleneck leads to an increase of commuters’ individual mean trip cost. In addition, both a time-varying toll scheme and a single-step coarse toll scheme are designed within the proposed stochastic bottleneck model. We provide an analytical method to determine the detailed toll-charging schemes for both toll strategies. The numerical results show that the proposed toll schemes can indeed improve the efficiency of the stochastic bottleneck in terms of decreasing mean total social cost, and the time-varying toll scheme is more efficient than the single-step coarse toll scheme. However, as the uncertainty of the capacity of the bottleneck increases, the efficiency of the time-varying toll scheme decreases, whereas the efficiency of the single-step coarse toll scheme fluctuates slightly.
{"title":"Departure Time Choice Equilibrium and Tolling Strategies for a Bottleneck with Stochastic Capacity","authors":"J. Long, Hai Yang, W. Y. Szeto","doi":"10.1287/trsc.2021.1039","DOIUrl":"https://doi.org/10.1287/trsc.2021.1039","url":null,"abstract":"This paper develops a bottleneck model in which the capacity of the bottleneck is assumed to be stochastic and follow a general distribution that has a positive upper bound. The user equilibrium principle in terms of mean trip cost is adopted to formulate commuters’ departure time choice in the stochastic bottleneck. We find that there exist five possible equilibrium departure patterns, which depend on both commuters’ unit costs of travel time, schedule delay early and late, and the uncertainty of the stochastic capacity of the bottleneck. All possible equilibrium departure patterns are analytically derived. Both the analytical and numerical results show that increasing the uncertainty of the capacity of the bottleneck leads to an increase of commuters’ individual mean trip cost. In addition, both a time-varying toll scheme and a single-step coarse toll scheme are designed within the proposed stochastic bottleneck model. We provide an analytical method to determine the detailed toll-charging schemes for both toll strategies. The numerical results show that the proposed toll schemes can indeed improve the efficiency of the stochastic bottleneck in terms of decreasing mean total social cost, and the time-varying toll scheme is more efficient than the single-step coarse toll scheme. However, as the uncertainty of the capacity of the bottleneck increases, the efficiency of the time-varying toll scheme decreases, whereas the efficiency of the single-step coarse toll scheme fluctuates slightly.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"93 1","pages":"79-102"},"PeriodicalIF":0.0,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72623952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kai Wang, L. Zhen, Jun Xia, Roberto Baldacci, Shuaian Wang
The consistent vehicle routing problem (ConVRP) aims to design synchronized routes on multiple days to serve a group of customers while minimizing the total travel cost. It stipulates that customers should be visited at roughly the same time (time consistency) by several familiar drivers (driver consistency). This paper generalizes the ConVRP for any level of driver consistency and additionally addresses route consistency, which means that each driver can traverse at most a certain proportion of different arcs of routes on planning days, which guarantees route familiarity. To solve this problem, we develop two set partitioning-based formulations, one based on routes and the other based on schedules. We investigate valid lower bounds on the linear relaxations of both of the formulations that are used to derive a subset of columns (routes and schedules); within the subset are columns of an optimal solution for each formulation. We then solve the reduced problem of either one of the formulations to achieve an optimal solution. Numerical results show that our exact method can effectively solve most of the medium-sized ConVRP instances in the literature and can also solve some newly generated instances involving up to 50 customers. Our exact solutions explore some managerial findings with respect to the adoption of consistency measures in practice. First, maintaining reasonably high levels of consistency requirements does not necessarily always lead to a substantial increase in cost. Second, a high level of time consistency can potentially be guaranteed by adopting a high level of driver consistency. Third, maintaining high levels of time consistency and driver consistency may lead to lower levels of route consistency.
