This paper introduces the Dial-a-Ride Problem with Transfers and Walking (DARPTW), a generalization of the classical DARP in which passenger itineraries may include multiple transfers and walking segments. The objective is to minimize a bi-criteria function comprising total vehicle travel time and the total journey time of all users. Incorporating transfers and walking provides operational flexibility, enabling load balancing, reduced service areas, and walking shortcuts to avoid unnecessary vehicle detours, but also substantially increases problem complexity, as DARPTW generalizes the already NP-hard DARP.To address this challenge, we propose an Adaptive Large Neighborhood Search (ALNS) framework that integrates a feasibility check and a scheduling heuristic. The feasibility check is accurate and computationally efficient, while the scheduler is highly efficient, allowing the approach to support iterative or near real-time routing. Computational experiments based on real-world data from Bubble-Dan in Tel Aviv demonstrate that ALNS consistently produces high-quality feasible solutions across diverse instances and scales with problem size, whereas exact methods quickly become intractable. A focused analysis of transfer policies shows that transfers are most beneficial under constrained conditions, such as limited walking flexibility or vehicle capacity, where they improve feasibility and routing efficiency.
The capacity of many railway networks in Europe is highly utilized, but planning norms such as headways and buffer times in the timetable are already optimized given the available infrastructure. Thus, planning norms in busy networks can only be further decreased by implementing new technologies for increased automation, including Driver Controlled Operation, European Rail Traffic Management Systems, Automatic Train Operation, and Traffic Management Systems. Implementing all these technologies directly on a national level would be too complex and would require high investments. Furthermore, since the technologies are relatively new, there is the need to assess their implementation on different corridors and rolling stock based on their effect on the timetable, before deploying them nationally. To address this challenge, we propose a novel railway timetable optimization model that extends the periodic event scheduling problem by allowing the implementation of planning norm decreasing technologies under a budget constraint. Specifically, the model can choose what technologies to implement on what corridors and train series such that the optimized timetable benefits the most. Numerical experiments on single-line and regional railway networks in the Netherlands provide insights into the effectiveness of different technologies, the identification of specific corridors and train series for implementation, and reveal that relatively small investments (15%–20% of the total) can lead to 60% of the potential timetable improvements. The proposed model can thus be used as a decision support tool for railway operators and infrastructure managers to prioritize the implementation of technologies and their locations in a railway network.
Demand Responsive Transport (DRT) systems have emerged as viable alternatives to traditional public transport (PT), especially in low-demand areas where PT has proven to be inefficient. However, the large number of possible configurations, the heterogeneity of service geographical areas, and the lack of expertise of planners makes designing these systems a considerable challenge. This work aims to support the design of DRT systems at a strategic level by proposing a categorization of key DRT design variables along with a methodology to aid decision-makers in selecting the most suitable configurations, considering the purposes, target passengers, service geographical area, and operational hours of the system. For this purpose, a strategic-level decision support framework (APOLO) was developed. This framework was designed based on the analysis of real-world DRT implementations and existing literature, and it is composed of three interconnected modules. MUSE evaluates the suitability of values of the "operation" variables using a matrix adapted to the user defined system objectives and perceptions of flexibility. ARTEMIS simulates the daily operations of candidate configurations in virtual scenarios; generating a broad set of KPIs across four dimensions: passenger perception, accessibility; operational efficiency; and environmental impact. DELOS applies a cost-benefit analysis to determine the most appropriate service-level design choices. Globally, the APOLO framework provides both a theoretical foundation and a practical tool to guide data-informed, participatory, and context-sensitive DRT design.
We consider the tactical planning of a demand-responsive connector system, where passengers are transported by on-demand vehicles within a zone that is connected to a tram line via a scheduled transfer station. The system combines characteristics of fixed-route and demand-responsive transit systems. We propose the concept of service patterns that indicate the number of arriving and departing vehicles at the transfer station per tram arrival and give a hint on how the fleet should be utilized. Based on a network flow formulation on a time-expanded network, we use a two-stage stochastic programming model to determine service patterns. We conduct an extensive computational study to analyze the impact of several design factors on selected performance indicators from both an operator and customer perspective. The results show that service patterns are not only able to adapt to different demand distributions and describe the relations between system parameters in a concise way, but are also able to reduce the time spent on empty runs between 28%-80% compared to benchmark policies that use the same fixed number of vehicles at the transfer station for all tram arrivals. Lastly, we present a post-processing model to assess the quality of the tactical solutions on an operational level. The results indicate that solutions derived from our approximation are of high-quality and may thus help the operator to communicate their service to customers and obtain realistic estimates of the required fleet size.
