Benders decomposition is a broadly used exact solution method for stochastic programs, which has been increasingly applied to solve transportation and logistics planning problems under uncertainty. However, this strategy comes with important drawbacks, such as a weak master problem following the relaxation step that confines the dual cuts to the scenario subproblems. In this paper, we propose a partial Benders decomposition methodology, based on the idea of including explicit information from the scenario subproblems in the master. To investigate the benefits of this methodology, we apply it to solve a general class of two-stage stochastic multicommodity network design models. Specifically, we solve the challenging variant of the model where both the demands and the arc capacities are stochastic. Through an extensive experimental campaign, we clearly show that the proposed methodology yields significant benefits in computational efficiency, solution quality, and stability of the solution process.
{"title":"Partial Benders Decomposition: General Methodology and Application to Stochastic Network Design","authors":"T. Crainic, Mike Hewitt, F. Maggioni, W. Rei","doi":"10.1287/trsc.2020.1022","DOIUrl":"https://doi.org/10.1287/trsc.2020.1022","url":null,"abstract":"Benders decomposition is a broadly used exact solution method for stochastic programs, which has been increasingly applied to solve transportation and logistics planning problems under uncertainty. However, this strategy comes with important drawbacks, such as a weak master problem following the relaxation step that confines the dual cuts to the scenario subproblems. In this paper, we propose a partial Benders decomposition methodology, based on the idea of including explicit information from the scenario subproblems in the master. To investigate the benefits of this methodology, we apply it to solve a general class of two-stage stochastic multicommodity network design models. Specifically, we solve the challenging variant of the model where both the demands and the arc capacities are stochastic. Through an extensive experimental campaign, we clearly show that the proposed methodology yields significant benefits in computational efficiency, solution quality, and stability of the solution process.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"2 1","pages":"414-435"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88695711","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}
S. Kumarage, Mehmet Yildirimoglu, Mohsen Ramezani Ghalenoei, Zuduo Zheng
Demand management aiming to optimize system cost while ensuring user compliance in an urban traffic network is a challenging task. This paper introduces a cooperative demand redistribution strategy to optimize network performance through the retiming of departure times within a limited time window. The proposed model minimizes the total time spent in a two-region urban network by incurring minimal disruption to travelers’ departure schedules. Two traffic models based on the macroscopic fundamental diagram (MFD) are jointly implemented to redistribute demand and analyze travelers’ reaction. First, we establish equilibrium conditions via a day-to-day assignment process, which allows travelers to find their preferred departure times. The trip-based MFD model that incorporates individual traveler attributes is implemented in the day-to-day assignment, and it is conjugated with a network-level detour ratio model to incorporate the effect of congestion in individual traveler route choice. This allows us to consider travelers with individual preferences on departure times influenced by desired arrival times, trip lengths, and earliness and lateness costs. Second, we develop a nonlinear optimization problem to minimize the total time spent considering both observed and unobserved demand—that is, travelers opting in and out of the demand management platform. The accumulation-based MFD model that builds on aggregated system representation is implemented as part of the constraints in the nonlinear optimization problem. The results confirm the resourcefulness of the model to address complex two-region traffic dynamics and to increase overall performance by reaching a constrained system optimum scenario while ensuring the applicability at both full and partial user compliance conditions.
