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This paper considers the problem of how to determine an optimal fueling schedule and contracting policy with fuel suppliers so as to minimize the total cost of the fueling operation. The problem is formulated as a mixed integer program and the formulation is enhanced by valid inequalities and domination rules. The enhanced model allows us to obtain near optimal solutions for large scale instances.
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An integrated line planning and timetabling model is formulated with the objective of minimizing both user inconvenience and operational costs. User inconvenience is modeled as the total time passengers spend in a railway system, including waiting at origin and transfer stations. The model is solved using a cross-entropy metaheuristic. The line plan and timetable of Israel Railways is used as a benchmark. Using the same amount of resources, the average journey time of passengers is reduced by 20%.
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In this study, we propose improving the performance of one-way vehicle sharing systems by incorporating parking reservation policies. In particular, we study a parking space reservation policy in which, upon rental, the users are required to state their destination and the system then reserves a parking space for them until they arrive at their destinations. We measure the performance of the vehicle sharing system by the total excess time users spend in the system. The excess time is defined as the difference between the actual journey time and the shortest possible travel time from the desired origin to the desired destination. A Markovian model of the system is formulated. Using this model, we prove that under realistic demand rates, this policy improves the performance of the system. This result is confirmed via a simulation study of a large real system, Tel-O-Fun, the bike-sharing system in Tel-Aviv. For all the tested demand scenarios, the parking reservation policy reduces the total excess time users spend in the system, with a relative reduction varying between 14% and 34%. Through the simulation we examine additional service-oriented performance measures and demonstrate that they all improve under the parking reservation policy.
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We study the regulation of one-way station-based vehicle sharing systems through parking reservation policies. We measure the performance of these systems in terms of the total excess travel time of all users caused as a result of vehicle or parking space shortages. We devise mathematical programming based bounds on the total excess travel time of vehicle sharing systems under any passive regulation (i.e., policies that do not involve active vehicle relocation) and, in particular, under any parking space reservation policy. These bounds are compared to the performance of several partial parking reservation policies, a parking space overbooking policy and to the complete parking reservation (CPR) and no-reservation (NR) policies introduced in a previous paper. A detailed user behavior model for each policy is presented, and a discrete event simulation is used to evaluate the performance of the system under various settings. The analysis of two case studies of real-world systems shows the following: (1) a significant improvement of what can theoretically be achieved is obtained via the CPR policy; (2) the performances of the proposed partial reservation policies monotonically improve as more reservations are required; and (3) parking space overbooking is not likely to be beneficial. In conclusion, our results reinforce the effectiveness of the CPR policy and suggest that parking space reservations should be used in practice, even if only a small share of users are required to place reservations.
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In bike-sharing systems, a small percentage of the bicycles become unusable every day. Currently, there is no reliable on-line information that indicates the usability of bicycles. We present a model that estimates the probability that a specific bicycle is unusable as well as the number of unusable bicycles in a station, based on available trip transaction data. Further on, we present some information based enhancements of the model and discuss an equivalent model for detecting locker failures.
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In bike-sharing systems, at any given moment, a certain share of the bicycle fleet is unusable. This phenomenon may significantly affect the quality of service provided to the users. However, to date this matter has not received any attention in the literature. In this article, the users' quality of service is modeled in terms of their satisfaction from the system. We measure user dissatisfaction using a weighted sum of the expected shortages of bicycles and lockers at a single station. The shortages are evaluated as a function of the initial inventory of usable and unusable bicycles at the station. We analyze the convexity of the resulting bivariate function and propose an accurate method for fitting a convex polyhedral function to it. The fitted polyhedral function can later be used in linear optimization models for operational and strategic decision making in bike-sharing systems. Our numerical results demonstrate the significant effect of the presence of unusable bicycles on the level of user dissatisfaction. This emphasizes the need to have accurate real-time information regarding bicycle usability.
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In this paper, we study the operations of a one-way station-based carsharing system implementing a complete journey reservation policy. We consider the percentage of served demand as a primary performance measure and analyze the effect of several dynamic staff-based relocation policies. Specifically, we introduce a new proactive relocation policy based on Markov chain dynamics that utilizes reservation information to better predict the future states of the stations. This policy is compared to a state-of-the art staff-based relocation policy and a centralistic relocation model assuming full knowledge of the demand. Numerical results from a real-world implementation and a simulation analysis demonstrate the positive impact of dynamic relocations and highlight the improvement in performance obtained with the proposed proactive relocation policy.
