The intelligent upgrading of metropolitan rail transit systems has made it feasible to implement demand-side management policies that integrate multiple operational strategies in practical operations. However, the tight interdependence between supply and demand necessitates a coordinated approach combining demand-side management policies and supply-side resource allocations to enhance the urban rail transit ecosystem. In this study, we propose a mathematical and computational framework that optimizes train timetables, passenger flow control strategies, and trip-shifting plans through the pricing policy. Our framework incorporates an emerging trip-booking approach that transforms waiting at the stations into waiting at home, thereby mitigating station overcrowding. Additionally, it ensures service fairness by maintaining an equitable likelihood of delays across different stations. We formulate the problem as an integer linear programming model, aiming to minimize passengers’ waiting time and government subsidies required to offset revenue losses from fare discounts used to encourage trip shifting. To improve the computational efficiency, we develop a Benders decomposition-based algorithm within the branch-and-cut method, which decomposes the model into train timetabling with partial passenger assignment and passenger flow control subproblems. We propose valid inequalities based on our model's properties to strengthen the linear relaxation bounds at each node of the branch-and-bound tree. Computational results from proof-of-concept and real-world case studies on the Beijing metro show that our solution method outperforms commercial solvers in terms of computational efficiency. We can obtain high-quality solutions, including optimal ones, at the root node with reduced branching requirements thanks to our novel decomposition framework and valid inequalities. Our integrated optimization approach reduces the fleet size for operators by at least 8.33 % and decreases the waiting time of passengers on the tested instances, thereby validating the effectiveness of our proposed methods.

The evolving field of electric moped sharing systems is shaped by various determinants influencing user preferences, including range anxiety, pricing strategies, and regulatory changes. Utilizing a stated preference approach with a hybrid choice model, this research explores how these factors, along with attitudinal constructs, impact user decisions. The findings reveal that remaining driving range plays a critical role, with significant individual variability in its sensitivity, while perceived range anxiety did not significantly influence choices. Recent changes in helmet regulations have shifted preferences towards faster vehicles. Furthermore, dynamic pricing strategies, such as adjusting ride or unlock fees, can incentivize the use of less desirable vehicles with lower battery range or aid in user-based relocation. Nevertheless, low-range vehicles are less likely to be chosen, even with incentives. These insights provide valuable guidance for operators of electric moped sharing system to improve fleet management and optimize user satisfaction through strategic pricing and battery management.

Ride-sharing services operated by transportation network companies (TNCs) have the potential to expand capacity and accommodate increasing urban mobility demands, presenting an alternative to traditional ride-hailing services. This study introduces a high-capacity ride-sharing (HCRS) system that leverages user-specific travel choices and incentive-based pricing schemes. This innovative system enhances the dynamic matching problem of HCRS by incorporating a nested choice model and dynamic fare adjustment strategies to boost profitability while encouraging shared travel behaviours. Additionally, a rolling horizon solution approach is employed, including a shared choice set generation algorithm for creating shared alternatives and an Adaptive Large Neighborhood Search (ALNS)-based method for optimal matching. By leveraging a real dataset from Beijing's ride-hailing services, this research underscores that the HCRS service can significantly improve system efficiency and service quality, achieving more than 10.44% reduction in operating costs, and reducing average fares (¥3.31) and emissions (3.49 kg) across various users, compared to traditional ride-hailing services. The findings also demonstrate that users' decision-making is profoundly affected by changes in incentives, highlighting the importance of incentive settings in enhancing user engagement and system performance.

Supply chain networks face the critical challenge of enhancing resilience to disruptions while controlling the costs associated with resilience improvements. In this paper, we introduce an adaptive resilience improvement framework designed to sustain material flow by responding dynamically to emerging network vulnerabilities. Our framework centers on the production chain as a core element in resilience planning, integrating vulnerability assessment and reinforcement strategies through a tri-level optimization model. This model adapts to the network's changing conditions by (i) incorporating disruption scenario generation as an integral part of the decision-making process, allowing for the dynamic identification of vulnerabilities, and (ii) optimizing reinforcement strategies in response to them. We demonstrate the framework's effectiveness through two distinct case studies: a steel supply chain, where production flexibility improves resilience by 30%, and a pharmaceutical supply chain affected by climate-related disruptions. Our computational results confirm the scalability and effectiveness of this approach in strengthening network-wide resilience as vulnerabilities evolve.