{"title":"Routing Optimization with Generalized Consistency Requirements","authors":"Kai Wang, L. Zhen, Jun Xia, Roberto Baldacci, Shuaian Wang","doi":"10.1287/trsc.2021.1072","DOIUrl":"https://doi.org/10.1287/trsc.2021.1072","url":null,"abstract":"The consistent vehicle routing problem (ConVRP) aims to design synchronized routes on multiple days to serve a group of customers while minimizing the total travel cost. It stipulates that customers should be visited at roughly the same time (time consistency) by several familiar drivers (driver consistency). This paper generalizes the ConVRP for any level of driver consistency and additionally addresses route consistency, which means that each driver can traverse at most a certain proportion of different arcs of routes on planning days, which guarantees route familiarity. To solve this problem, we develop two set partitioning-based formulations, one based on routes and the other based on schedules. We investigate valid lower bounds on the linear relaxations of both of the formulations that are used to derive a subset of columns (routes and schedules); within the subset are columns of an optimal solution for each formulation. We then solve the reduced problem of either one of the formulations to achieve an optimal solution. Numerical results show that our exact method can effectively solve most of the medium-sized ConVRP instances in the literature and can also solve some newly generated instances involving up to 50 customers. Our exact solutions explore some managerial findings with respect to the adoption of consistency measures in practice. First, maintaining reasonably high levels of consistency requirements does not necessarily always lead to a substantial increase in cost. Second, a high level of time consistency can potentially be guaranteed by adopting a high level of driver consistency. Third, maintaining high levels of time consistency and driver consistency may lead to lower levels of route consistency.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"130 2-3 1","pages":"223-244"},"PeriodicalIF":0.0,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75497495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes a two-tier last-mile delivery model that optimally selects mobile depot locations in advance of full information about the availability of crowd-shippers and then transfers packages to crowd-shippers for the final shipment to the customers. Uncertainty in crowd-shipper availability is incorporated by modeling the problem as a two-stage stochastic integer program. Enhanced decomposition solution algorithms including branch-and-cut and cut-and-project frameworks are developed. A risk-averse approach is compared against a risk-neutral approach by assessing conditional-value-at-risk. A detailed computational study based on the City of Toronto is conducted. The deterministic version of the model outperforms a capacitated vehicle routing problem on average by 20%. For the stochastic model, decomposition algorithms usually discover near-optimal solutions within two hours for instances up to a size of 30 mobile depot locations, 40 customers, and 120 crowd-shippers. The cut-and-project approach outperforms the branch-and-cut approach by up to 85% in the risk-averse setting in certain instances. The stochastic model provides solutions that are 3.35%–6.08% better than the deterministic model, and the improvements are magnified with increased uncertainty in crowd-shipper availability. A risk-averse approach leads the operator to send more mobile depots or postpone customer deliveries to reduce the risk of high penalties for nondelivery.
{"title":"Stochastic Last-Mile Delivery with Crowd-Shipping and Mobile Depots","authors":"Kianoush Mousavi, Merve Bodur, M. Roorda","doi":"10.1287/trsc.2021.1088","DOIUrl":"https://doi.org/10.1287/trsc.2021.1088","url":null,"abstract":"This paper proposes a two-tier last-mile delivery model that optimally selects mobile depot locations in advance of full information about the availability of crowd-shippers and then transfers packages to crowd-shippers for the final shipment to the customers. Uncertainty in crowd-shipper availability is incorporated by modeling the problem as a two-stage stochastic integer program. Enhanced decomposition solution algorithms including branch-and-cut and cut-and-project frameworks are developed. A risk-averse approach is compared against a risk-neutral approach by assessing conditional-value-at-risk. A detailed computational study based on the City of Toronto is conducted. The deterministic version of the model outperforms a capacitated vehicle routing problem on average by 20%. For the stochastic model, decomposition algorithms usually discover near-optimal solutions within two hours for instances up to a size of 30 mobile depot locations, 40 customers, and 120 crowd-shippers. The cut-and-project approach outperforms the branch-and-cut approach by up to 85% in the risk-averse setting in certain instances. The stochastic model provides solutions that are 3.35%–6.08% better than the deterministic model, and the improvements are magnified with increased uncertainty in crowd-shipper availability. A risk-averse approach leads the operator to send more mobile depots or postpone customer deliveries to reduce the risk of high penalties for nondelivery.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"20 1","pages":"612-630"},"PeriodicalIF":0.0,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78821403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The “asymmetry” between spatiotemporally varying passenger demand and fixed-capacity transportation supply has been a long-standing problem in urban mass transportation (UMT) systems around the world. The emerging modular autonomous vehicle (MAV) technology offers us an opportunity to close the substantial gap between passenger demand and vehicle capacity through station-wise docking and undocking operations. However, there still lacks an appropriate approach that can solve the operational design problem for UMT corridor systems with MAVs efficiently. To bridge this methodological gap, this paper proposes a continuum approximation (CA) model that can offer near-optimal solutions to the operational design for MAV-based transit corridors very efficiently. We investigate the theoretical properties of the optimal solutions to the investigated problem in a certain (yet not uncommon) case. These theoretical properties allow us to estimate the seat demand of each time neighborhood with the arrival demand curves, which recover the “local impact” property of the investigated problem. With the property, a CA model is properly formulated to decompose the original problem into a finite number of subproblems that can be analytically solved. A discretization heuristic is then proposed to convert the analytical solution from the CA model to feasible solutions to the original problem. With two sets of numerical experiments, we show that the proposed CA model can achieve near-optimal solutions (with gaps less than 4% for most cases) to the investigated problem in almost no time (less than 10 ms) for large-scale instances with a wide range of parameter settings (a commercial solver may even not obtain a feasible solution in several hours). The theoretical properties are verified, and managerial insights regarding how input parameters affect system performance are provided through these numerical results. Additionally, results also reveal that, although the CA model does not incorporate vehicle repositioning decisions, the timetabling decisions obtained by solving the CA model can be easily applied to obtain near-optimal repositioning decisions (with gaps less than 5% in most instances) very efficiently (within 10 ms). Thus, the proposed CA model provides a foundation for developing solution approaches for other problems (e.g., MAV repositioning) with more complex system operation constraints whose exact optimal solution can hardly be found with discrete modeling methods.