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In the Dial-a-Ride-Problem (DARP) a fleet of vehicles provides shared-ride services to users specifying their origin, destination, and preferred arrival time. Typically, the problem consists of finding minimum cost routes, satisfying operational constraints such as time-windows, origin-destination precedences, user maximum ride-times, and vehicle maximum route-durations. This paper presents a problem variant for the DARP which considers the use of electric autonomous vehicles (e-ADARP). The problem covers battery management, detours to charging stations, recharge times, and selection of destination depots, along with classic DARP features. The goal of the problem is to minimize a weighted objective function consisting of the total travel time of all vehicles and excess ride-time of the users. We formulate the problem as a 3-index and a 2-index mixed-integer-linear program and devise a branch-and-cut algorithm with new valid inequalities derived from e-ADARP properties. Computational experiments are performed on adapted benchmark instances from DARP literature and on instances based on real data from Uber Technologies Inc. Instances with up to 5 vehicles and 40 requests are solved to optimality.
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Semi-autonomous transportation systems are an intermediate step towards full automation of transportation systems. They use and benefit from the technological advances brought by automation while being already implementable at larger scale under the current regulations and within the existing urban environment.
In this paper, we present a new type of semi-autonomous transportation system referred to as Multi-Layered Personal Transit System (MuLPeTS). It consists of convoys composed of one human-driven lead vehicle guiding several autonomous small capacity trailers in which the passengers travel. These trailers can detach from a convoy and travel autonomously in a protected environment before attaching later to another convoy. The interest of this transportation concept is threefold: (i) this assembly of vehicles is able and allowed to move in mixed-traffic conditions whereas fully autonomous driving is still largely restricted; (ii) a trailer can travel autonomously in the vicinity of stations to pick-up and drop-off passengers while the convoy it was previously part of continues its route without further delay; and (iii) passengers complete their entire journey on board a single trailer, that is they avoid the need to transfer. We analyze how this new type of transportation system relates to existing alternatives and propose an operational concept for it, in which we account for passenger assignment, lead vehicle routes and trailer movements, including empty trailer relocation. We extensively test this concept within a purpose-built simulation environment to evaluate the performance of this kind of system based on real-world data instances. The results highlight the most promising operational policies and characterize favorable system configurations.
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This survey article provides an overview on future directions for research in urban mobility and city logistics. It sets a focus on three particularly serious changes in the business models: vehicle autonomy, crowdsourced logistics, and urban micro-consolidation centers. In the future, service fleets might fully or partially be autonomous which brings new operational opportunities and challenges. In many business models, crowdsourcing jobs are already common. While this might save costs, it also leads to uncertainty in the available workforce and their behavior. Finally, micro-consolidation centers enable the use of smaller, cheaper, and emission-friendlier vehicles, but lead to more complex planning and operations. For each topic, the article presents an overview on the relevant literature as well as important and open research challenges.
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This paper contributes to the intersection of operations research and machine learning in the context of autonomous ridesharing. In this work, autonomous ridesharing operations are reproduced through an event-based simulation approach and are modeled as a sequence of static subproblems to be optimized. The optimization framework consists of a novel data-driven metaheuristic within a two phase approach. The first phase consists of a greedy insertion heuristic that assigns new online requests to vehicles. The second phase consists of a local-search based metaheuristic that iteratively revisits previously-made vehicle-trip assignments through intra- and inter-vehicle route exchanges. These exchanges are performed by selecting from a pool of destroy–repair operators using a machine learning approach that is trained offline on a large dataset composed of more than one and a half million examples of previously-solved autonomous ridesharing subproblems.
Computational results are performed on multiple dynamic instances extracted from real ridesharing data published by Uber Technologies Inc. Results show that the proposed machine learning-based optimization approach outperforms benchmark state-of-the-art data-driven metaheuristics by up to about nine percent, on average. Managerial insights highlight the correlation between selected vehicle routing features and the performance of the metaheuristics in the context of autonomous ridesharing operations.
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Decision-making is a crucial aspect for winning a basketball game. In particular, choosing the players who will take game-decisive shots (‘clutch shots’). While some coaches prefer the teams’ stars, others may prefer players who seemingly excel during clutch time (‘clutch players’) or are shooting well during a specific game (‘hot players’). In this study, we consider a variety of policies for choosing the shot-taker (for example, according to field goal percentage). Then, we compare the policies and rank them to create a policy hierarchy, which serves as a decision guide for the coach. We show that when our recommendations are implemented (i.e., the highest ranked player takes the shot) the success rate is significantly greater: 51.2%, compared to 41.3% in commonly taken clutch shots. Furthermore, our results indicate that players who excelled in past clutch shots are more likely to succeed, independently to their performance in the current game.
