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    <title>Transport Research International Documentation (TRID)</title>
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    <copyright>Copyright © 2026. National Academy of Sciences. All rights reserved.</copyright>
    <docs>http://blogs.law.harvard.edu/tech/rss</docs>
    <managingEditor>tris-trb@nas.edu (Bill McLeod)</managingEditor>
    <webMaster>tris-trb@nas.edu (Bill McLeod)</webMaster>
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      <title>Transport Research International Documentation (TRID)</title>
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      <link>https://trid.trb.org/</link>
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    <item>
      <title>Input Misallocation and Cost Penalties in U.S. Airlines: A Pre/Post COVID-19 Comparison of Full-Service Airlines and Low-Cost Carriers</title>
      <link>https://trid.trb.org/View/2669573</link>
      <description><![CDATA[Labor shortages triggered by the COVID-19 pandemic have significantly constrained U.S. airlines’ ability to allocate resources efficiently and minimize costs. This study investigates how these labor disruptions affect cost structures across different airline business models, specifically full-service airlines (FSAs) and low-cost carriers (LCCs). Using a primal approach, we examine how airlines adjust their use of labor, fuel, and capital inputs, and quantify the resulting cost penalties from input misallocation over the period 2010 to 2024. Our results reveal that, during the pre-pandemic period, FSAs consistently overused labor, while LCCs disproportionately relied on capital and fuel relative to labor. The associated cost penalties from these allocative inefficiencies were 1.7% for FSAs and 3.4% for LCCs. In the post-pandemic period, both FSAs and LCCs increasingly overused labor in response to staffing shortages and rising wages. However, the cost impact of labor overuse remained relatively modest, averaging 1.2% across both models as labor exhibits a lower marginal cost relative to capital and fuel. A key insight for decision makers is that not all input distortions carry equal cost risk. While labor shortages remain a critical operational concern, the short-term cost of labor overuse may be less severe than the consequences of underutilizing higher-cost inputs like capital and fuel. For FSAs, rigid legacy labor structures reduce workforce flexibility, whereas for LCCs, constraints from decreasing returns to scale require more precise resource planning. To maintain cost efficiency amid persistent labor challenges, improving workforce productivity and adopting upgauging strategies emerge as practical and effective solutions.]]></description>
      <pubDate>Tue, 12 May 2026 09:11:57 GMT</pubDate>
      <guid>https://trid.trb.org/View/2669573</guid>
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    <item>
      <title>Approximating Shapley values with subcoalition Shapley values in routing problems</title>
      <link>https://trid.trb.org/View/2682115</link>
      <description><![CDATA[The Shapley value is a widely recognized method for fair cost allocation in cooperative game theory. However, its computational intensity makes it challenging to apply in routing problems, particularly for allocating costs among customers. To address this issue, we propose a new approximation method called β Subcoalition Shapley Approximation, which is based on the mean weighted Shapley values of subcoalitions with exactly β customers. We test this approximation method for the traveling salesman problem as well as for the capacitated vehicle routing problem. Through an extensive numerical study, we demonstrate that our approximation provides excellent results, representing a good trade-of between approximation quality and computational intensity compared to other methods. Moreover, our approximation method is not limited to routing problems but can also be applied to other Shapley value applications, particularly suitable for NP-hard underlying problems where computation time increases dramatically with increasing instance size.]]></description>
      <pubDate>Mon, 27 Apr 2026 15:01:16 GMT</pubDate>
      <guid>https://trid.trb.org/View/2682115</guid>
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    <item>
      <title>Decision-focused learning for optimal subsidy allocation in ride-hailing services</title>
      <link>https://trid.trb.org/View/2594536</link>
      <description><![CDATA[Effective subsidy strategies are essential for ride-hailing platforms. The key is to accurately predict trip completion rates before determining the optimal subsidy decision. However, the classic predict-then-optimize framework often falls short due to discrepancies between the prediction model, which minimizes fitting error, and the decision model, which minimizes decision error. To tackle the above issues, this paper presents a decision-focused learning (DFL) approach for optimal subsidy allocation in ride-hailing services at the city level. First, we formulate the subsidy allocation as a bi-level optimization problem, in which the lower-level individual distribution can be approximated via a threshold-based strategy. Moreover, the effect of the subsidy is explicitly modeled, which considers