The increase in congestion in surface traffic, airborne pollution, and other environmental issues has motivated transit authorities to promote public transit worldwide. In large cities and metropolitan areas, adding new rapid transit lines attracts more commuters to the public system, as they often reduce travel time compared to the private mode (car) that faces high congestion. In addition, the travel time has less variability with respect to preset schedules, and rapid lines are more efficient than slow modes operated by buses. When a new rapid transit line is constructed, it partially replaces the traffic of existing slow transit lines. As a consequence, some of the slow-mode lines must be either canceled or their routes modified to work properly with the new rapid transit line. This process is usually carried out sequentially, thus leading to suboptimal solutions.In this paper, we consider an integrated model for simultaneously designing rapid and redesigning slow networks. The model’s main aim is social: to maximize the demand covered (or captured) by both public modes, through offering a shorter commuting time. In addition, we also take care of the costs, keeping them within limits. We present a mathematical programming formulation that is solved by using a specially improved Benders decomposition. For this purpose, we include a partial decomposition to speed up the computation. The computational experiments are done on a case study based on real data obtained from a survey of mobility among transportation zones in the city of Seville. In terms of performance, for small instances, the Branch and Benders Cut (B&BC) yields solution networks that cover at least 5.2% more demand than other methods in the literature, within a time limit of 4 h. The advantage is even higher for the larger instances, for which B&BC found solutions that the other methods did not find.
Large-scale single-track railway timetabling is a combinatorial NP-hard problem characterized by a high-dimensional decision space and stringent coupling constraints. While multi-agent deep reinforcement learning (MADRL) has shown promise in addressing such problems by decomposing them into multiple resource-defined units while preserving optimality-seeking capabilities, existing methods often suffer from non-stationarity, slow convergence, and high computational cost. This paper proposes a novel MADRL framework that integrates a Transformer architecture with the Heterogeneous Agent Proximal Policy Optimization (HAPPO) algorithm to overcome the above challenges. The proposed approach models each train as an agent operating within a block-sequence environment, where agents sequentially make dwell-time decisions while implicitly coordinating via the Transformer’s attention mechanism. This design eliminates explicit communication channels and reduces computational overhead by using a weight-shared neural network. The HAPPO algorithm ensures monotonic policy improvement through an auto-regressive trust-region update scheme. Large-scale cases demonstrate that the proposed method outperforms state-of-the-art MADRL algorithms and heuristic methods in both solution quality and computational efficiency, achieving stable convergence and superior scalability.
We study the operation of load-based buses alongside a conventional service. The load-based service only departs once it has accumulated sufficient passengers similar to paratransit services operated in some countries. In our case, the two types of services are, however, regulated and co-designed. We investigate pricing structures where the fare is sequence based, so that passengers are charged less if more seats are empty. We derive “vertical equitable” fares, where the fare compensates appropriately for the boarding number depending expected waiting time. Under the assumption of a fixed total vehicle fleet we derive an optimal allocation of vehicles between the two services and show conditions under which a load-based service is feasible and profitable. It is proven that optimal revenues are obtained when the operator adjusts the fares and fleet assignment in such a way that it can be expected that there is always a load-based service to take on passengers. We include a discussion on potential implementation issues including “time-out” to avoid overly long waiting times and lumpy demand arrivals.