We address the distribution problem of a company that ships goods from a single depot to multiple customers. This distribution is outsourced to several carriers, each with distinct transportation rates and limited, heterogeneous vehicle fleets. Multiple carriers provide Full-Truckload (FTL) transportation via predefined routes operated by diverse vehicle types, with each carrier offering a limited number of trucks. Additionally, the Less-Than-Truckload (LTL) mode can be used to transport goods from origin to destination. We formulate this problem as a variant of the vehicle routing problem with a private fleet and common carriers. To solve it, we propose a matheuristic approach that combines a Large Neighborhood Search (LNS) metaheuristic with a set partitioning component. Our algorithm integrates filtering strategies to efficiently incorporate specific constraints into the LNS operators. We demonstrate that our method is competitive on established problem benchmarks and introduce new instances. Finally, we present a case study from the French retail industry, illustrating how combining FTL and LTL shipping can generate significant cost savings compared to relying solely on FTL or LTL.
Understanding and addressing uncertainty is crucial for effective public transport design. This literature review examines key aspects of modelling and optimisation on network design, line planning and timetabling under uncertain conditions. We restrict the analysis to the case where some parameters in those mathematical problems have an uncertain value, that is, either characterised as a probability distribution, scenarios, or updated over multiple stages. The literature reveals the use of a wide range of concepts and models, the most common ones being robustness, multi-period planning, and stochastic programming. The research varies significantly in the selection of parameters to be unknown and/or uncertain and, in turn, those that are predetermined and deterministic. A critical analysis leads us to the following insights. The value of including uncertainty in the optimisation is often not quantified, and real-life applications that can estimate its benefits are scarce. The analysis reveals variations in terminology across different papers, with multiple overlapping and/or different concepts benefiting from similar mathematical approaches, highlighting the complexities researchers face. Our analysis indicates that only few articles use data to derive realistic or accurate scenarios and distributions to be used in stochastic optimisation approaches. Despite these complexities, ongoing advancements in modelling and optimisation techniques offer a promising path towards more effective and resilient public transport systems. These improvements ultimately enhance service quality and increase passenger satisfaction.
The increasing volume of parcels leads to challenges due to unauthorized parking especially in cities. This paper considers the concept of loading areas which are the only allowed parking spaces for delivery services. Loading areas are installed by cities and include one or several parking spaces. Via a smartphone app these parking spaces can be reserved and opened (bollards) by companies or drivers. We introduce a model to collaboratively assign parking times in loading areas. The model is investigated in a comprehensive computational study and compared with the state-of-the-art, where delivery services may stop in unauthorized positions, and loading areas without collaborative reservation with a first-come-first-serve scheme. Our results show that the concept can be a useful solution for the trade-off between safety (no unauthorized parking) and tour duration. Tour durations can be improved substantially by collaborative planning, an increased number of loading areas and parking spaces, and high delivery speeds between loading areas and customers.
On-demand restaurant meal delivery platforms, such as DoorDash and Meituan, have recently introduced a multi-order delivery service: Customers may combine delivery requests from different restaurants in a single multi-order with the service promise of a synchronized delivery. However, the platform must not only ensure the synchronization of multi-orders but also improve punctuality and freshness for all customers. This is challenging because, as we show, synchronization, delay, and freshness are conflicting objectives. Uncertainty in the delivery process and unknown future orders further complicate the decision making. This raises several research questions: How does the introduction of a multi-order service affect the overall delivery operations with regard to service quality and operational expenses? How should a multi-order service be strategically rolled out? How can we balance the competing objectives of synchronizing deliveries while minimizing delay and maximizing freshness? To answer the research questions, we propose an effective policy that allows for a careful and controlled balance between the competing objectives and employ it in an extensive computational study. We evaluate the effect of different trade-offs between delay, freshness, and synchronization on delivery operations over varying demand for multi-orders. We observe that enforcing strict synchronization of multi-orders by assigning each multi-order to a single delivery driver is hardly operational feasible. Occasionally using split-deliveries provides the flexibility to better balance all objectives. Our detailed experiments further generate insights on how platforms may roll-out multi-orders as a new service offering without negatively affecting their existing delivery operation while benefiting from reduced operational expenses.