This study introduces an optimization framework for deploying Mobile Fleet Inventories (MFIs) to address operational inefficiencies in on-demand delivery systems. Traditionally, these systems rely on stationary facilities to organize operations and manage resources. While stationary facilities provide stability and structured coverage, they are inherently rigid and struggle to adapt to the spatial and temporal fluctuations characteristic of urban service demand. By leveraging urban waterways, MFIs act as dynamic, mobile facilities, enabling real-time resource redistribution and offering greater flexibility to meet evolving demand patterns efficiently. We formulate the problem as a mixed-integer linear programming model to optimize MFI deployment, minimizing total system costs. The model incorporates both capital investments (e.g., MFI leasing and docking infrastructure) and operational expenses (e.g., rider idle time). Key decisions include determining the optimal number, placement of MFIs, and fleet size. To validate the approach, we apply it to a meal delivery platform in Amsterdam, demonstrating its practicality and scalability. Results show that implementing MFIs reduces overall system costs by 17% and decreases rider idle time by 35% compared to stationary facility operations. These findings underscore the transformative potential of MFIs to enhance the efficiency, sustainability, and adaptability of on-demand delivery systems in urban settings.

This paper addresses the challenges of charging infrastructure design (CID) for electrified public transport networks using Battery Electric Buses (BEBs) under conditions of sparse energy consumption data. Accurate energy consumption estimation is critical for cost-effective and reliable electrification but often requires costly field experiments, resulting in limited data. To address this issue, we propose two mathematical models designed to handle uncertainty and data sparsity in energy consumption. The first is a robust optimization model with box uncertainty, addressing variability in energy consumption. The second is a data-driven distributionally robust optimization model that leverages observed data to provide more flexible and informed solutions. To evaluate these models, we apply them to the Rotterdam bus network. Our analysis reveals three key insights: (1) Ignoring variations in energy consumption can result in operational unreliability, with up to 55% of scenarios leading to infeasible trips. (2) Designing infrastructure based on worst-case energy consumption increases costs by 67% compared to using average estimates. (3) The data-driven distributionally robust optimization model reduces costs by 28% compared to the box uncertainty model while maintaining reliability, especially in scenarios where extreme energy consumption values are rare and data exhibit skewness. In addition to cost savings, this approach provides robust protection against uncertainty, ensuring reliable operation under diverse conditions.

Revenue Management (RM) and Pricing have a long tradition of elegant mathematical formulations, typically as large-scale stochastic dynamic programs, see, for instance, Gallego and van Ryzin (1994), Talluri and van Ryzin (1998), or Talluri and van Ryzin (2004). These models capture, in full generality, the trade-offs among capacity, uncertainty, and customer choice that define RM. Yet, as already noted by Talluri and van Ryzin (1998), the resulting problems are often simply too large to solve exactly. The enduring challenge, therefore, lies not in formulating the “perfect” model but in extracting useful, implementable decision policies from systems that defy exact optimization.

This Special Issue on Revenue Management for Complex Systems brings together five contributions that embody precisely this philosophy. Each paper begins with a theoretically sound model that captures the richness of real-world complexity (multi-dimensional heterogeneity, dynamic decisions under uncertainty, coupled subsystems, and data-driven learning) but then forges a computational path that makes the model tractable and actionable. Although they operate across diverse domains from pricing consumer products to managing transportation, logistics, and mobility networks, they share a unifying spirit: to turn complexity into structure, and structure into insight.

Automated driving developments should be considered when making decisions about investments in physical and digital infrastructure. This paper proposes four scenarios for automated driving developments in the Netherlands in 2040 and 2060 taking into account uncertainties regarding future penetration rates, the level of connectivity, the operational design domain, and the expected impacts of automated driving: 1) Late transition, 2) Automated vehicles on main roads, 3) Car-topia, and 4) Share-topia. To derive these scenarios, an extended switchboard method is introduced in which multiple driving forces for automated driving can be varied. The main driving forces were identified based on expert surveys. For each scenario, a modelling approach is used to compute the impact of automated driving on vehicle kilometres driven and congestion. The extended switchboard method offered more flexibility than existing scenario methods. The model-based impact assessment provided more conservative and probably more accurate insights into the expected impacts of automated driving on vehicle kilometres driven and congestion than expert estimates from the literature. The results show that in all scenarios automation leads to an increase in the number of trips, vehicle kilometres driven and congestion. In the scenarios with autonomous vehicles, congestion is expected to increase up to 17%. The higher the penetration rates of connected automated vehicles, the smaller the increase in congestion (1.5%-11%). The results indicate that investments in digital infrastructure are needed to prevent capacity reduction due to autonomous driving. The scenarios “car-topia” and “share-topia” may require additional physical infrastructure on motorways and regional roads, and/or the implementation of demand management strategies.