Urban transportation systems are under increasing pressure to efficiently accommodate both passenger and freight mobility within limited infrastructure and operational budgets. Operators face growing pressure to make more efficient use of existing infrastructure due to economic and environmental constraints. In this regard, we investigate the capacitated line planning problem with integrated truck routing for passenger and freight co-modal mobility in an intermodal network composed of an urban rail transit (URT) system and road-based truck services. Different from existing research that either focuses on passenger-oriented line planning in a single-modal network or optimizes tactical- and operational-level decisions for passenger and freight co-modal mobility based on fixed line plans, we consider a strategic-level problem where urban planners aim to fundamentally re-optimize the allocation of existing infrastructure resources and budget across the intermodal network. We formulate this problem as a path-based mixed-integer linear programming model. The model determines line plans and frequency for both URT and truck services, as well as the passenger and freight routing, with the aim of optimizing the total weighted travel time of passengers and freight. To solve large-scale instances, we develop a column generation algorithm with a two-phase diving procedure. Our algorithm incorporates acceleration techniques and budget reservation strategies derived from the mathematical properties of the formulation. We evaluate our approaches on both artificial instances and real-world case studies from the Rotterdam intermodal network. The results show that our algorithm obtains solutions with an average optimality gap of 0.77%, while reducing computation time by 95.53% compared to GUROBI. Using the existing Rotterdam URT line plan with optimized frequencies as a benchmark, we demonstrate that our approach improves service quality by 6.50% without increasing operational costs. From a practical perspective, real-life case studies suggest that accommodating the passenger and freight co-modal mobility in existing passenger-oriented metro systems requires redesigning the line plan from scratch, rather than merely adjusting frequencies or incrementally expanding the current network. The results further indicate that effective freight integration depends on reallocating budget across modes, with URT serving as the backbone of the intermodal system and truck services providing a complementary function.
As pollution and climate change intensify, mitigating emissions from the shipping sector has become a global priority for protecting public health and biodiversity. All-electric ships (AESs) have consequently emerged as a promising low-carbon alternative, supported by increasingly stringent policy mandates. In parallel, Ship-to-Grid (S2G) technology enables bidirectional energy exchange between AESs and port power grids, effectively transforming vessels into mobile energy storage units. This dual operational role, however, fundamentally complicates traditional ship scheduling problem. In this study, we develop a dynamic AES scheduling model on a spatial-temporal network that jointly determines freight routing, vessel relocation, and coordinated charging/discharging decisions. To capture context-dependent uncertainty in freight demand, we propose a contextual joint estimation-prediction-optimization framework that establishes a unified data-to-decision paradigm by embedding estimation and prediction procedures directly into the uncertainty set. By adopting linear decision rules together with a lifted uncertainty set construction, we show that the resulting model admits a tractable reformulation. We validate the model using both simulation studies and real-world instances from the ports in the North Sea region of Europe. Results show that our framework delivers superior out-of-sample performance in both average and risk-averse settings. Moreover, comparative experiments indicate that incorporating S2G operations provides additional revenue improvements, particularly during periods of pronounced electricity price fluctuations.
This study addresses globally optimal solutions to discrete network design problems under traffic equilibrium conditions, or DNDPs. Given a network and a budget, DNDPs aim to model all-or-nothing decisions such as link addition to minimize network congestion effects. Congestion is measured using traffic equilibrium theory where link travel times are modeled as convex flow-dependent functions and where users make selfish routing decisions. In this context, the collective route choice of users is a Wardropian equilibrium and DNDPs admit a bilevel optimization formulation where the leader represents the network designer, and the follower is a parameterized traffic assignment problem (TAP). This study introduces a novel and exact branch-and-price-and-cut (BPC) algorithm for DNDPs that exploits the structure of the problem and harnesses the potential of path-based formulations for column generation (CG). Leveraging the convexity and the separability of the objective function, we explore multiple outer approximation (OA) schemes that lead to linear programming relaxations. We develop a CG approach whose pricing subproblem can be solved in polynomial time. This scheme is embedded within a single-tree BPC algorithm to determine lower bounds while upper bounds are computed by solving parameterized TAPs. Numerical experiments conducted on a range of DNDP instances based on three transportation networks reveal that our BPC algorithm significantly outperforms state-of-the-art methods for DNDPs. Notably, we close several open instances of the literature, and we show that our BPC algorithm can solve DNDP instances based on networks whose number of nodes and of commodities is one order of magnitude larger than any previously solved instance; and DNDP instances whose number of candidate links is twice as large as any previously solved instance.