{"title":"A Continuous Model for Designing Corridor Systems with Modular Autonomous Vehicles Enabling Station-wise Docking","authors":"Zhiwei Chen, X. Li, X. Qu","doi":"10.1287/trsc.2021.1085","DOIUrl":"https://doi.org/10.1287/trsc.2021.1085","url":null,"abstract":"The “asymmetry” between spatiotemporally varying passenger demand and fixed-capacity transportation supply has been a long-standing problem in urban mass transportation (UMT) systems around the world. The emerging modular autonomous vehicle (MAV) technology offers us an opportunity to close the substantial gap between passenger demand and vehicle capacity through station-wise docking and undocking operations. However, there still lacks an appropriate approach that can solve the operational design problem for UMT corridor systems with MAVs efficiently. To bridge this methodological gap, this paper proposes a continuum approximation (CA) model that can offer near-optimal solutions to the operational design for MAV-based transit corridors very efficiently. We investigate the theoretical properties of the optimal solutions to the investigated problem in a certain (yet not uncommon) case. These theoretical properties allow us to estimate the seat demand of each time neighborhood with the arrival demand curves, which recover the “local impact” property of the investigated problem. With the property, a CA model is properly formulated to decompose the original problem into a finite number of subproblems that can be analytically solved. A discretization heuristic is then proposed to convert the analytical solution from the CA model to feasible solutions to the original problem. With two sets of numerical experiments, we show that the proposed CA model can achieve near-optimal solutions (with gaps less than 4% for most cases) to the investigated problem in almost no time (less than 10 ms) for large-scale instances with a wide range of parameter settings (a commercial solver may even not obtain a feasible solution in several hours). The theoretical properties are verified, and managerial insights regarding how input parameters affect system performance are provided through these numerical results. Additionally, results also reveal that, although the CA model does not incorporate vehicle repositioning decisions, the timetabling decisions obtained by solving the CA model can be easily applied to obtain near-optimal repositioning decisions (with gaps less than 5% in most instances) very efficiently (within 10 ms). Thus, the proposed CA model provides a foundation for developing solution approaches for other problems (e.g., MAV repositioning) with more complex system operation constraints whose exact optimal solution can hardly be found with discrete modeling methods.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"45 1","pages":"1-30"},"PeriodicalIF":0.0,"publicationDate":"2021-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89069396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. V. D. Broek, H. Hoogeveen, M. Akker, B. Huisman
In this paper we consider the train unit shunting problem extended with service task scheduling. This problem originates from Dutch Railways, which is the main railway operator in the Netherlands. Its urgency stems from the upcoming expansion of the rolling stock fleet needed to handle the ever-increasing number of passengers. The problem consists of matching train units arriving on a shunting yard to departing trains, scheduling service tasks such as cleaning and maintenance on the available resources, and parking the trains on the available tracks such that the shunting yard can operate conflict-free. These different aspects lead to a computationally extremely difficult problem, which combines several well-known NP-hard problems. In this paper, we present the first solution method covering all aspects of the shunting and scheduling problem. We describe a partial order schedule representation that captures the full problem, and we present a local search algorithm that utilizes the partial ordering. The proposed solution method is compared with an existing mixed integer linear program in a computational study on realistic instances provided by Dutch Railways. We show that our local search algorithm is the first method to solve real-world problem instances of the complete shunting and scheduling problem. It even outperforms current algorithms when the train unit shunting problem is considered in isolation, that is, without service tasks. Although our method was developed for the case of the Dutch Railways, it is applicable to any shunting yard or service location, irrespective of its layout, that uses self-propelling train units and that does not have to handle passing trains.