the combined impacts of both pricing and matching aspects. Second, the prediction model for the completion rate is trained to directly minimize downstream decision loss, integrating the prediction module and optimization task in an end-to-end manner. To address the challenge of conducting gradient backpropagation from the decision model to the prediction model, we utilize a surrogate decision-focused loss function, whose convexity in the context of the subsidy allocation problem is theoretically proven. Third, we develop a decision-focused fine-tuning mechanism to handle the non-differentiable prediction model, allowing any upstream prediction model to be adjusted based on the downstream decision loss. The proposed DFL framework is tested on real-world data from DiDi Chuxing. Results show that decision-focused learning can increase platform revenue by 1.51% compared to traditional predict-then-optimize solutions, as the prediction model effectively learns the weights of different cities in the decision objective.]]></description>
      <pubDate>Thu, 20 Nov 2025 17:06:25 GMT</pubDate>
      <guid>https://trid.trb.org/View/2594536</guid>
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    <item>
      <title>Analysis of Truck Use and Highway Cost Allocation in Texas</title>
      <link>https://trid.trb.org/View/2549167</link>
      <description><![CDATA[The highway cost allocation problem is one of determining equitable charges for each of the vehicle classes sharing transportation facilities such as highways and bridges. Previous attempts at solving this problem can essentially be reduced to two major approaches: (a) proportional allocation methods, which determine costs in proportion to one or more measures of highway usage; and (b) incremental methods, which allocate costs on the basis of highway design differences necessary to accommodate gradually heavier vehicle classes. This report develops two new highway cost allocation methodologies that actually extend the basic concepts of the incremental and proportional allocation procedures. The new methods are referred to as the "Modified Incremental Approach" and the "Generalized Method." Both methods fulfill the following conditions: (a) highway costs are completely financed by users (completeness condition); (b) vehicle classes reduce their cost responsibilities by sharing the facilities with other vehicle classes (rationality principle); and (c) vehicle classes are charged at least enough to cover their corresponding marginal costs (marginality principle). An example using Texas pavement data is utilized to illustrate the application of the proposed methods.]]></description>
      <pubDate>Tue, 24 Jun 2025 17:43:09 GMT</pubDate>
      <guid>https://trid.trb.org/View/2549167</guid>
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    <item>
      <title>Texas Highway Cost Allocation Study</title>
      <link>https://trid.trb.org/View/2536075</link>
      <description><![CDATA[The present research project will investigate the fairness of the structure of taxes and charges imposed on Texas highway users. The focus will be on equity between vehicle classes. For each defined vehicle class, the project will estimate the share of total revenues from highway user taxes and charges that the class contributes. For comparison, it will also estimate the share of highway system costs that stem from each class. If the structure of taxes and charges is fully equitable, each class’s revenue share will equal its cost share. This report describes the first phase of the study, which entailed the development of models and databases. The second phase will include scenario-testing based on the results of the first phase; the authors will examine how potential changes to taxes on Texas road users would affect the tax burden on different vehicle classes. Also planned for the second phase are certain refinements to the authors' models and databases.]]></description>
      <pubDate>Tue, 15 Apr 2025 12:06:13 GMT</pubDate>
      <guid>https://trid.trb.org/View/2536075</guid>
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    <item>
      <title>Highway Cost Allocation in Texas: Executive Summary</title>
      <link>https://trid.trb.org/View/2536076</link>
      <description><![CDATA[Vehicle travel on Texas highways generates revenue from state and federal taxes on highway users, such as fuel taxes, and it also creates costs in highway construction and maintenance. This study estimates the 1998 revenue contribution and cost responsibility by class of motor vehicle. If fairness requires that each class pay a share of tax revenue that equals its share of highway system costs, then the findings of the study suggest that passenger cars and pickup trucks are paying more than their fair share, and combination trucks less. The study concludes with recommendations for future research that would complement and enhance the framework developed for this study.]]></description>
      <pubDate>Tue, 15 Apr 2025 12:06:13 GMT</pubDate>
      <guid>https://trid.trb.org/View/2536076</guid>
    </item>
    <item>
      <title>Optimization model for electric aircraft tow tractors scheduling under operator cooperation</title>
      <link>https://trid.trb.org/View/2509629</link>