Demand-Responsive Transport (DRT) presents significant potential to address the inefficiencies of conventional public transport, particularly in low-demand areas where conventional fixed-route services struggle with poor cost-efficiency and coverage. This study develops a unified agent-based modelling (ABM) framework to evaluate DRT performance across different urban contexts, addressing the lack of systematic evaluation tools for context-specific service design. The research introduces a novel parametric ABM integrating a comprehensive real-time matching algorithm that balances passenger utility and operator costs through a composite cost function. Unlike existing approaches, the model incorporates passenger walking behaviour, automatically adjusting service flexibility based on demand intensity whilst enabling systematic comparison across diverse operational scenarios. Three representative contexts are evaluated: small cities (many-to-many demand), large cities during offpeak periods (lower spatial demand density due to expanded service areas), and suburban feeder services (directional many-to-one patterns). Each scenario is analysed across fleet sizes (2-40 vehicles) and demand rates (10-200 requests/hour), with performance assessed through integrated passenger, operator, and economic indicators. Results demonstrate that DRT performance is fundamentally context-dependent. Suburban feeder services emerge as the optimal application, achieving total unit costs of 4-6 per passenger and requiring minimal fleet investments (4-6 vehicles), representing 40-60 % cost advantages over urban scenarios. Small city operations achieve viable performance with moderate resources (8-12 vehicles, 6-8 /pax), whilst large city deployments require substantial commitments (16-28 vehicles, 10-18 /pax). The analysis reveals critical minimum viable fleet thresholds scaling proportionally with urban complexity, with capital investment ratios of 1:2:4 across scenarios, and confirming that spatial density fundamentally determines DRT viability. The findings provide evidence-based guidance for transport authorities, positioning suburban feeder applications as optimal entry points for DRT implementation.
Shared mobility-on-demand (SMOD) systems allow customers to request customized rides that the provider bundles through ridepooling. Owing to their flexibility and efficiency in low-demand settings, SMOD systems are expected to become a cornerstone of rural public transport. Operationally, dynamic pricing can influence which rides customers order, thereby enhancing system performance. In the literature on SMOD, dynamic pricing is exclusively applied to maximize profit. However, rural SMOD services that complement or replace existing scheduled services primarily provide basic mobility as a public service. Further, they should contribute to reducing the emissions of passenger transportation. With this work, we present the first multi-objective, sustainable dynamic pricing approach that considers all three dimensions of sustainability, i.e., social, environmental, and economic objectives. The core idea is to set prices that maximize served demand while adhering to a dynamic lower price bound ensuring that the price of each ride at least covers its expected marginal cost. Thereby, our approach carefully balances the partially conflicting sustainability objectives. To accurately approximate expected demand displacement and marginal cost of rides, which is crucial for making dynamic pricing decisions, we propose a post-decision rollout algorithm that anticipates the future evolution of the booking process. We comprehensively evaluate our approach based on a real-world data set of a rural SMOD provider and derive managerial insights regarding the practical impact of sustainable dynamic pricing. Our findings show that sustainable dynamic pricing achieves substantially better performance than static pricing while preventing monopoly markups, which would result from profit-based dynamic pricing.
Hydrogen is produced from water using renewable electricity. Unlike electricity, hydrogen can be stored in large quantities for long periods. This storage ability acts as a green battery, allowing solar and wind energy to be generated and used at different times. As a result, green hydrogen plays a central role in facilitating a climate-neutral economy. However, the logistics for hydrogen are complex. As new pipelines are developed for hydrogen, there is a trend toward repurposing the natural gas network for hydrogen, due to its economic and environmental benefits. Yet, a rapid conversion could disrupt the balance of natural gas supply and demand. Furthermore, technical and economic developments surrounding the transition contribute additional complexity, which introduces uncertainty in future supply and demand levels for both commodities. To address these challenges, we introduce a multi-period stochastic network design problem for the transition of a natural gas pipeline network into a green hydrogen pipeline network. We develop a progressive-hedging-based metaheuristic to solve the problem. Results demonstrate our matheuristic is efficient, both in computation time and in solution quality. We show that factoring in uncertainty avoids premature expansion and ensures the development of an adequate pipeline network meeting long-term needs. In a case study in the Northern Netherlands for Hydrogen Energy Applications in Valley Environments for Northern Netherlands initiative, we focus on two key scenarios: local production and importation, exploring their impacts on performance indicators. Our case insights exemplify the solid foundation for strategic decision-making in energy transitions through our approach.