{"title":"Schedule-Constrained Demand Management in Two-Region Urban Networks","authors":"S. Kumarage, Mehmet Yildirimoglu, Mohsen Ramezani Ghalenoei, Zuduo Zheng","doi":"10.1287/trsc.2021.1052","DOIUrl":"https://doi.org/10.1287/trsc.2021.1052","url":null,"abstract":"Demand management aiming to optimize system cost while ensuring user compliance in an urban traffic network is a challenging task. This paper introduces a cooperative demand redistribution strategy to optimize network performance through the retiming of departure times within a limited time window. The proposed model minimizes the total time spent in a two-region urban network by incurring minimal disruption to travelers’ departure schedules. Two traffic models based on the macroscopic fundamental diagram (MFD) are jointly implemented to redistribute demand and analyze travelers’ reaction. First, we establish equilibrium conditions via a day-to-day assignment process, which allows travelers to find their preferred departure times. The trip-based MFD model that incorporates individual traveler attributes is implemented in the day-to-day assignment, and it is conjugated with a network-level detour ratio model to incorporate the effect of congestion in individual traveler route choice. This allows us to consider travelers with individual preferences on departure times influenced by desired arrival times, trip lengths, and earliness and lateness costs. Second, we develop a nonlinear optimization problem to minimize the total time spent considering both observed and unobserved demand—that is, travelers opting in and out of the demand management platform. The accumulation-based MFD model that builds on aggregated system representation is implemented as part of the constraints in the nonlinear optimization problem. The results confirm the resourcefulness of the model to address complex two-region traffic dynamics and to increase overall performance by reaching a constrained system optimum scenario while ensuring the applicability at both full and partial user compliance conditions.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"47 1","pages":"857-882"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76851496","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}
{"title":"Thank You and Goodbye","authors":"M. Savelsbergh","doi":"10.1287/trsc.2020.1037","DOIUrl":"https://doi.org/10.1287/trsc.2020.1037","url":null,"abstract":"","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"7 1","pages":"1"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81015905","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}
In this paper, we formally introduce a variant of the inventory routing problem (IRP) that we call the fixed-partition policy IRP (FPP-IRP). In contrast to the classical IRP in which delivery routes are arbitrary, the FPP-IRP partitions customers into mutually exclusive clusters that are fixed throughout the optimization horizon, and distribution is performed separately for each cluster. By restricting the flexibility inherent in the classical IRP, the FPP-IRP attains many potential advantages. First, partitioning reduces the operational complexity of the system and allows a simpler organization of the distribution service. Second, it improves the robustness of the system by isolating disruptions to affected clusters. Third, it can fit the needs and requirements of specific applications in which consistency in the distribution policy, such as familiarity between customers and drivers and route invariance, is required. We present two fixed-partition policies for the IRP together with mathematical formulations and valid inequalities. We also present a worst-case analysis on the performance of these policies. Extensive computational results are presented to show the behavior of these policies and glean insights into their potential benefits.
{"title":"The Fixed-Partition Policy Inventory Routing Problem","authors":"Ali H. Diabat, C. Archetti, Waleed Najy","doi":"10.1287/trsc.2020.1019","DOIUrl":"https://doi.org/10.1287/trsc.2020.1019","url":null,"abstract":"In this paper, we formally introduce a variant of the inventory routing problem (IRP) that we call the fixed-partition policy IRP (FPP-IRP). In contrast to the classical IRP in which delivery routes are arbitrary, the FPP-IRP partitions customers into mutually exclusive clusters that are fixed throughout the optimization horizon, and distribution is performed separately for each cluster. By restricting the flexibility inherent in the classical IRP, the FPP-IRP attains many potential advantages. First, partitioning reduces the operational complexity of the system and allows a simpler organization of the distribution service. Second, it improves the robustness of the system by isolating disruptions to affected clusters. Third, it can fit the needs and requirements of specific applications in which consistency in the distribution policy, such as familiarity between customers and drivers and route invariance, is required. We present two fixed-partition policies for the IRP together with mathematical formulations and valid inequalities. We also present a worst-case analysis on the performance of these policies. Extensive computational results are presented to show the behavior of these policies and glean insights into their potential benefits.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"87 1","pages":"353-370"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89622043","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}
Reducing fuel consumption is a unifying goal across the aviation industry. One fuel-saving opportunity for airlines is reducing contingency fuel loading by dispatchers. Many airlines’ flight planning systems (FPSs) provide recommended contingency fuel for dispatchers in the form of statistical contingency fuel (SCF). However, because of limitations of the current SCF estimation procedure, the application of SCF is limited. In this study, we propose to use quantile regression–based machine learning methods to account for fuel burn uncertainties and estimate more reliable SCF values. Utilizing a large fuel burn data set from a major U.S.-based airline, we find that the proposed quantile regression method outperforms the airline’s FPS. The benefit of applying the improved SCF models is estimated to be in the range $19 million–$65 million in fuel expense savings as well as 132 million–451 million kilograms of carbon dioxide emission reductions per year, with the lower savings being realized even while maintaining the current, extremely low risk of tapping the reserve fuel. The proposed models can also be used to predict benefits from reduced fuel loading enabled by increasing system predictability, for example, with improved air traffic management.
