Vehicle Fleet Size Research Articles

Design a robust joint service of integrating demand responsive connectors (DRC) and shared bikes

ABSTRACT The integration of shared bikes and flexible transit services offers significant potential and benefits for urban transit systems. This paper presents a novel robust optimization framework for designing demand responsive connectors (DRC) that are fed by shared bikes. A two-stage model is formulated, with the first stage focusing on prereserved requests and the second stage addressing en-route random requests. The findings demonstrate that incorporating shared bikes can enhance the efficiency of serving en route late requests and reduce the required DRC vehicle fleet size. Additionally, it is observed that e-bikes are particularly suitable for this joint service due to their adaptability.

An aggregate matching and pick-up model for mobility-on-demand services

This paper presents an Aggregate Matching and Pick-up (AMP) model to delineate the matching and pick-up processes in mobility-on-demand (MoD) service markets by explicitly considering the matching mechanisms in terms of matching intervals and matching radii. With passenger demand rate, vehicle fleet size and matching strategies as inputs, the AMP model can well approximate drivers’ idle time and passengers’ waiting time for matching and pick-up by considering batch matching in a stationary state. Properties of the AMP model are then analyzed, including the relationship between passengers’ waiting time and drivers’ idle time, and their changes with market thickness, which is measured in terms of the passenger arrival rate (demand rate) and the number of active vehicles in service (supply). The model can also unify several prevailing inductive and deductive matching models used in the literature and spell out their specific application scopes. In particular, when the matching radius is sufficiently small, the model reduces to a Cobb–Douglas type matching model proposed by Yang and Yang (2011) for street-hailing taxi markets, in which the matching rate depends on the pool sizes of waiting passengers and idle vehicles. With a zero matching interval and a large matching radius, the model reduces to Castillo model developed by Castillo et al. (2017) that is based on an instant matching mechanism, or a bottleneck type queuing model in which passengers’ matching time is derived from a deterministic queue at a bottleneck with the arrival rate of idle vehicles as its capacity and waiting passengers as its customers. When both the matching interval and matching radius are relatively large, the model also reduces to the bottleneck type queuing model. The performance of the proposed AMP model is verified with simulation experiments.

Multiple shared mobility services under competition: Empirical evidence for public acceptance and policy insights to sustainable transport

Traffic congestion and roadside emissions are severe and common problems in metropolitans. As a promising and sustainable solution to mitigating these vehicle externalities, shared mobility reduces the required vehicle fleet size for serving a given level of demand by sharing a vehicle among travelers with similar schedules and itineraries. Public acceptance is the key to the success of shared mobility development. This study investigates the acceptance of drivers and passengers of two typical competing shared mobility modes, car-pooling and taxi ride sharing, taking Hong Kong as a case study. For an empirical evaluation, an on-street stated preference survey was conducted, and 829 respondents, including 257 private car owners and 572 non-private car owners were interviewed about their travel preferences in three given hypothetical scenarios. In total, 2,487 observations were collected for calibrating two proposed logit-based discrete choice models for drivers and passengers. The model results show that the out-of-pocket cost, in-vehicle travel time, and out-of-vehicle time are key factors influencing travelers’ decisions toward car-pooling and taxi ride-sharing. An equilibrium model was proposed and an iteration solution procedure was applied to obtain a convergent solution to balance the demand and supply of drivers and passengers for car-pooling services. Furthermore, sensitivity analyses were carried out to examine the effects of variations in proportions of travel cost and taxi fare shared by passengers for car-pooling and taxi ride-sharing, and to assist in the formulation of relevant transport policies.

Optimizing routing and scheduling of shared autonomous electric taxis considering capacity constrained parking facilities

This paper focuses on routing and scheduling of autonomous electric vehicles to provide reservation-based shared ride services, while a set of parking facilities with limited capacity are used for vehicle intermittent charging. A mixed-integer linear program model is formulated in the form of a vehicle routing problem with satellite facilities (VRPSF), subject to a series of additional time and capacity-related constraints. The objective of the model is to minimize the total operating costs of the system, including those related to vehicle miles traveled and the deployed vehicle fleet size. The number of vehicles inside each parking facility is tracked so as to ensure that the capacity is never exceeded throughout the service horizon. A customized solution method based on an adaptive large neighborhood search algorithm with an explicit treatment of parking facility choices is developed. A series of numerical experiments, consisting of both hypothetical examples and a real-world case study in Hangzhou, China, have been conducted to evaluate the effectiveness and applicability of the proposed model and algorithm. The results demonstrate that ride-sharing services and parking facilities have the potential to significantly reduce the total vehicle energy consumption and operating costs for a shared autonomous electric taxi (SAET) operator in practical scenarios.