{"title":"A Local Search Algorithm for Train Unit Shunting with Service Scheduling","authors":"R. V. D. Broek, H. Hoogeveen, M. Akker, B. Huisman","doi":"10.1287/trsc.2021.1090","DOIUrl":"https://doi.org/10.1287/trsc.2021.1090","url":null,"abstract":"In this paper we consider the train unit shunting problem extended with service task scheduling. This problem originates from Dutch Railways, which is the main railway operator in the Netherlands. Its urgency stems from the upcoming expansion of the rolling stock fleet needed to handle the ever-increasing number of passengers. The problem consists of matching train units arriving on a shunting yard to departing trains, scheduling service tasks such as cleaning and maintenance on the available resources, and parking the trains on the available tracks such that the shunting yard can operate conflict-free. These different aspects lead to a computationally extremely difficult problem, which combines several well-known NP-hard problems. In this paper, we present the first solution method covering all aspects of the shunting and scheduling problem. We describe a partial order schedule representation that captures the full problem, and we present a local search algorithm that utilizes the partial ordering. The proposed solution method is compared with an existing mixed integer linear program in a computational study on realistic instances provided by Dutch Railways. We show that our local search algorithm is the first method to solve real-world problem instances of the complete shunting and scheduling problem. It even outperforms current algorithms when the train unit shunting problem is considered in isolation, that is, without service tasks. Although our method was developed for the case of the Dutch Railways, it is applicable to any shunting yard or service location, irrespective of its layout, that uses self-propelling train units and that does not have to handle passing trains.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"50 1","pages":"141-161"},"PeriodicalIF":0.0,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87024075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Computer-aided air traffic management has increasingly attracted the interest of the operations research community. This includes, among other tasks, the design of decision support tools for the detection and resolution of conflict situations during flight. Even if numerous optimization approaches have been proposed, there has been little debate toward homogenization. We synthesize the efforts made by the operations research community in the past few decades to provide mathematical models to aid conflict detection and resolution at a tactical level. Different mathematical representations of aircraft separation conditions are presented in a unifying analysis. The models, which hinge on these conditions, are then revisited, providing insight into their computational performance.
{"title":"Aircraft Deconfliction via Mathematical Programming: Review and Insights","authors":"Mercedes Pelegrín, C. D’Ambrosio","doi":"10.1287/trsc.2021.1056","DOIUrl":"https://doi.org/10.1287/trsc.2021.1056","url":null,"abstract":"Computer-aided air traffic management has increasingly attracted the interest of the operations research community. This includes, among other tasks, the design of decision support tools for the detection and resolution of conflict situations during flight. Even if numerous optimization approaches have been proposed, there has been little debate toward homogenization. We synthesize the efforts made by the operations research community in the past few decades to provide mathematical models to aid conflict detection and resolution at a tactical level. Different mathematical representations of aircraft separation conditions are presented in a unifying analysis. The models, which hinge on these conditions, are then revisited, providing insight into their computational performance.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"71 1","pages":"118-140"},"PeriodicalIF":0.0,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91477319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper focuses on designing a facility network, taking into account that the system may be congested. The objective is to minimize the overall fixed and service capacity costs, subject to the constraints that for any demand the disutility from travel and waiting times (measured as the weighted sum of the travel time from a demand to the facility serving that demand and the average waiting time at the facility) cannot exceed a predefined maximum allowed level (measured in units of time). We develop an analytical framework for the problem that determines the optimal set of facilities and assigns each facility a service rate (service capacity). In our setting, the consumers would like to maximize their utility (minimize their disutility) when choosing which facility to patronize. Therefore, the eventual choice of facilities is a user-equilibrium problem, where at equilibrium, consumers do not have any incentive to change their choices. The problem is formulated as a nonlinear mixed-integer program. We show how to linearize the nonlinear constraints and solve instead a mixed-integer linear problem, which can be solved efficiently.