This study investigates the potential of link-and path-based incentives to mitigate congestion in urban transportation networks under a budget constraint. Both incentive schemes are formulated as non-linear optimisation problems with complementarity constraints. Mathematically, it is demonstrated that the feasible region of the link-based model is a subset of the feasible region of the path-based model under the same budget constraint. Consequently, path-based incentives exhibit greater potential to shift the user equilibrium flow pattern toward the system optimum compared to link incentives. A column generation-based iterative solution technique, which generates new paths at each iteration, is devised to efficiently solve both optimisation problems. Numerical experiments conducted for various transport networks also highlight the efficiency and scalability of the proposed algorithm, and the superiority of path-based incentives in reducing total travel time in urban transportation networks.
With the increasing penetration of electric vehicles, the shortage of public charging piles impacts the charging experience of electric vehicle drivers, exacerbating their range anxiety. In particular, low charging power at a high state of charge (SOC) reduces the service efficiency of public charging facilities, leads to long access time for drivers waiting for charging, and restrains the profit of a public charging operator. To address this challenge, we develop a market equilibrium model and introduce an adjustable pricing scheme in which the price per unit amount of charging (i.e., unit price) changes linearly with the SOC to affect drivers' charging decisions (i.e., whether to charge and when to stop charging) and improve social welfare, which includes drivers' utility from charging and the operator’s profit. We further formulate three optimization scenarios (i.e., social welfare maximization, profit maximization, and second best), and deduce the properties of the optimal solutions. We theoretically prove that the welfare-oriented operator should adopt a zero unit price at the minimum SOC and gradually raise the unit price as the current SOC increases. Moreover, whether in pursuit of maximum profit or maximum social welfare, the operator should avoid the 'inefficient charging' behavior of drivers (i.e., persisting in charging at a high SOC), even with low potential demand or sufficient charging piles. We also compare the proposed adjustable pricing scheme with traditional static pricing strategies, proving that the adjustable pricing scheme is superior in improving social welfare. We further conduct numerical experiments to verify the above analytical findings. The proposed adjustable pricing scheme is demonstrated to be able to allow the public charging operator to achieve a higher welfare or profit. Its practical feasibility and policy implications are discussed. The proposed model is also extended to account for heterogeneous VOT and EV charging specifications, quadratic pricing, and pricing linearly dependent on charging power. The numerical results of the extended models show that the welfare-oriented operator still sets a high unit price at high SOC levels to deter drivers from inefficient charging.
The rapid growth of ride-sourcing platforms has revolutionized urban mobility, creating new challenges in balancing service quality with operational efficiency. This paper examines optimal priority strategies for ride-sourcing platforms in markets where customers value both driver availability and service quality. A game-theoretic model is developed to analyze how prioritizing high-quality drivers, those exceeding a service quality threshold, impacts platform profitability and social welfare. This study introduces a continuum of priority levels and incorporates inefficiencies arising from prioritization (e.g., increasing matching time), enabling a systematic analysis of the trade-off between service quality and supply utilization. Our results reveal that well-designed priority strategies can achieve Pareto improvements, benefiting platforms, customers and drivers (including non-prioritized ones). Optimal prioritization depends critically on market conditions. In supply-rationing markets, strong prioritization leverages excess capacity to enhance perceived service quality, while in demand-rationing markets, moderate prioritization is preferred to avoid worsening shortages. Compared with wage discrimination, prioritization dominates in market with sufficient supply by reallocating resources strategically and then enhancing perceived service quality, whereas wage adjustments remain superior in demand-rationing settings or when prioritization inefficiencies offset potential gains.