A Multi-Objective Mathematical Programming Model for Transit Network Design and Frequency Setting Problem

In this study, we propose a novel multi-objective nonlinear mixed-integer mathematical programming model for the transit network design and frequency setting problem that aims at designing the routes and determining the frequencies of the routes to satisfy passenger demand in a transit network. The proposed model incorporates the features of real-life transit network systems and reflects the views of both passengers and the transit agency by considering the in-vehicle travel time, transfers, waiting times at the boarding and transfer stops, overcrowding and under-utilization of vehicles, and vehicle fleet size. Unlike previous studies that simplify several aspects of the transit network design and frequency setting problem, the proposed model is the first to determine routes and their frequencies simultaneously from scratch, i.e., without using line and frequency pools while considering the aforementioned issues, such as transfers and waiting. We solve the proposed model using Gurobi. We provide the results of what-if analyses conducted using a real-world public bus transport network in the city of Kayseri in Türkiye. We also present the results of computational tests implemented to validate and verify the model using Mandl benchmark instances from the literature. The results indicate that the model produces better solutions than the state-of-the-art algorithms in the literature and that the model can be used by public transit planners as a decision aid.

Vehicle dynamic dispatching using curriculum-driven reinforcement learning

This study focuses on optimizing resource allocation problems in complex dynamic environments, specifically vehicle dispatching in closed bipartite queuing networks. We present a novel curriculum-driven reinforcement learning (RL) approach that seamlessly incorporates domain knowledge and environmental feedback, effectively addressing the challenges associated with sparse reward scenarios in RL applications. This approach involves a scalable reinforcement learning framework for dynamic vehicle fleet size. We design dense artificial rewards using domain knowledge and incorporate artificial action–reward pairs into the original experience sequence forming the basic structure of the training instances. A difficulty momentum boosting strategy is proposed to produce a series of training instances with progressively increasing difficulty, ensuring that the RL agent learns decision strategies in an organized and smooth manner. Experimental results demonstrate that the proposed method significantly surpasses existing approaches in enhancing productivity and model learning efficiency for transport tasks in open-pit mines, while confirming the superiority of a flexible and automated curriculum learning process over a rigid setting. This approach has vast potential for application in dynamic resource allocation problems across industries, such as manufacturing and logistics.

A smart framework for municipal solid waste collection management: A case study in Greater Cairo Region

Around 28 million tons of municipal solid wastes (MSW) are annually generated in Egypt, with 40% in Greater Cairo Region (GCR). Although, the government aims at improving the MSW service coverage and collection efficiency, formal collection service is still limited and operates with low transportation efficiency resulting in illegal waste collection and dumping. This research aims at providing optimized collection systems to accommodate various housing levels and considering the available resources. As a case study, the collection routes in Al-Mostakbal City, are optimized by selecting the appropriate location and containers order. Meanwhile, the pick-up time is optimized using the appropriate vehicle type, fleet size, and rounds. In addition, dynamic routing is applied using developed production models. A simulation model is developed to assess various improvement scenarios and recommend the effective one for various schemes. The outcome is a highly-efficient framework; with potential to be extended to cover other urban areas.

Service Operation Vessels Fleet Size and Mix Location Routing for the Maintenance of an Offshore Floating Wind Farm

Mixed-integer linear programming is adopted to translate the routing of service operation vessels that support the logistic aspects of the maintenance of offshore floating wind farms into mathematical language. The models attempt to help the decision-makers by providing quantified tools to screen out the optimal planning for preventive maintenance. The models search for the optimal offshore base location, vessel’s routing per day, vessel’s capacity, and vessel fleet composition that minimize the total fixed and variable infrastructure cost. The integration of the vehicle fleet size and mix problem, facility location–allocation problem, and vehicle-routing problem with time window advances the state of the art. A realistic case study is shown, and the results and discussions demonstrated that the practical insights of the solutions, as well as the identification of the route patterns through a navigation route table, may improve the decision planning of preventive maintenance.