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Shared mobility services involving electric autonomous shuttles have increasingly been implemented in recent years. Due to various restrictions, these services are currently offered on fixed circuits and operated with fixed schedules. This study introduces a service variant with flexible stopping patterns and schedules. Specifically, in the Electric Dial-a-Ride Problem on a Fixed Circuit (eDARP-FC), a fleet of capacitated electric shuttles operates on a given circuit, consisting of a recharging depot and a sequence of stations where users can be picked-up/dropped-off. The shuttles may perform multiple laps between which they may need to recharge. The goal of the problem is to determine the vehicles’ stopping sequences and schedules, including recharging plans, so as to minimize a weighted sum of the total user excess time and the total number of laps. The eDARP-FC is formulated as a non-standard lap-based MILP and is shown to be NP-Hard. Efficient polynomial time algorithms are devised for two special scheduling sub-problems. These algorithms and several heuristics are then applied as sub-routines within a Large Neighborhood Search metaheuristic. Experiments on instances derived from a real-life service demonstrate that the flexible service results in a 60%-85% decrease in the excess time at the same operational costs.
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This paper offers a new algorithm to efficiently optimize scheduling decisions for dial-a-ride problems (DARPs), including problem variants considering electric and autonomous vehicles (e-ADARPs). The scheduling heuristic, based on linear programming theory, aims at finding minimal user ride time schedules in polynomial time. The algorithm can either return optimal feasible routes or it can return incorrect infeasibility declarations, on which feasibility can be recovered through a specifically-designed heuristic. The algorithm is furthermore supplemented by a battery management algorithm that can be used to determine charging decisions for electric and autonomous vehicle fleets. Timing solutions from the proposed scheduling algorithm are obtained on millions of routes extracted from DARP and e-ADARP benchmark instances. They are compared to those obtained from a linear program, as well as to popular scheduling procedures from the DARP literature. Results show that the proposed procedure outperforms state-of-the-art scheduling algorithms, both in terms of compute-efficiency and solution quality.
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Mobility On Demand (MOD) services, such as ride-pooling, have gained global popularity in providing on-demand transit services. By offering convenient and affordable trips, MOD services aim to attract users, reduce congestion, and alleviate parking demand in dense urban areas.
While prior research primarily focuses on operational costs and service measures, this study takes a broader perspective by considering the external costs associated with autonomous MOD ride-pooling services. Incorporating external costs into the design and evaluation of MOD services enables a comprehensive understanding of their impact on the entire urban population, informing effective regulations and incentives. A dynamic approach is proposed for calculating external costs, accounting for factors like air pollution, climate impact, noise and accidents. These costs are integrated into FleetPy, an agent-based simulation tool for ridesharing analysis and optimization.
A case study of Munich reveals tradeoffs between external costs, internal costs, and service quality. Results suggest mid-sized vehicles with three-person capacity strike a balance between energy efficiency and transport capacity. Optimized routing and pooling algorithms can significantly reduce external costs (up to 47%), although trip time may be affected due to speed-cost correlation. Considering external costs enables policymakers to formulate regulations supporting sustainable on-demand mobility. Continued research will advance understanding of external transportation costs, aiding the integration of autonomous on-demand mobility into urban transportation planning.
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The Israeli Queue is a batch service polling system in which a single server attends a collection of queues according to a seniority order. An arriving customer may belong to one of multiple classes. Upon arrival, she either joins a queue with customers from her class or opens a new queue in case she is the first in line from her class. Members of the class with the most senior customer are served together as a batch within a service time that is independent of their amount. This service regime is encountered in applications such as advanced elevator systems and on-demand shared mobility, where passengers with the same destinations may share a ride. However, in many systems, the vehicles' capacities are small and binding. Thus, calling for an implicit modeling investigating the Israeli Queue with a capacitated server (IQCS). In this paper, we introduce the IQCS model, in which only a limited number of customers can be served in a single service time. If the queue length of the served class exceeds the server's capacity, a capacity sized batch of customers is served and the seniority of the class is set according to its senior un-served customer. We approximate this system by formulating a corresponding quasi-birth-death process, and derive approximations for various performance measures. To validate our approach, we implement an ad-hoc simulation model and use it to compare the IQCS, the approximate model, and the Israeli Queue. Our analysis across various settings demonstrates the accuracy of the approximate model. Nonetheless, the presence of a remaining gap underscores the ongoing challenge of precisely and efficiently modeling the IQCS, posing an open question for the Operations Research community.