Efficient arrival management in congested Terminal Maneuvering Areas (TMAs) requires coordinated decisions on sequencing and descent-mode selection. Existing studies typically address these problems separately, overlooking their coupled effects on minimum separation requirements and system-wide fuel efficiency. This paper develops an integrated arrival management framework based on a Predict-then-Optimize (PO) approach that combines high-accuracy Estimated Time of Arrival (ETA) prediction with a mixed-integer linear programming (MILP) formulation for the joint optimization of arrival sequencing and descent-mode assignment. In the prediction stage, a Kolmogorov-Arnold Network (KAN) estimates boundary ETAs from real-time operational features, capturing stochastic variations induced by weather, traffic density, and other disturbances. The subsequent optimization stage minimizes total fuel consumption while ensuring separation and operational constraints. The core innovation lies in the MILP formulation, which, unlike conventional scheduling models that define minimum separation times (MSTs) solely by wake-turbulence categories, incorporates the combined effects of aircraft type and descent-mode pairings on separation requirements. The framework is validated using real-world data from Hong Kong International Airport (HKIA), demonstrating substantial reductions in fuel consumption and emissions. With the objective of minimizing total fuel consumption, the proposed approach achieves a 4.4% reduction compared to actual operational baselines. Crucially, findings challenge the assumption that maximizing Continuous Descent Operations (CDOs) is universally beneficial. Under high-density traffic, the rigidity of mandating CDOs (PO-C) strategy induces excessive delays, increasing fuel burn and emissions (CO2, SO2, NOx), which are penalties that escalate with rising traffic density.
This study investigates a rolling stock circulation planning problem under enhanced operational conditions, including the consideration of multi-day maintenance periods, the feasibility of coupling and decoupling operations, and the arrangement of deadhead movements. A tailored branch-and-price algorithm and a decomposition structure with observable upper and lower bounds are proposed to solve this problem. First, the problem is formulated into a path-based generation model for single-day routes and an assignment model to obtain multi-day circulation plans satisfying maintenance constraints. Then, regarding the feasibility of coupling and decoupling operations, circulation type variables with set covering constraints are introduced, and tailored type-and-state-based branching rules are designed to explore the solution space within the branch-and-price framework effectively. Next, to improve computational efficiency, additional relaxation techniques based on the deadhead movements in the network are designed. Lastly, extensive experiments are conducted on large-scale instances with up to 785 trips and 66 stations, which demonstrate the effectiveness of the proposed decomposition structure, additional relaxation techniques, and branching rules in both solution quality and performance. Comparisons under different maintenance rules and coupling/decoupling modes further validate the practical significance of the problem under enhanced operational conditions considered in this study.
Accurate estimation of on-road energy consumption is often assumed to be critical in Electric Vehicle Routing Problems with Time Windows (EVRPTW). Yet the actual impact of estimation inaccuracies on routing feasibility and optimality remains largely unexplored. This paper focuses on assessing and tackling this impact through realistic testing and the development of an intuitive solution methodology based on a bi-objective ɛ-constraint optimisation framework. The proposed methodology relies only on the basic consumption rate reported by the vehicle manufacturer and builds on new intuitive results that suggest that despite the general tendency towards overestimating methods to remain conservative and risk-averse, the incorporation of an underestimating method might be more beneficial in implicitly ensuring the on-road optimality of routing decisions. Our results show that ignoring instantaneous speed variations and acceleration/deceleration rates can lead to significant inaccuracies, but the impact of disregarding factors such as slope, weather, or variable rolling resistance individually and collectively is rather negligible. Regardless of the size of estimation inaccuracy, however, we find inaccuracies to have very little impact on route-level outcomes as these rarely translate into infeasibility or meaningful optimality loss. Our analyses of the Pareto-optimal solutions on the generated efficient frontier of the considered EVRPTW instances, on the other hand, indicate that while the optimal solution of an instance is highly likely to also be on-road optimal, with a marginal sacrifice in instance optimality, significant allowance for inaccuracy is achievable to suit a strictly risk-averse decision maker.