Micro-delivery services offer promising solutions for on-demand city logistics, but their success relies on efficient real-time delivery operations and fleet management. On-demand meal delivery platforms seek to optimize real-time operations based on anticipatory insights into city-wide demand distributions. To address these needs, this study proposes a short-term predict-then-cluster framework for on-demand meal delivery services. In the forecasting stage, point and distributional predictions are generated using multivariate features, including temporal, contextual, and lagged-dependent features to capture complex demand dynamics. In the clustering stage, we propose two methods: Constrained K-Means Clustering (CKMC) and Contiguity Constrained Hierarchical Clustering with Iterative Constraint Enforcement (CCHC-ICE). These approaches form dynamic, geographically coherent clusters based on predicted demand, while accommodating user-defined operational constraints. Case studies on European and Taiwanese datasets demonstrate that lagged-dependent ensemble learning models perform robustly under sparse, zero-inflated demand conditions, whereas deep learning models such as LSTM excel in denser data regimes. Furthermore, results from the European case study highlight that incorporating distributional forecasts effectively captures demand uncertainty, thereby enhancing the quality of clustering outcomes and operational decision-making. By integrating demand uncertainty and operational constraints, the proposed framework delivers forward-looking, actionable insights for optimizing real-time meal delivery operations. The approach is adaptable to other on-demand platform-based city logistics and passenger mobility services, contributing to more sustainable and efficient urban operations.

The shift from private vehicles to public and shared transport is crucial to reducing emissions and meeting climate targets. Consequently, there is an urgent need to develop a multi-modal transport trip planning approach that integrates public transport and shared mobility solutions, offering viable alternatives to private vehicle use. To this end, we propose a preference-based optimization framework for multi-modal trip planning with public transport, ride-pooling services, and shared micro-mobility fleets. We introduce a mixed-integer programming model that incorporates preferences into the objective function of the mathematical model. We present a meta-heuristic framework that incorporates a customized Adaptive Large Neighborhood Search algorithm and other tailored algorithms, to effectively manage dynamic requests through a rolling horizon approach. Numerical experiments are conducted using real transport network data in a suburban area of Rotterdam The Netherlands Model application results demonstrate that the proposed algorithm can efficiently obtain near-optimal solutions. Managerial insights are gained from comprehensive experiments that consider various passenger segments, costs of micro-mobility vehicles, and availability fluctuation of shared mobility.

We study a class of assortment optimization problems where customers choose products according to the cross-nested logit (CNL) model and the number of products offered in the assortment cannot exceed a fixed number. Currently, no exact method exists for this NP-hard problem that can efficiently solve even small instances (e.g., 50 products with a cardinality limit of 10). In this paper, we propose an exact solution method that addresses this problem by finding the fixed point of a function through binary search. The parameterized problem at each iteration corresponds to a nonlinear binary integer programming problem, which we solve using a tailored Branch-and-Bound algorithm incorporating a novel variable-fixing mechanism, branching rule and upper bound generation strategy. Given that the computation time of the exact method can grow exponentially, we also introduce two polynomial-time heuristic algorithms with different solution strategies to handle larger instances. Numerical results demonstrate that our exact algorithm can optimally solve all test instances with up to 150 products and more than 90% of instances with up to 300 products within a one-hour time limit. Using the exact method as a benchmark, we find that the best-performing heuristic achieves optimal solutions for the majority of test instances, with an average optimality gap of 0.2%.

The rapid growth of the online food delivery industry has led to a significant increase in the number of delivery riders navigating urban streets, predominantly using bikes and e-bikes. This growth has been accompanied by a concerning rise in crashes involving these riders, posing a critical challenge for city authorities and policymakers. Promoting safer riding behavior, such as choosing safer routes while delivering food, can potentially reduce crash risks. With this motivation, this paper aims to evaluate the effectiveness of strategies that encourage riders to choose safer routes and estimate the value riders place on reducing the risk of road crashes. The paper presents a stated preference experiment conducted with food delivery riders in Amsterdam and Copenhagen to assess two targeted strategies: ’safety information’ and ’monetary incentives’, designed to encourage riders toward selecting safer routes. The results from the route choice model show that presenting information about safety against crashes on different routes and offering monetary incentives can effectively motivate riders to choose safer routes, even if these are longer. The trade-offs riders make between safer and shorter routes were quantified by calculating the Value of Risk Reduction (VRR) and Willingness to Accept (WTA) indicators, which offer valuable insights into riders’ safety preferences. These indicators highlight how much riders value risk reduction and the compensation required to choose safer routes. Furthermore, the findings reveal that factors related to riders’ working arrangements and socio-demographic profiles significantly influence their route choice decisions. The paper concludes with a discussion about the practical challenges associated with implementing the strategies to enhance rider safety and proposing potential solutions that can be useful for food delivery platforms and policymakers.