The social force model is widely applied to simulate pedestrian movements in space and time. In this study, we propose an alternative calibration approach for the social force model by using the base acceleration a0 = v0/tau as the central parameter. Rather than assigning a fixed reaction time tau to all agents, as is common practice, we assume a constant a0 across agent types and compute individual tau values accordingly. The problem resulting from a fixed tau is, that when calibrated on macroscopic level, this can lead to microscopically implausible behavior. We therefore calibrate on macroscopic flow rates but evaluate on sub-macroscopic empirical travel-time distributions from a bottleneck experiment to verify whether the constant a0 parametrization preserves realistic microscopic behavior. The results indicate that our calibration based on a constant a0 improves the agreement between simulated and empirical data, particularly in the variance and distribution of individual travel times under high occupancy. We define a measure for comparing travel time distributions of the experiment to the two simulation approaches. This overlap measure increases from 0.149 to 0.257 using our proposed approach, corresponding to an improvement of 0.108. The variance of rank changes further supports this: the traditional approach exhibits a standard deviation of 5.63 compared to 2.76 in the experiment, while our approach reduces this to 4.05, lying closer to the empirical data. This suggests that calibrating on a0 enhances the model's ability to reproduce realistic microscopic behavior.
We tackle the integrated planning problem of periodic timetabling and electric vehicle scheduling, crucial for cities transitioning to electric bus fleets. Given existing timetables, we allow only minor modifications and propose an iterative solution approach that addresses the Electric Vehicle Scheduling Problem (EVSP) in each iteration. Due to the NP-hard nature of EVSP, we employ well-established heuristics and evaluate the quality of the solutions obtained. Specifically, we establish tight approximation bounds for certain iterative heuristics that first solve the Vehicle Scheduling Problem and subsequently adjust solutions to meet battery constraints. We make several key contributions: We provide general insights into heuristic solution quality, establish theoretical performance bounds, and validate these findings through a case study using real-world data from Aachen, Germany. Additionally, we employ our iterative framework to derive managerial insights for bus operators in Aachen by quantifying potential gains from adjusting the timetable to support the transition to a fully electric bus fleet.
In addressing the challenge of large-scale packing of strongly heterogeneous cargo in logistics loading, this paper proposes a three-dimensional container loading algorithm that integrates a block-building heuristic, an optimized placement strategy, and an enhanced genetic algorithm. The proposed approach accounts for six practical constraints inherent in logistics packaging and establishes an optimization model aimed at maximizing container space utilization while adhering to permissible center of gravity deviations. First, a block construction heuristic is employed to preprocess the cargo by aggregating items into larger blocks, thereby significantly reducing problem size and computational complexity. Subsequently, an improved placement strategy, combined with a genetic algorithm, is applied to identify an initial feasible packing layout. Finally, a simulated annealing operator is introduced to further refine the solution through local optimization, thereby obtaining an enhanced loading solutions with improved loading efficiency. Through comparative experiments with other leading algorithms using public datasets, the results demonstrate that the proposed algorithm performs on par with existing methods in solving the three-dimensional packing problem for strongly heterogeneous items while satisfying multiple constraints. It is capable of providing high-quality loading solutions for logistics enterprises and offers valuable insights for addressing more realistic container loading problems in future research.
This research investigates the strategic design of bus line networks by incorporating the operational objectives and constraints relevant to network operators. Drawing on industry expertise from a public transportation software company, we formulate the problem as a line planning optimization problem aimed at minimizing network operating costs while simultaneously addressing two critical service quality metrics: the deviation between passengers' actual travel times and their respective shortest-path travel times, and the proportion of passengers completing trips without transfers. To address problem instances of realistic scale and complexity, we develop and implement a column generation heuristic framework wherein both bus lines and passenger routing paths are generated dynamically throughout the solution process. Our methodological approach combines column generation and column enumeration algorithms, demonstrating computational efficiency when evaluated against established benchmark instances. Furthermore, we present a comprehensive case study examining a medium-sized French municipality, through which we demonstrate the practical integration of real-world design principles within our optimization framework. This empirical analysis yields novel insights regarding the sensitivity of both our proposed parameters and commonly employed parameters in bus network design literature.