      <description><![CDATA[Collaborating among operators can significantly reduce transportation costs—a concept already proven in the logistics industry. With growing transportation demand and the added complexity of electric vehicle (EV) charging times, airport ground support services face increasing pressure to optimize operations. This study introduces a novel concept of operator-cooperate mode for airport ground support services for the first time, where operators share vehicle fleets to enhance efficiency. This paper develops vehicle scheduling and cost allocation methods under the cooperation framework. Two models are established for scheduling electric tow tractors: one for the traditional operator-separate mode and another for the operator-cooperate mode. Using an adaptive large neighborhood search framework, algorithms are designed to generate scheduling plans that minimize costs and delays. To support cooperation, the study proposes a cost allocation method that considers differentiated unit delay costs and level of sharing among operators to ensure the feasibility and fairness of cooperation. Finally, numerical experiments are conducted based on one day of flight schedule data from a major international airport, validating the effectiveness of the algorithm and cost allocation method across 21 experimental scenarios. The results show that the algorithm delivers solutions faster than traditional solvers while keeping the weighted objective function gap within 2%.Moreover, the improved cost allocation method ensures greater fairness than the traditional Shapley method. The numerical experiments indicate that cooperation can save 5–16% in operating costs and 15–33% in delay times for airports, with the savings varying based on the sharing parameters. The study also uses sensitivity analysis and other quantitative methods to examine changes in overall and individual cooperated utility changes. It provides recommendations and decision-making strategies for configuring and managing airport ground operations.]]></description>
      <pubDate>Wed, 19 Mar 2025 10:12:08 GMT</pubDate>
      <guid>https://trid.trb.org/View/2509629</guid>
    </item>
    <item>
      <title>Study on the Cost Allocation of Charging Stations Site Selection Based on the Improved Shapley Value Method</title>
      <link>https://trid.trb.org/View/2475483</link>
      <description><![CDATA[In the current scenario, with the vigorous promotion of electric vehicles, there is a growing demand for charging stations among users. Consequently, the strategic selection of optimal site areas for these charging stations has become the key. Considering that after forming the cooperative alliance between the different site areas, the apportionment cost of the cooperative alliance is lower than the cost of separate construction, the authors use the Shapley value method to solve and verify. Furthermore, recognizing that site selection is influenced by various external factors, the study incorporates the Technique for Order of Preference by Similarity to the Ideal Solution (TOPSIS) method to optimize the original method. This integration improves the Shapley value method, rendering the cost allocation within cooperative alliances fairer and more reasonable. In conclusion, the efficiency of this approach is demonstrated through a practical example. The outcomes indicate that the improved Shapley value method comprehensively accounts for the factors affecting the cost allocation of all parties in the alliance, consequently facilitating a more equitable allocation of costs.]]></description>
      <pubDate>Fri, 27 Dec 2024 15:27:22 GMT</pubDate>
      <guid>https://trid.trb.org/View/2475483</guid>
    </item>
    <item>
      <title>Updating Cost Allocation and Revenue Attribution</title>
      <link>https://trid.trb.org/View/2464371</link>
      <description><![CDATA[This report presents the method and results of the 2024 study commissioned by the Indiana Department of Transportation (INDOT) in fall 2023 at the request of the Indiana General Assembly to update Indiana's 2015 Highway Cost Allocation Study. Findings include: (1) Expenditures: Lighter vehicle classes saw their share of cost responsibility decline between 2015 and 2024, while the heavier vehicle classes saw their responsibilities increase within this period. This change is explained by a diametric shift in expenditure type patterns between the two eras from construction-dominant to maintenance-dominant expenditures. In this context, it is worth noting that these expenditure types have different ratios of attributable costs to common costs. (2) Revenues: Fifty-two percent (52%) of all user and non-user revenues are generated at the state level, 36% at the federal level, and 13% at the local level. Vehicle Classes 2 and 9 still contribute the highest shares of revenues—42% and 22%, respectively. Vehicle Class 3 contributes 21% of the revenues, while all other vehicles contribute less than 10% each. Vehicle Class 13 contributes the lowest percentage share at 0.1%. Across the two eras (2015 vs. 2024), Class 2 vehicles saw their revenue share decline from 47% to 42%, but Vehicle Class 9 increased from 20% in the earlier study (2015) to 22% in the current study (2024). Vehicle Class 3 held steady at 21% in both periods, while Classes 5 and 6 saw marginal