Integrating emerging shared mobility with traditional fixed-line public transport is a promising solution to the mismatch between supply and demand in urban transportation systems. The advent of modular vehicles (MVs) provides opportunities for more flexible and seamless intermodal transit. The MVs, which have been implemented, are comprised of automated modular units (MUs), and can dynamically change the number of MUs comprising them at different times and stops. However, this innovative intermodal urban transit brings with it a new level of dynamism and uncertainty. In this paper, we study the problem of jointly optimizing the timetable and the vehicle schedule within an intermodal urban transit network utilizing MVs within the context of distributionally robust optimization (DRO), which allows MVs to dynamically (de)couple at each stop and permits flexible circulations of MUs across different transportation modes. We propose a DRO formulation to explore the trade-off between operators and passengers, with the objective of minimizing the worst-case expectation of the weighted sum of passengers’ and operating costs. Furthermore, to address the computational intractability of the proposed DRO model, we design a discrepancy-based ambiguity set to reformulate it into a mixed-integer linear programming model. In order to obtain high-quality solutionss of realistic instances, we develop a customized decomposition-based algorithm. Extensive numerical experiments demonstrate the effectiveness of the proposed approach. The computational results of real-world case studies based on the operational data of Beijing Bus Line illustrate that the proposed integrated timetabling and vehicle scheduling method reduces the expected value of passengers’ and operating costs by about 6% in comparison with the practical timetable and fixed-capacity vehicles typically used in the Beijing bus system.

The volume of instant delivery has witnessed a significant growth in recent years. Given the involvement of numerous heterogeneous stakeholders, instant delivery operations are inherently characterized by dynamics and uncertainties. This study introduces two order dispatching strategies, namely task buffering and dynamic batching, as potential solutions to address these challenges. The task buffering strategy aims to optimize the assignment timing of orders to couriers, thereby mitigating demand uncertainties. On the other hand, the dynamic batching strategy focuses on alleviating delivery pressure by assigning orders to couriers based on their residual capacity and extra delivery distances. To model the instant delivery problem and evaluate the performances of order dispatching strategies, Adaptive Agent-Based Order Dispatching (ABOD) approach is developed, which combines agent-based modelling, deep reinforcement learning, and the Kuhn-Munkres algorithm. The ABOD effectively captures the system's uncertainties and heterogeneity, facilitating stakeholders learning in novel scenarios and enabling adaptive task buffering and dynamic batching decision-makings. The efficacy of the ABOD approach is verified through both synthetic and real-world case studies. Experimental results demonstrate that implementing the ABOD approach can lead to a significant increase in customer satisfaction, up to 275.42%, while simultaneously reducing the delivery distance by 11.38% compared to baseline policies. Additionally, the ABOD approach exhibits the ability to adaptively adjust buffering times to maintain high levels of customer satisfaction across various demand scenarios. As a result, this approach offers valuable support to logistics providers in making informed decisions regarding order dispatching in instant delivery operations.

The collaborative design of the timetable and dynamic-capacity allocation plan of emerging modular vehicles (MVs) is a promising solution to the mismatch between supply and demand in public transportation studies; however, such efforts are subject to high-level dynamics and uncertainty inherent in operating environments. In this study, we focus on the timetabling and dynamic-capacity allocation problem of MVs within the context of distributionally robust optimization under time-dependent demand uncertainty. The dynamic capacity refers to the number of modular units (MUs) comprising an MV can be potentially changed at different times and stops. A Wasserstein distance-based ambiguity set with a time-dependent and station-wise perturbation parameter is adopted to incorporate all potential distributions within a 1-Wasserstein distance for addressing the uncertainty of passenger demand. Further, a data-driven distributionally robust optimization model that considers time-varying capacity is formulated to minimize passenger waiting costs and dispatching costs of operators over all possible demand distributions within the ambiguity set. Subsequently, an expansion that allows for flexible formations of MVs assigned to each trip at each stop is proposed, and this results in more customized operational plans driven by the passenger demand. To improve the computational efficiency of realistic problems, we design a customized integer L-shaped method to exactly solve the models, which incorporates a class of valid equalities to further speed up the computation. The effectiveness of the proposed approaches in reducing the costs for both passengers and operators compared with the practical fixed-capacity operations is verified by real-world case studies based on the operating data of Beijing Bus Line 468. Furthermore, the superiority of the distributionally robust optimization method in comparison to the stochastic programming and the robust optimization approaches is demonstrated.