{"title":"Quantile Regression-Based Estimation of Dynamic Statistical Contingency Fuel","authors":"Lei Kang, M. Hansen","doi":"10.1287/trsc.2020.0997","DOIUrl":"https://doi.org/10.1287/trsc.2020.0997","url":null,"abstract":"Reducing fuel consumption is a unifying goal across the aviation industry. One fuel-saving opportunity for airlines is reducing contingency fuel loading by dispatchers. Many airlines’ flight planning systems (FPSs) provide recommended contingency fuel for dispatchers in the form of statistical contingency fuel (SCF). However, because of limitations of the current SCF estimation procedure, the application of SCF is limited. In this study, we propose to use quantile regression–based machine learning methods to account for fuel burn uncertainties and estimate more reliable SCF values. Utilizing a large fuel burn data set from a major U.S.-based airline, we find that the proposed quantile regression method outperforms the airline’s FPS. The benefit of applying the improved SCF models is estimated to be in the range $19 million–$65 million in fuel expense savings as well as 132 million–451 million kilograms of carbon dioxide emission reductions per year, with the lower savings being realized even while maintaining the current, extremely low risk of tapping the reserve fuel. The proposed models can also be used to predict benefits from reduced fuel loading enabled by increasing system predictability, for example, with improved air traffic management.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"62 1","pages":"257-273"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83987805","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. Oliveira, Alessandro V. M. Oliveira, G. Lohmann
By focusing on the intrinsic relationship between business models and network configurations in the airline industry, this paper develops a two-stage methodology to estimate the strategic drivers of network design of the major carriers in Brazil. The empirical approach decomposes their domestic network-building rationales into the ones adopted by virtual archetypical carriers. We consider the previously conceived low-cost, full-service, and regional carrier archetypes. Our main contribution is the development of a model that allows airlines' networks to be strategically designed in a timeevolving pattern, reflecting a dynamically chosen blend of these archetypes. Moreover, we also consider the effects that mergers and acquisitions may have had in inducing changes in these blends. Our results suggest that all analyzed airlines have repositioned themselves through their trajectories to adopt a hybrid configuration, aiming at the intersection of at least two archetypical networkdesign rationales. Besides, the effects of consolidations point to certain diversions of the acquiring airlines' domestic network-building rationales towards the ones of the acquired carriers, providing evidence that the consolidations may have served as stepping stones for market-repositioning moves.