increases. (3) Equity Ratios: The equity ratio results follow a trend that is like those of past studies in Indiana and elsewhere. Generally, the lower vehicle classes are overpaying their share of cost responsibility and the higher vehicle classes are underpaying their share of cost responsibility. Notable shifts in equity ratios between the previous-era study and the current-era study were observed. Several lighter vehicle classes increased their equity ratios, while the heavier vehicles saw their equity ratios decline significantly between the two periods. Electric vehicles (EVs) in Class 2 and Class 3 generally have lower equity ratios than their internal combustion engine vehicle (ICEV) counterparts, a finding that is intuitive because EVs are associated with relatively higher damage but slightly lower, or similar, revenue contributions. For the forecast years (2030 and 2035), it was observed that EVs in Vehicle Classes 2 and 3 will be underpaying their share of the cost responsibility, while those in Classes 4 and 9 will be overpaying. The current EV fee that exists for these vehicles (if left unchanged) will not adequately cover their cost responsibility or recover the lost fuel tax revenues in 2030 and 2035.]]></description>
      <pubDate>Mon, 16 Dec 2024 09:11:11 GMT</pubDate>
      <guid>https://trid.trb.org/View/2464371</guid>
    </item>
    <item>
      <title>A Profit Distribution Model among Enterprises in Mixed Alliance Based on the Shapley Value</title>
      <link>https://trid.trb.org/View/2283272</link>
      <description><![CDATA[The profit distribution is much important to the formation and management of alliance. Based on the definition of mixed alliance and the explanation of the complexity of profit distribution among enterprises in mixed alliance, the profit distribution model among enterprises in mixed alliance is built by the Shapely value, and each cost distribution value of a supplier and each buyer is obtained.]]></description>
      <pubDate>Thu, 17 Oct 2024 09:15:21 GMT</pubDate>
      <guid>https://trid.trb.org/View/2283272</guid>
    </item>
    <item>
      <title>Optimized Shapley Value Cost Allocation Model for Carriers’ Collaboration in Road Haulage Transportation</title>
      <link>https://trid.trb.org/View/2408239</link>
      <description><![CDATA[Transportation carriers can achieve significant profit or cost savings if they collaborate rather than engage in wasteful competition among themselves. However, the challenge in cooperative game theory is finding the optimal cost allocation methods to support pecuniary expectations of coalition members. In this paper, the authors determine cost allocation model that supports horizontal collaboration among transportation carriers involved in downstream distribution of packaged cement from shipper’s processing plant to customer locations in selected states in Nigeria. The study focuses on the relationship between the shipper and haulage carriers that service the transport needs of its geographically distributed customers. A cost allocation mechanism based on game theory is proposed to implement win-win collaboration among the carriers. The authors applied a Shapley value cost allocation model to fairly distribute the cost savings from operation of five grand coalitions (S) formed by the carriers. The Shapely values were then optimized with mixed integer programming model to realize optimal cost savings from the coalition. The result revealed that the coalitions: S3 (N165,173,700.00) and S4 (N27,200,960.00) contributed significantly to the optimal savings apart from their initial contributions. The path that corresponds to S3 (X3) is the coalition providing service from Calabar to Jos while the path that corresponds to S4 (X4) is the coalition providing service from Calabar to Owerri and the optimal savings is N48,286,760,000.00. Based on these results, the authors therefore encourage horizontal collaboration among haulage transport providers in their overall interest, that of the shipper and hence ensure supply or distribution chain cost efficiency.]]></description>
      <pubDate>Sat, 31 Aug 2024 21:06:08 GMT</pubDate>
      <guid>https://trid.trb.org/View/2408239</guid>
    </item>
    <item>
      <title>A new highway cost allocation framework in the day of connected and autonomous vehicles</title>
      <link>https://trid.trb.org/View/2354476</link>
      <description><![CDATA[The objectives of the present study are to explore potential changes expected in highway infrastructure expenditures and revenues, and develop a robust framework that will facilitate highway cost allocation when connected and autonomous vehicles (CAVs) are in operation. The scope of this study covered both federal and state expenditures and revenue sources. The highway cost allocation elements covered in the paper include vehicle miles of travel, highway expenditures highway revenues, and equity analysis. In the day of CAVs, significant changes are expected in all these elements, and these changes are incorporated into the proposed highway cost allocation framework. Pavement-related expenditures would increase due to the addition of CAV-related infrastructure integrated into the pavement infrastructure to ensure it is an intelligent pavement. Bridge-related expenditures are expected to increase due to the infrastructure technologies on the bridges making them smart bridges, and the design loads of these bridges may have to be increased due to potential platooning on long span bridges. It is expected that many of the CAVs on the road will be electric vehicles. All these changes are incorporated into the proposed highway cost allocation framework.]]></description>