Shockwaves represent one of the most consequential and pervasive disturbances in highway operations, yet existing shockwave identification methods struggle to capture the underlying causal mechanisms. This paper introduces a novel framework that fundamentally reconceptualizes driver dynamics through graph theory, redefining shockwave formation and dissipation as chains of causally linked braking and acceleration behaviors. The methodology employs an optimized Change Point Detection (CPD) algorithm to segment individual vehicle trajectories and identify significant acceleration and deceleration events at the microscopic level. A graph-based clustering technique then connects these events across multiple vehicles, explicitly capturing the inherent causation of shockwave propagation by tracing how one vehicle's deceleration triggers a cascade of braking responses in following vehicles, propagating upstream against the direction of traffic flow. This approach transforms shockwave identification from a statistical classification problem into a network propagation perspective, ensuring the detection of physically reasonable propagation waves that reflect actual driver-to-driver interactions. Comprehensive performance evaluation against baseline methods demonstrates the superiority of the framework in characterizing key shockwave properties, including propagation speed, spatial extent, duration, and oscillation intensity. Through sensitivity analysis and ablation study, this approach has been proved a robust foundation for traffic flow analysis, effectively bridging microscopic driver behaviors with macroscopic flow phenomena through the lens of graph modeling methodology.
Accurate knowledge of passenger movement patterns across the transit network is essential for public transportation agencies, particularly through the estimation of network-level Origin-Destination (OD) matrices. Traditional scaling methods can only scale a single seed dataset to marginal totals from count data, making results heavily dependent on seed quality. To address this limitation, this study presents a hierarchical Bayesian framework that estimates network-level OD matrices by extending Bayesian inference beyond route-level OD flows to also estimate transfer flows constrained by Automatic Passenger Counter (APC) data. The framework leverages transfer information from Automated Fare Collection (AFC) systems or portable device data sources, and introduces transfer blocks, defined as groups of nearby stops served by multiple routes, to localize transfer flow estimation and enable scalability to networks of any size. By preserving posterior variability through a random prior and a non-informative hyperprior, the framework provides a robust alternative to scaling methods even when auxiliary data sources are sparse or incomplete. Validation on the simulated Sioux Falls network shows the method consistently outperforms the Itinerary Scaling Factors (ISF) method across all AFC penetration rates, with the largest improvement at low penetration. A real-world application to Calgary Transit's bus network, where only a fraction of trips are fare-validated through the MyFare mobile ticketing AFC system, demonstrates that the framework scales to large networks and produces results consistent with both observed transfer rates and earliest-arrival travel-time benchmarks. This makes the framework particularly valuable in modern systems where credit card-based fare collection increasingly fragments passenger mobility data.
Truck congestion in a container terminal yard is usually caused by the imbalance between the arrival demand of external trucks and the supply of yard service capacity. In the absence of infrastructure expansions, the terminal yard congestion can only be mitigated by optimal control of truck arrivals and the management of yard resource allocation. This paper proposes an integrated modelling framework that mitigates terminal yard congestion by joint optimization of the truck arrival demand and the utilization of yard capacity, subject to truck arrival demand shifting, yard queueing, and yard resource allocation constraints. This integrated model consists of a truck demand management model that manages the distribution of truck arrivals over a planning horizon, a descriptive queueing model that captures the dynamics of truck arrival and service processes, and a yard capacity utilization model that controls the yard resource configuration and the consequent inbound and outbound truck service rates over time. For solving the integrated model, we develop a tailored iterative solution method that decomposes the demand and supply decisions and effectively strikes the balance between truck throughput and yard congestion level. A core contribution of this approach is the interaction between an expansion rule, which iteratively enriches the master problem's restricted service option set with service rate configurations identified by the subproblem, and a dynamic update rule that strictly tightens the master problem's congestion threshold. This mechanism is novel in the sense that it offers a convergent and tractable approach to coordinate the demand and supply management decisions that used to be intricate in the literature. We evaluate the computation performance and solution quality of the integrated framework on instances generated from the operational data of a large container terminal. Based on the computation results, we provide insights into truck demand and service management for congestion mitigation in a container terminal.
