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%.

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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.

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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.

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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.

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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.

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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.

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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.

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Sparsely populated areas tend to be poorly served by Fixed Line and Schedule (FLS) public transport systems as the operation of a regular bus line is not economically viable for such areas. Therefore, introducing a Demand Responsive Transport (DRT) to partially replace FLS can result in increasing mobility service accessibility and inclusion. In this paper, a mixed-integer linear problem (MILP) is proposed to design an integrated FLS and DRT network for a transport operator. Passengers behavior is implicitly incorporated in our proposed approach via a discrete choice model. In addition, a tailored Adaptive Large Neighborhood Search (ALNS) coupled with tabu search and simulated annealing are introduced. We test our algorithm on real instances from a public transport operator in the Netherlands. The proposed algorithm can solve the problem up to 170 times faster than the MILP within 4% to 10% gap. Our proposed resolution approach investigates the temporal and spatial feasibility of deploying these integrated mobility systems based on the service level and provides recommendations to public transport operators.

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Urban mobility services face the challenge of planning their operations efficiently while complying with user preferences. In this paper, we introduce a new mathematical model called a choice-driven dial-a-ride problem (CD-DARP) which is a generalization of the dynamic DARP where passenger behavior is integrated in the operational planning using choice models and assortment optimization. We look at two types of mobility services, private and shared. Our problem extends the dynamic DARP by (i) changing its objective function to profit maximization, where both cost and revenue are variables, and (ii) incorporating assortment optimization with routing decisions in a dynamic setting. We propose a pricing scheme based on a choice model designed to offer service alternatives at the time a customer makes a request. We introduce a tailored algorithm to efficiently solve the dynamic CD-DARP. Computational results indicate that our proposed approach outperforms dynamic DARP in terms of reducing routing costs and improving the number of customers served.

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In this paper, we evaluate the cost of the electrification of an existing bus network. We propose a family of bi-objective mathematical models to demonstrate the trade-off between strategic (i.e., battery sizing and the locations of charging stations) and operational decisions (i.e., battery degradation). The proposed mathematical models investigate different charging policies and measure their impacts on overall cost. Battery degradation is estimated by a tailored and linearized semi-empirical approach and is explicitly incorporated in the proposed mixed-integer linear models. The impact of different charging policies on reducing the overall costs is evaluated for a bus network in Rotterdam. The results show that allowing for flexibility in the loss of energy levels at each bus cycle results in savings up to 17% in battery aging.

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Choice-based optimization problems are the family of optimization problems that incorporate the stochasticity of individual preferences according to discrete choice models to make planning decisions. This integration brings non-convexity and nonlinearity to the associated mathematical formulations. Previously, the authors have tackled these issues by introducing a simulation-based approximation of the choice model with the aim of linearizing it. Nevertheless, already existing exact methods and state-of-the-art commercial solvers fail to solve relevant instances. In this paper, we propose a novel Lagrangian decomposition method inspired by scenario decomposition and scenario grouping in the stochastic programming framework for the purpose of solving choice-based optimization problems. In addition, we develop a tailored algorithm to generate feasible solutions to the original problem from the solution of the Lagrangian subproblem. Hence, at each iteration of the subgradient method, which is used to solve the Lagrangian dual, we provide both an upper and a lower bound to the original problem. This enables the calculation of the duality gap to assess the quality of the generated solutions. Computational results show that the decomposition method provides solutions with optimality gaps below 0.5% and restricted duality gaps within low computational times. We also show that scenario grouping leads to high-quality feasible solutions and lower duality gaps.