{"title":"A Network-Design Analysis of Airline Business Model Adaptation in the Face of Competition and Consolidation","authors":"R. Oliveira, Alessandro V. M. Oliveira, G. Lohmann","doi":"10.1287/trsc.2020.1025","DOIUrl":"https://doi.org/10.1287/trsc.2020.1025","url":null,"abstract":"By focusing on the intrinsic relationship between business models and network configurations in the airline industry, this paper develops a two-stage methodology to estimate the strategic drivers of network design of the major carriers in Brazil. The empirical approach decomposes their domestic network-building rationales into the ones adopted by virtual archetypical carriers. We consider the previously conceived low-cost, full-service, and regional carrier archetypes. Our main contribution is the development of a model that allows airlines' networks to be strategically designed in a timeevolving pattern, reflecting a dynamically chosen blend of these archetypes. Moreover, we also consider the effects that mergers and acquisitions may have had in inducing changes in these blends. Our results suggest that all analyzed airlines have repositioned themselves through their trajectories to adopt a hybrid configuration, aiming at the intersection of at least two archetypical networkdesign rationales. Besides, the effects of consolidations point to certain diversions of the acquiring airlines' domestic network-building rationales towards the ones of the acquired carriers, providing evidence that the consolidations may have served as stepping stones for market-repositioning moves.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"35 1","pages":"532-548"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84683397","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}
Camilo Ortiz-Astorquiza, J. Cordeau, Emma Frejinger
Some of the most important optimization problems faced by railway operators arise from the management of their locomotive fleet. In this paper, we study a general version of the locomotive assignment problem encountered at the tactical level by one of the largest railroads in North America: the Canadian National Railway Company (CN). We present a modeling framework with two integer linear programming formulations and contribute to the state of the art by allowing to decide each train's operating mode (distributed power or not) over the whole (weekly) planning horizon without partitioning it into smaller time windows. Given the difficulty to solve the problem, one of the formulations is enhanced through various refinements such as constraint relaxations, preprocessing and fixed cost approximations. We thus achieve a significant reduction in the required computational time to solve instances of realistic size. We also present two versions of a Benders decomposition-based algorithm to obtain feasible solutions. On average, it allows to reduce the associated computational time by two hours. Results from an extensive computational study and a case study with data provided by CN confirm the potential benefits of the model and solution approach.
{"title":"The Locomotive Assignment Problem with Distributed Power at the Canadian National Railway Company","authors":"Camilo Ortiz-Astorquiza, J. Cordeau, Emma Frejinger","doi":"10.1287/trsc.2020.1030","DOIUrl":"https://doi.org/10.1287/trsc.2020.1030","url":null,"abstract":"Some of the most important optimization problems faced by railway operators arise from the management of their locomotive fleet. In this paper, we study a general version of the locomotive assignment problem encountered at the tactical level by one of the largest railroads in North America: the Canadian National Railway Company (CN). We present a modeling framework with two integer linear programming formulations and contribute to the state of the art by allowing to decide each train's operating mode (distributed power or not) over the whole (weekly) planning horizon without partitioning it into smaller time windows. Given the difficulty to solve the problem, one of the formulations is enhanced through various refinements such as constraint relaxations, preprocessing and fixed cost approximations. We thus achieve a significant reduction in the required computational time to solve instances of realistic size. We also present two versions of a Benders decomposition-based algorithm to obtain feasible solutions. On average, it allows to reduce the associated computational time by two hours. Results from an extensive computational study and a case study with data provided by CN confirm the potential benefits of the model and solution approach.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"7 1","pages":"510-531"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76765583","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}
Emergency Medical Service systems aim to respond to emergency calls in a timely manner and provide prehospital care to patients. This paper addresses the problem of locating multiple types of emergency vehicles to stations while taking into account that vehicles are dispatched to prioritized patients with different health needs. We propose a two-stage stochastic-programming model that determines how to locate two types of ambulances in the first stage and dispatch them to prioritized emergency patients in the second stage after call-arrival scenarios are disclosed. We demonstrate how the base model can be adapted to include nontransport vehicles. A model formulation generalizes the base model to consider probabilistic travel times and general utilities for dispatching ambulances to prioritized patients. We evaluate the benefit of the model using two case studies, a value of the stochastic solution approach, and a simulation analysis. The case study is extended to study how to locate vehicles in the model extension with nontransport vehicles. Stochastic-programming models are computationally challenging for large-scale problem instances, and, therefore, we propose a solution technique based on Benders cuts.