      <pubDate>Tue, 23 Apr 2024 10:53:17 GMT</pubDate>
      <guid>https://trid.trb.org/View/2354476</guid>
    </item>
    <item>
      <title>Study on Location Selection of Urban Two-Level Joint Express Delivery Stations Considering Fair Cost Allocation among Enterprises</title>
      <link>https://trid.trb.org/View/2368135</link>
      <description><![CDATA[The rapid growth of e-commerce has heightened the importance for express delivery companies to ensure timely deliveries. Consequently, it is essential to explore ways to deliver more packages to customers while simultaneously reducing costs through the adoption of a joint distribution mode. This study presents a two-level delivery location selection model within the joint distribution mode, considering factors such as delivery station capacity and the number of transport vehicles, with the objective of minimizing the total cost associated with selecting delivery station locations. The proposed model is addressed using a combination of the k-means algorithm and the improved discrete firefly algorithm. In addition, to facilitate equitable cost allocation among enterprises, the Shapley value method is introduced in this study. A case study based on real data from an urban distribution network in the city of Hebei Province, China, is adopted to perform the experiments. The results of this study indicate that the improved algorithm not only improves solution accuracy but also reduces solution time when compared to both the particle swarm optimization and artificial bee colony methods. Furthermore, the application of the Shapley value method demonstrates the efficacy of a rational allocation of costs.]]></description>
      <pubDate>Thu, 18 Apr 2024 09:26:38 GMT</pubDate>
      <guid>https://trid.trb.org/View/2368135</guid>
    </item>
    <item>
      <title>Highway toll allocation</title>
      <link>https://trid.trb.org/View/2329986</link>
      <description><![CDATA[An important operational aspect in the management of tolled highways is how the collected tolls should be allocated over the different highway segments, either operated by different operators or by different units of one operator. This paper analyzes this toll allocation problem both from an axiomatic and a game theoretic perspective. Based on different toll charging systems, specifically the distance-based toll system and the fixed toll system, the authors propose three allocation or sharing methods: the Segments Equal Sharing method, the Exits Equal Sharing method, and the Entrances Equal Sharing method. After direct and game theoretic characterizations of these methods, the authors apply them to several real-life highways.]]></description>
      <pubDate>Mon, 11 Mar 2024 15:56:17 GMT</pubDate>
      <guid>https://trid.trb.org/View/2329986</guid>
    </item>
    <item>
      <title>Development of a Mechanistic-Empirical-Based Highway Cost Allocation Model for Flexible Pavements</title>
      <link>https://trid.trb.org/View/2325577</link>
      <description><![CDATA[Construction, operation, and maintenance of a pavement network requires funding, partially sourced from road user taxes. Recent studies showed that lightweight vehicles are typically taxed higher compared with heavy trucks that damage the roads the most. To facilitate the equity and fairness of the allocated costs to different vehicles in the United States (U.S.), Highway Cost Allocation Studies (HCAS) were performed using various pavement performance prediction models. Reviewed literature showed the lack of mechanistic-empirical (ME)-based HCAS models for the flexible pavement network. In this study, a national-level ME-based HCAS model was developed, and the damage shares of different vehicle classes have been estimated for 67,583 pavement sections in the U.S. Highway Performance Monitoring System (HPMS) database. The proposed HCAS model was compared with the existing Federal Highway Administration (FHWA) HCAS model (i.e., National Pavement Cost Model [NAPCOM]). The analysis of the traffic data showed that two-axle single-unit trucks (SU2) and tractor-semitrailers with two tandem and one single axle (CS5T) were the most frequent users of the pavement network. The results showed that the damage share of SU2 is dominant in minor roadways, while the damage share of the heavier vehicles in the CS5T class is dominant in major arterials and interstates. In addition, it was found that, although the geographical location and environmental condition of the pavement section affects the magnitude of the pavement distresses, the distribution of the damage shares remains almost the same. This can be attributed to the similarities in the traffic data, for example, vehicle class distribution and axle load spectra.]]></description>
      <pubDate>Tue, 23 Jan 2024 09:13:02 GMT</pubDate>
      <guid>https://trid.trb.org/View/2325577</guid>
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