This paper studies the morning commute problem in a linear transportation corridor that is connected by a general purpose (GP) lane, a high-occupancy vehicle (HOV) lane, and a transit line. Commuters can choose solo-driving or carpooling, or take transit to fulfill their journeys between home and the workplace in the morning. In previous studies, carpoolers are often to be assumed to use the HOV lane only for facilitating model formulations and derivations. In reality, carpooling users can and will opt for using the GP lane when they perceive a congested HOV lane. Although a few studies have relaxed this assumption, they intentionally separated solo-driven vehicle and carpooling vehicle flows on GP lanes, and unrealistically considered fixed carpooling-related extra costs and money-cost savings, because both fuel and inconvenience costs are travel-time/distance-dependent. Moreover, very limited attention has been paid to analyze the impact of parking availability on carpooling and HOV-lane choice behavior in the literature. To address these issues, we firstly relax the assumption and formulate a multimodal user equilibrium (UE) model for the commute problem with GP lane, HOV lane, and sufficient parking spot supply to characterize users' behaviors of carpooling, departure time, and mode choices. Our analysis is then extended to address the case where the impact of insufficient parking supply on the departure time choice of solo drivers and carpoolers is incorporated. On top of this, we propose three parking permit management schemes for traffic management, namely, undifferentiated, tradable undifferentiated and system-optimum parking permit schemes. A couple of numerical analyses are conducted to evaluate and compare the effectiveness of the three parking permit schemes. Numerical results reveal several managerial insights. First, increasing the number of carpooling participants per vehicle enhances the comparative advantage of carpooling. Second, restricting carpoolers to use only the HOV lane yields a bias in measuring the system cost, especially for the case with moderately insufficient parking provision. Third, if carpoolers are restricted to the HOV lane, the effectiveness of the undifferentiated parking permit allocation scheme is overestimated and if carpoolers are allowed to use the GP lane, it is only effective for the case with severe shortage of parking provision at the destination. Fourth, the tradable undifferentiated parking permit scheme consistently improves system performance when parking provision is inadequate and it plays the same role as the system-optimum parking permit scheme in enhancing travel efficiency when parking provision is severely inadequate.
The evaluation of theories and models is key to the progress of science. This paper shows that current methodologies for assessing and comparing driver models - typically based on error distributions - are intrinsically flawed. A comprehensive methodology is proposed to evaluate driver models under both nominal and safety-critical driving conditions. Rooted in Popper's epistemology, the methodology relies on the execution of "risky tests" and on model "verisimilitude", i.e., the idea of a degree of better or worse correspondence to truth. The approach involves extensive testing of models via pair-wise calibration against individual trajectories and variancebased sensitivity analysis, enabling a systematic examination of how the trade-off between model accuracy and uncertainty evolves with increasing model complexity. The methodology is applied to 800 variants of the Intelligent Driver Model (IDM) and its improved formulations, augmented with human factors (HF) layers - namely perception errors and delays, temporal and spatial anticipation, and adaptive driving behaviours. A full factorial design isolates the explanatory contribution of each HF addon and its interaction effects. A novel formulation of the IDM, the MIDM, is introduced and consistently outperforms both the original and all tested improved formulations across three diverse naturalistic trajectory datasets. The study, therefore, provides a falsifiability-oriented foundation for rigorous, transparent comparison and validation of HFaugmented driver models.