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Worldwide, cities and urbanised areas attract more people and economic activities. In addition, new ways of working, shopping and recreation, mobility and ‘ownership’ are introduced– all influenced by digitalisation. The United Nations (2018) expect the world-wide population living in urbanised regions to grow from 55% to 68% by 2050. However, concentration of residential, industrial, commercial, and recreational activities leads to an increasing pressure on land use and accessibility, potentially causing adverse environmental, health and liveability effects. Increasing housing density and decreasing space for transport infrastructure and parking call for new smart mobility approaches to ensure sustainable and inclusive accessibility.@en

In many transportation systems, a mismatch between the associated design and planning decisions and the demand is typically encountered. A tailored system is not only appealing to operators, which could have a better knowledge of their operational costs, but also to users, since they would benefit from an increase in the level of service and satisfaction. Hence, it is important to explicitly allow for the interactions between the two in the model governing the decisions of the system. Discrete choice models (DCM) provide a disaggregate demand representation that is able to capture the impact on the behavior of these decisions by taking into account the heterogeneity of tastes and preferences of the users, as well as subjective aspects related to attitudes or perceptions. Despite their advantages, the demand expressions derived from DCM are non-linear and non-convex in the explanatory variables, which restricts their integration in optimization problems. In this paper, we overcome the probabilistic nature of DCM by relying on simulation in order to specify the demand directly in terms of the utility functions (instead of the choice probabilities). This allows us to define a mixed-integer linear formulation that characterizes the preference structure and the behavioral assumption of DCM, which can then be embedded in a mixed-integer linear programming (MILP) model. We provide an overview of the extent of the framework with an illustrative MILP model that is designed to solve a profit maximization problem of a parking services operator. The obtained results show the potential of the proposed methodology to adjust supply-related decisions to the users.@en

Unexpected disruptions commonly occur in the railway network, causing delays, and extra cost for operators and inconvenience for passengers by missing their connection and facing overcrowded trains. This paper presents a passenger-centric approach for timetable rescheduling in case of disruption. We study a railway system in which passengers are free to choose their itinerary and compete over limited train capacity. We explicitly model the passengers’ decisions using a choice model. We propose a multi-objective algorithmic approach to solve the problem. Service punctuality, operating cost, and passengers’ inconvenience are selected as objectives. Computational experiments are performed on the Swiss and Dutch railway networks. The results demonstrate the performance of the algorithm in finding high-quality solutions in a computationally efficient manner.

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Interconnected logistics system can play an important role towards having a more sustainable green freight transport. Recently, after introducing the concept of Physical Internet (PI), researchers have started to explore the opportunities and challenges that a collaborative and interconnected network could create in different aspects of the supply chain. In this research, we study the last mile delivery as well as vehicle dispatching problems under the assumptions of collaborative supply chain networks while assuming that modularized boxes are applied inside the network from the provider to the final customer. Our research aims at proposing a more efficient resource planning with the minimal number of empty vehicle movements running on roads that ultimately leads to decrease carbon dioxide emission. The assumptions have been tested and verified using real data coming from a major retail company in Europe.@en

This paper presents a route optimization algorithm for light aircraft operating under visual flight rules. The problem aims at finding a minimum-duration, collision-free route in three spatial dimensions with possible aircraft maneuvers. The optimal route takes into account the aircraft kinodynamic characteristics and its interaction with external wind. A data processing approach is presented to recast the flying environment as a series of polyhedrons based on which a mixed-integer linear model is formulated. A two-stage route optimization model is then introduced to solve real-life instances. Computational experiments depict the efficiency of this approach.@en

A passenger centric timetable is such a timetable that the satisfaction of the passengers is maximized. However, these timetables only maximize the probability of a passenger to take the train, but provide no insight on the actual choices of the passengers. Therefore, in this manuscript we replace the deterministic passenger satisfaction function with a probabilistic demand forecasting model inside of the passenger centric train timetable design. The actual forecasts lead to a realistic train occupation. Knowing the train occupation, we can estimate the revenue and to use pricing as a mobility management to further improve the level-of-service. We use a logit model that we calibrate to reflect the known demand elasticities. We further include a competing operator as an opt-out option for the passengers. Subsequently, we integrate the passenger centric train timetabling problem with a ticket pricing problem. We solve the elastic passenger centric train timetabling problem for various types of timetables using a simulated annealing heuristic on a case study of Israeli Railways. The results of our case study show that the generated revenues can be increased by up to 15% when taking into account the passengers’ behavior along with a specific pricing scheme. This study further confirms the advantages of hybrid cyclicity.

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