{"title":"A Stochastic Programming Approach for Locating and Dispatching Two Types of Ambulances","authors":"Soovin Yoon, Laura A. Albert, V. White","doi":"10.1287/trsc.2020.1023","DOIUrl":"https://doi.org/10.1287/trsc.2020.1023","url":null,"abstract":"Emergency Medical Service systems aim to respond to emergency calls in a timely manner and provide prehospital care to patients. This paper addresses the problem of locating multiple types of emergency vehicles to stations while taking into account that vehicles are dispatched to prioritized patients with different health needs. We propose a two-stage stochastic-programming model that determines how to locate two types of ambulances in the first stage and dispatch them to prioritized emergency patients in the second stage after call-arrival scenarios are disclosed. We demonstrate how the base model can be adapted to include nontransport vehicles. A model formulation generalizes the base model to consider probabilistic travel times and general utilities for dispatching ambulances to prioritized patients. We evaluate the benefit of the model using two case studies, a value of the stochastic solution approach, and a simulation analysis. The case study is extended to study how to locate vehicles in the model extension with nontransport vehicles. Stochastic-programming models are computationally challenging for large-scale problem instances, and, therefore, we propose a solution technique based on Benders cuts.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"95 1","pages":"275-296"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78542023","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}
In the future, road traffic will incorporate a random mix of manual vehicles and cooperative adaptive cruise control (CACC) vehicles, where a CACC vehicle will degrade to an adaptive cruise control (ACC) vehicle when vehicle-to-vehicle communications are not available. This paper proposes a generalized framework of the Lighthill-Whitham-Richards (LWR) model for such mixed vehicular flow under different CACC penetration rates. In this approach, the kinematic wave speed propagating through the mixed platoon was theoretically proven to be the slope of mixed fundamental diagram. In addition, the random degradation from CACC to ACC was captured in mathematical expectation for traffic scenarios where the CACC only monitors one vehicle ahead. Three concrete car-following models, the intelligent driver model (IDM) and CACC/ACC models validated by Partners for Advanced Transit and Highways (PATH) program, were selected as examples to investigate the propagation of small perturbations and shock waves. Numerical simulations were also performed based on the selected car-following models. Moreover, the derived mixed LWR model was applied to solve some traffic flow problems. It indicates that the proposed LWR model is able to describe the propagation properties of both small perturbations and shock waves. The mixed LWR model can also be used to solve some practical problems, such as the queue caused by a traffic accident and the impact of a moving bottleneck. More importantly, the proposed generalized framework admits other CACC/ACC/regular car-following models, including those developed from further experiments.
{"title":"Lighthill-Whitham-Richards Model for Traffic Flow Mixed with Cooperative Adaptive Cruise Control Vehicles","authors":"Yanyan Qin, Hao Wang, Daiheng Ni","doi":"10.1287/trsc.2021.1057","DOIUrl":"https://doi.org/10.1287/trsc.2021.1057","url":null,"abstract":"In the future, road traffic will incorporate a random mix of manual vehicles and cooperative adaptive cruise control (CACC) vehicles, where a CACC vehicle will degrade to an adaptive cruise control (ACC) vehicle when vehicle-to-vehicle communications are not available. This paper proposes a generalized framework of the Lighthill-Whitham-Richards (LWR) model for such mixed vehicular flow under different CACC penetration rates. In this approach, the kinematic wave speed propagating through the mixed platoon was theoretically proven to be the slope of mixed fundamental diagram. In addition, the random degradation from CACC to ACC was captured in mathematical expectation for traffic scenarios where the CACC only monitors one vehicle ahead. Three concrete car-following models, the intelligent driver model (IDM) and CACC/ACC models validated by Partners for Advanced Transit and Highways (PATH) program, were selected as examples to investigate the propagation of small perturbations and shock waves. Numerical simulations were also performed based on the selected car-following models. Moreover, the derived mixed LWR model was applied to solve some traffic flow problems. It indicates that the proposed LWR model is able to describe the propagation properties of both small perturbations and shock waves. The mixed LWR model can also be used to solve some practical problems, such as the queue caused by a traffic accident and the impact of a moving bottleneck. More importantly, the proposed generalized framework admits other CACC/ACC/regular car-following models, including those developed from further experiments.","PeriodicalId":23247,"journal":{"name":"Transp. Sci.","volume":"146 1","pages":"883-907"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77523124","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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