The self-driving capability enables fully autonomous vehicles (AVs) to drive empty and park remotely, offering new opportunities to enhance urban land use efficiency by reallocating public parking spaces for other uses. However, existing studies often focus either on mitigating the adverse impacts of empty trips on transportation systems or on evaluating land use implications of AV adoption, without providing an integrated network-wide parking planning framework that balances land use efficiency enhancement and potential transportation system performance degradation. To address this gap, this study presents an integrated perspective on the strategic parking provision problem in the era of AVs. To capture the influences of AVs' joint (and inseparable) routing and parking behaviors on network traffic flows, we develop a journey-based modeling toolkit that analyzes the network-wide distribution of self-parking AVs. Built upon this toolkit, we propose a bi-level parking provision model that maximizes transportation network capacity subject to land supply and land use efficiency constraints. This bi-level model incorporates trip generation/distribution to account for the impact of land use patterns on AV travel demand, which is then allocated to the network through the journey-based modeling toolkit. A gradient-based algorithm is presented to solve the bi-level model. Numerical experiments show that the self-parking capability can improve network capacity under limited parking supply. Additionally, prioritizing the development of areas surrounding the central business district (CBD) may further enhance network capacity compared to development within the CBD, but the induced empty trips of AVs may create new traffic bottlenecks.
Ramp merging in the mixed traffic environment of weaving segments requires connected and autonomous vehicle (CAV) technologies to achieve precise trajectory control. However, pre-merge one-dimensional trajectory optimization (1DTO), which coordinates longitudinal speeds among multi-vehicles to create merging gaps (global optimization), and lane-changing twodimensional trajectory optimization (2DTO), which plans precise lateral maneuvers for the merging vehicle (individual optimization), are typically addressed separately. This separation causes each stage to employ independent risk assessment criteria and trajectory optimization objectives, thereby leading to suboptimal merging performance in terms of safety, efficiency, and stability. To overcome these limitations, we propose a unified merging sequence (MS), 1DTO, and 2DTO framework for multi-lane mixed traffic in weaving segments based on a risk field paradigm. First, we introduce a subjective-objective driving risk assessment method: CAVs utilize an objective risk field, while human-driven vehicles (HDVs) employ a subjective field coupling driver cognition. We then developed car-following models (SORFCF-CAV and SORFCF-HDV) to resolve the accuracy deficiencies of the IDM. Furthermore, we design a joint optimization framework integrating MS, 1DTO, and 2DTO. Strategies include: (i) SORFCF-CAV with virtual car-following for 1DTO; (ii) extending 1DTO for cooperative 2DTO via fifth-order polynomials; and (iii) a spatial-temporal risk occupancy map for safety-oriented 2DTO in non-cooperative cases. Extensive experiments demonstrate that the proposed strategy: (i) significantly outperforms multiple baselines in enhancing safety, merging efficiency, and traffic stability across various scenarios; (ii) exhibits a steady upward performance trend as the CAV penetration rate increases; and (iii) maintains excellent real-time computational efficiency even in extremely complex environments.
All-electric ships (AESs) have emerged as a promising solution for decarbonizing the waterborne transport sector. However, their limited sailing range compared to conventional fuel-powered ships presents a significant operational challenge, which necessitates the integration of energy refueling decisions into the scheduling process. Therefore, this study investigates the joint optimization problem of cargo transport and energy refueling for AESs in inland waterways. First, we establish an inland waterway shipping network for the main waterway and its tributaries. Based on this network, we formalize our problem into a pickup and delivery problem with on-site refueling and develop a mixed-integer linear programming model that jointly optimizes cargo transport, involving both pickup and delivery, and a flexible on-site energy refueling policy, aiming to minimize the total operational cost. To address instances of practical scale, we develop a specialized branch-and-price framework. The efficiency of this exact method is driven by several tailored acceleration strategies, including a state-reduction-based construction heuristic, a graph-reduction-based heuristic-then-exact pricing strategy, and a multi-state labeling algorithm with two customized dominance rules. Computational results validate that our algorithm achieves superior performance in both solution quality and efficiency compared to the solver. Finally, our comprehensive sensitivity analysis yields valuable managerial insights by assessing the influence of key parameters, such as network density and planning horizon, on operational costs and ship scheduling metrics.