{"title":"Probabilistic Set Covering Location Problem in Congested Networks","authors":"Robert Aboolian, O. Berman, Majidreza Karimi","doi":"10.1287/trsc.2021.1096","DOIUrl":"https://doi.org/10.1287/trsc.2021.1096","url":null,"abstract":"This paper focuses on designing a facility network, taking into account that the system may be congested. The objective is to minimize the overall fixed and service capacity costs, subject to the constraints that for any demand the disutility from travel and waiting times (measured as the weighted sum of the travel time from a demand to the facility serving that demand and the average waiting time at the facility) cannot exceed a predefined maximum allowed level (measured in units of time). We develop an analytical framework for the problem that determines the optimal set of facilities and assigns each facility a service rate (service capacity). In our setting, the consumers would like to maximize their utility (minimize their disutility) when choosing which facility to patronize. Therefore, the eventual choice of facilities is a user-equilibrium problem, where at equilibrium, consumers do not have any incentive to change their choices. The problem is formulated as a nonlinear mixed-integer program. We show how to linearize the nonlinear constraints and solve instead a mixed-integer linear problem, which can be solved efficiently.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"33 1","pages":"528-542"},"PeriodicalIF":0.0,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85138269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the problem of collaborative less-than-truckload (LTL) transportation in the form of a shipper consortium, which is operated by a third-party logistics provider (3PL) through a cross-dock/pooling network. The 3PL has responsibility for planning the combined loads prior to actual shipments, hiring and routing carriers to execute shipping, and allocating the cost to the shippers in the consortium. Shippers receive substantial cost savings from combined truckload shipments. However, achieving consolidation and realizing this benefit requires addressing two essential issues: (i) how to find an approximately optimal consolidation solution in a large network with many freights and (ii) how to determine a fair cost allocation rule among the shippers’ consolidated freights that ensures budget balance while minimally violating coalitional stability. Our work resolves these two issues. We formulate a time-space network flow model of the problem under both incremental and all-unit discount structures of LTL rates and propose a computationally efficient algorithm based on local search heuristics. We model the problem of allocating cost to the shippers as a cooperative game. We decompose and linearize the Lagrangian dual problem by using total unimodularity and concavity. We propose an efficiently computable cost allocation rule from the linearized dual models. The dual rule ensures stable cooperation but may have underallocation equal to a duality gap. To cover the underallocation, we further develop a budget covering procedure and define an [Formula: see text]-core allocation with desirable properties. Through extensive computational experiments, we find that the shipper consortium reduces total shipping costs by more than 40% in most cases; meanwhile, the [Formula: see text]-core allocation is typically in the core for small-scale networks while violating stability by at most 5% for large-scale networks and provides consolidated freights with more than 50% individual cost savings on average.
{"title":"Cost Allocation for Less-Than-Truckload Collaboration via Shipper Consortium","authors":"Minghui Lai, Xiaoqiang Cai, Nicholas G. Hall","doi":"10.1287/trsc.2021.1066","DOIUrl":"https://doi.org/10.1287/trsc.2021.1066","url":null,"abstract":"We study the problem of collaborative less-than-truckload (LTL) transportation in the form of a shipper consortium, which is operated by a third-party logistics provider (3PL) through a cross-dock/pooling network. The 3PL has responsibility for planning the combined loads prior to actual shipments, hiring and routing carriers to execute shipping, and allocating the cost to the shippers in the consortium. Shippers receive substantial cost savings from combined truckload shipments. However, achieving consolidation and realizing this benefit requires addressing two essential issues: (i) how to find an approximately optimal consolidation solution in a large network with many freights and (ii) how to determine a fair cost allocation rule among the shippers’ consolidated freights that ensures budget balance while minimally violating coalitional stability. Our work resolves these two issues. We formulate a time-space network flow model of the problem under both incremental and all-unit discount structures of LTL rates and propose a computationally efficient algorithm based on local search heuristics. We model the problem of allocating cost to the shippers as a cooperative game. We decompose and linearize the Lagrangian dual problem by using total unimodularity and concavity. We propose an efficiently computable cost allocation rule from the linearized dual models. The dual rule ensures stable cooperation but may have underallocation equal to a duality gap. To cover the underallocation, we further develop a budget covering procedure and define an [Formula: see text]-core allocation with desirable properties. Through extensive computational experiments, we find that the shipper consortium reduces total shipping costs by more than 40% in most cases; meanwhile, the [Formula: see text]-core allocation is typically in the core for small-scale networks while violating stability by at most 5% for large-scale networks and provides consolidated freights with more than 50% individual cost savings on average.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"8 1","pages":"585-611"},"PeriodicalIF":0.0,"publicationDate":"2021-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75233523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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