Intercontinental rail freight transport has made significant strides in recent years, demonstrating its potential as a critical player in the global supply chain, such as Eurasian rail freight transport. However, Eurasian rail freight transport encounters challenges, including the presence of multiple rail systems with varying railway gauges, and especially in addressing the diverse requirements of the modern global supply chain. The traditional ’one service for all’ operational strategy is incapable of meeting the diverse transport requirements, emphasizing the need for more tailored solutions. We propose a time-space formulated Intercontinental Scheduled Service Network Design (I-SSND) for a relay intercontinental rail freight transport system, which necessitates an extension of the Scheduled Service Network Design (SSND). The I-SSND model, as a practical management tool, aims to move away from the traditional ’China-Europe Block Train’ business model, which offers only standard service, by enabling service differentiation. I-SSND model consider border crossing terminal times as well as train length variability across multiple different rail systems. It allows different orders from different origins to be consolidated at borders and share the same train service for the main transit based on their individual time constraints. The I-SSND model can assess demand variability and potential disruptions in the Eurasian rail network, including extended border crossing times, and evaluate their impact on overall network performance. The initial application of this model in Eurasian rail freight transport has yielded encouraging results. Mixed services demonstrate better performance compared to single standard services; the analysis shows an increase in profit growth and accepted orders. However, uneven demand distribution reduces overall network throughput and poses challenges for efficient capacity utilization, especially when compared to a more evenly distributed demand. Additionally, by integrating delay tolerance in mixed services, various metrics have significantly improved. On average, container acceptance increased by 10.44% and profits by 37.26%. These findings provide actionable managerial insights for intercontinental rail freight and highlight the necessity of establishing an entity to coordinate rail capacity planning across the various national rail networks involved.
The widespread adoption of digital distribution channels both enables and forces more and more logistics service providers to manage booking processes actively to maintain competitiveness. As a result, their operational planning is no longer limited to solving vehicle routing problems. Instead, demand management decisions and vehicle routing decisions are optimized integratively with the aim of maximizing revenue and minimizing fulfillment cost. The resulting integrated demand management and vehicle routing problems (i-DMVRPs) can be formulated as Markov decision process models and, theoretically, can be solved via the well-known Bellman equation. Unfortunately, the Bellman equation is intractable for realistic-sized instances. Thus, in the literature, i-DMVRPs are often addressed via decomposition-based solution approaches involving an opportunity costs approximation as a key component. Despite its importance, to the best of our knowledge, there is no technique to systematically analyze how the accuracy of the opportunity costs approximation affects the performance, e.g., the profit, the revenue, the number of accepted customers, or the cost of the overall logistics system, which is represented by a vehicle routing problem, nor are there general guidelines on when to apply which class of approximation approach. In this work, we address this research gap by proposing an explainability technique that quantifies and visualizes the magnitude of approximation errors, their immediate impact on the underlying vehicle routing problem and its profitability, and the relevance of approximation errors in specific regions of the state space. Exploiting reward decomposition, it further yields a characterization of different types of approximation errors. Applying the technique to a generic i-DMVRP in a full-factorial computational study and comparing the results with observations in existing literature, we show that the technique contributes to better explaining algorithmic performance and provides guidance for the algorithm selection and development process.
The planning and operations of public transport has benefited from the development and application of Operations Research (OR) techniques in the past half a century. In this article, we describe OR-related techniques and applications in the public transport domain in the last 50 years (1975-2025) since the origin of the intersection of these two research fields. Following a brief description of the public transport planning process, we outline how different topics, models, and solution approaches have evolved throughout this period. For each topic-varying from network assignment, line planning and crew scheduling to real-time management and demand-responsive transport-we review seminal works, key approaches and developments as well as comment on the applicability thereof and recent trends. In addition, we identify primary cross-cutting themes of research: integrating different planning stages, system resilience, dealing with uncertainties and energy-efficient public transport, as well as pricing and equity considerations. Moreover, reinforcement learning and quantum computing are expected to play an increasingly important role in OR applications in public transport. In the next half a century OR in public transport will undoubtedly continue to evolve in response to the technical developments in the transport sector, the developments in algorithms, software and hardware for computing, and by the challenges society faces.
The ever-growing diffusion of automation in road transport and the spreading of communication technologies applied to road infrastructures toward so-called smart roads is leading to a need for coordination methods for automated vehicles, to fully exploit the potentialities of such technologies to make road transport more efficient, safer, and greener. This study focuses on these issues, particularly determining the optimal scheduling and speeds of automated vehicles to cross intersections safely, without stopping and without the need for a traffic signal. To accomplish this, the problem is formulated as a mixed-integer linear programming (MILP) optimization problem for a generic intersection characterized by an arbitrary number of road segments and lanes. In addition, a discussion of the properties of the problem solutions, an application of the proposed approach to a case study, a solution strategy that can be used to solve large problem instances in a reasonable time, and a sensitivity analysis of the primary model parameters are provided. The considered case study shows that the proposed model can effectively avoid vehicle conflicts and increase the intersection capacity up to double with respect to both first-come first-served control policy and signalized intersections.