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Autonomous mobile robots (AMRs) are small, electric, wheeled vehicles that operate at pedestrian speeds. In the last-mile delivery service considered in this study, a fleet of AMRs is deployed across multiple recharging depots within a service area, from which they depart to perform point-to-point deliveries. We consider an operational setting in which AMRs are allowed to travel onboard public transit vehicles, with the objective of extending the service range and reducing energy consumption. To model this problem, we propose two mixed-integer linear programming formulations: an arc-based formulation and a path-based formulation. For the latter, we develop a column generation approach coupled with a four-stage dynamic programming algorithm to efficiently solve the underlying pricing subproblem. This solution approach is further embedded within a rolling horizon framework to address dynamic and large-scale operational settings. A case study conducted in a subregion of Tel Aviv demonstrates the ability of the proposed methodology to handle large-scale instances based on real-world parameters. A sensitivity analysis highlights the effects of request time-window widths, public transit capacity, and AMR battery range on the number of requests that can be served. Finally, the results obtained under the rolling horizon framework confirm the feasibility and practical applicability of the proposed column generation approach.
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Under Review
In semiautonomous transportation systems, vehicle autonomy capabilities are utilized in a partial manner to adhere to current regulations. This study focuses on a personal transit system in which convoys composed of human-driven lead vehicles and several autonomous cabins provide station-to-station transportation. While the lead vehicles travel nonstop between the stations of the system, the cabins have the ability to detach from the convoys in the proximity of stations and autonomously travel in and out of the stations to pick-up and drop-off passengers. In a previous study, the assignment of passengers to cabins and the routing of the cabins were determined dynamically, while static circular routes were determined for the lead vehicles.
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The Partial Set Covering Problem (PSCP) seeks a minimum number of sets to cover at least a prescribed fraction of a universe of elements, generalizing the classical Set Covering Problem that requires full coverage. While optimal solutions are known for most small and medium-sized OR-Library instances, large-scale instances, featuring many elements and sets, remain challenging, with existing methods exhibiting significant optimality gaps.
This paper focuses on large-scale PSCP instances and proposes two metaheuristic frameworks based on Large Neighborhood Search (LNS) and Variable Neighborhood Search (VNS). The LNS algorithm combines two destroy operators, random and greedy min-loss removal, with two complementary repair operators: a fast greedy repair and a time-limited Integer Linear Programming–based repair. The VNS algorithm performs local improvements through multiple search operators and escapes local optima via a shaking operator that partially destroys and greedily reconstructs the solution with coverage-focused repairs.
Numerical results for the 12 large benchmark instances show that the proposed approaches outperform the current state of the art in most cases. Their relatively simple implementation further supports the broader conclusion that local-search heuristics may be better suited for large-scale instances than population-based approaches. In addition, we introduce 30 new large-scale benchmark instances and report the best solutions found, providing a new reference set for future research on large-scale PSCP.
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Urban rail systems often operate with fixed schedules and large rolling stock that are difficult to adapt to temporal fluctuations in demand, resulting in overcrowding during peak periods and underutilized service during off-peak hours. This paper proposes Flexible Autonomous Shared Transit over Existing Rail (FASTER), a new transit concept that repurposes existing urban rail infrastructure to provide on-demand, shared, autonomous mobility using small electric vehicles operating on rail lines. To evaluate the operational feasibility of the approach, we develop both an analytical approximation model based on queueing theory and a detailed event-based simulation model. The proposed framework is applied to three rail lines in the Boston metropolitan area using real-world demand data. Results show that, during peak periods, FASTER can achieve service levels comparable to or better than existing operations while consuming only one-third to one-half of the energy required by conventional rail services. During off-peak periods, the system scales efficiently to lower demand levels while maintaining service quality with substantially smaller active fleets. The findings suggest that repurposing existing rail infrastructure for flexible autonomous shared transit may provide an energy-efficient and operationally adaptable pathway for improving urban public transportation systems.
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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 multi-criteria function comprising total vehicle distance and total walking distance. 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.