Nowadays, urban areas are exposed to various challenges such as climate change, social inequalities, and congestion. Shared mobility hubs present the opportunity to reshape our cities and mitigate the previously mentioned challenges by contributing to a more sustainable transport system. These are places where shared cars, mopeds, and e-bikes are offered to improve connectivity in urban areas. In this paper, we investigate the impact of efficiently allocating multimodal shared mobility hubs on modal split, service level, and environmental factors while assuring economic feasibility. Given a limited budget, cities would like to optimize the hubs’ locations to maximize the population's benefits. For that purpose, we introduce a multi-stage design algorithm model that distributes the hubs and allocates fleets of shared cars, mopeds, and e-bikes to maximize travel utility for all the population traveling using traditional and/or shared modes while accounting for multimodal trips. The model is divided into several modules: computational modules that calculate the demand for the hubs; an optimization module to optimize the hubs’ capacities, availability, and relocation of shared vehicles; and finally, a genetic algorithm to find the optimal hub distribution. Our proposed model is one of the first that optimizes the location and capacity of multimodal hubs by considering multimodal trips in a large network. Additionally, it allows to assess mobility, spatial, and environmental impact of shared modes. The model is applied to the case of Amsterdam, the capital of The Netherlands, with around 800,000 inhabitants. After running several scenarios with different budgets allocated to build the hubs, results show that having more hubs with a lower number of shared vehicles is more beneficial than having fewer hubs with higher capacity. That is because the travel time savings increase considerably when investments lead to complete coverage of the area by the hubs network. A modal split of 5% for the shared modes is expected when Amsterdam is covered by 288 hubs. From an environmental point of view, only 32% of the shared trips replace trips previously made by ICE and electric cars, leading to a limited CO2 emissions reduction of 1.27%. Hence, introducing shared modes and mobility hubs without push measures for the use of private cars appears to offer limited benefits to decrease the negative impacts of private car usage.

The exclusive and excessive use of long-distance road transportation is not suitable way to reduce the negative environmental impacts of logistics systems. Intermodal transport, combining road with other transport modes, has the potential to reduce both operating costs and carbon footprints. One of the reasons for the low share of intermodal transport is its requirement for the coordination of scheduled transport services that can result in reducing reliability in case of disruptions due to the arrival of new shipment orders, fluctuations in shipment quantities, delays, and service cancellations within the network. This calls for reliable and efficient algorithms to replan the shipments’ distribution. In this paper, the replanning problem is formulated as a path-based multi-commodity network flows. We provide two different network topologies, one of which is based on a time–space network, while the other embeds time aspect in a highly scalable alternative structure to large transportation networks. We propose a column generation method whose pricing sub-problems are presented as resource constrained shortest path problem solved via a tailored label-correcting algorithm. We look at the pros and cons of complete and partial replanning in case of disruption and provide managerial insights for intermodal networks. An extensive set of computational experiments is presented on realistic instances being generated with the consultation of our industrial partners for a logistic network including railways, waterways, and roads. The promising outcomes validate the efficiency of the proposed approach that can be easily adjusted to real-time intermodal logistic replanning.

This paper presents a novel framework for customised modular bus systems that leverages travel demand prediction and modular autonomous vehicles to optimise services proactively. The proposed framework addresses two prediction scenarios with different forward-looking operations: optimistic operation and pessimistic operation. A mixed integer programming model in a space-time-state network is developed for the optimistic operation to determine module routes, schedules, formations and passenger-to-module assignments. For the pessimistic case, a two-stage optimisation procedure is introduced. The first stage involves two formulations (i.e., deterministic and robust) to generate cost-saving plans, and the second stage adapts plans with control strategies periodically. A Lagrangian heuristic approach is proposed to solve formulations efficiently. The performance of the proposed framework is evaluated using smartcard data from Beijing and two state-of-the-art machine learning algorithms. Results indicate that the proposed framework outperforms the real-time approach in operating costs and highlights the role of module capacity and time dependency.