Integrated electric bus timetabling and scheduling problem

Vehicle timetabling and scheduling in a public transit system are usually performed separately, with the output of timetabling serving as the input of scheduling. An obvious drawback of this sequential planning method is that the trade-off between bus timetables and vehicle schedules may be neglected when determining solutions, which in turn results in that the obtained solutions may be inferior to those produced using an integrated framework. For example, a well-planned timetable may result in a schedule that requires a large vehicle fleet size with more operational cost, while a well-planned schedule may reduce the quality of a bus timetable by limiting the use of vehicles. In this paper, we introduce a time-space network-based framework for integrating electric bus timetabling and scheduling, with minimum and maximum headway times, depot requirements, deadheading and vehicle battery capacities considerations. The underlying time-space network is constructed with well-designed inventory arcs that represent multiple operations a bus may execute, thus decreasing the network size. Using the constructed network, we formulate the considered problem with a multi-commodity network flow model and develop a Lagrangian relaxation heuristic that consists of three phases, including generating relaxed solutions, making relaxed solutions feasible, and improving feasible solutions, to solve the integrated model. Tests on a set of instances confirm that the proposed integrated solution method can efficiently produce bus timetables and schedules with valid bounds, indicate that the integrated method can produce better solutions where the profit is increased by 5.29%–20.28%, and show how the headway times, service trip profit and operating cost settings affect the solution.

Assessment of health burden due to the emissions of fine particulate matter from motor vehicles: A case of Nakhon Ratchasima province, Thailand

Air pollution, owing to the ever-increasing transport vehicle fleet, and adverse health effects are increasing in provinces of Thailand. The study estimated that the vehicle fleet size of Nakhon Ratchasima (NR) province of Thailand will grow to 2 million vehicles by 2030, which was 1.36 million in 2021. In NR, the PM2.5 and PM10 concentrations already surpassed both WHO and NAAQS guidelines in 2019–2021. Using Pollution Control Department (PCD) approved Tier I and II Methodology of EMEP/EEA, this research estimated that the total tailpipe emission load will be 1039 tons of PM2.5, 16,630 tons of NO₂, 20,623 tons of CO, 195 tons NH₃, and 249 tons of SO₂ in NR during 2030. The emission load will increase to 1752 tons of PM2.5, 21,126 tons of NO2, 25,559 tons of CO, 361 tons of NH3 and 9344 tons of SO₂ during 2030 if upstream emissions are considered. This study has developed five control scenarios in line with the directives of PCD to mitigate the adverse health from vehicle-led air pollution in NR and implementation during 2024–2030.According to the study, different control scenarios to be implemented during 2024–2030, will be able to keep the fleet size of vehicles in the NR under control. The results show that the control scenarios will keep the annual tailpipe emission of PM2.5 at 604 tons in 2030, a 42 % reduction over the 2030 Business-As-Usual scenario (BAU). The health damage in the range of 6941 to 11,625 disability-adjusted life years (DALYs) under the 2030 BAU scenario in NR due to tailpipe and upstream emissions can be reduced to 4162–7318 DALYs with the implementation of different control scenarios. The control scenarios will also provide significant economic benefits ranging from 4465 to 6718 million THB during 2024–2030 through reduced DALYs and associated costs.

On-demand ride-sourcing markets with cryptocurrency-based fare-reward scheme

Cryptocurrency-based fare-reward scheme has been emerging from on-demand ride-sourcing platforms. The reward scheme provides each passenger with some units of cryptocurrency as rewards for use of ride service. The passengers can redeem the rewards for various redemption options. The redemption options offer the passengers economic benefits to offset a portion of costs of using ride services. In this way, the economic benefits serve as incentives for the passengers to repeatedly use ride services, which leads to increase in passenger demand for the platforms. From a passenger perspective, the reward scheme has a distinctive feature in that economic benefits can fluctuate according to changes in price of cryptocurrency in the future. Therefore, the passengers perceive the benefits differently based on their own risk preference and expectation of future price changes. It creates a challenge for the platforms because the optimal decisions for ride services vary by the value that the passengers place for their cryptocurrency rewards. To tackle this challenge, this paper analyzes the impacts of the reward scheme on on-demand ride-sourcing markets. The analysis is done with a mathematical model where a ride-sourcing platform makes decisions for trip fare, vehicle fleet size and cryptocurrency reward size. The reward decision is available under the assumption that the platform secures as many units of cryptocurrency as it rewards to passengers at their equilibrium price level. The model defines passengers’ perceived value of cryptocurrency rewards in terms of risk aversion level and expectation of future price growth of cryptocurrency. Afterwards, we investigate equilibrium and optimal properties of monopoly, social-optimum and second-best optimum ride-sourcing markets. Our analysis gives several key insights on the markets. First, the markets always locate at normal regime where interactions between passenger demand and vehicle supply for ride services converges to a stable equilibrium state. Second, this study shows that a ride-sourcing platform would make a decision to reward if passengers expect larger economic benefits from future redemption of cryptocurrency rewards than their current value. Third, it is shown that the quality of ride services would get worse because average pick-up time for passengers and drivers gets longer with more passenger retention. Fourth, this paper finds that the markets have more room to improve profit or social welfare as passengers expect larger speculative gains from reward redemption.

How managerial perspectives affect the optimal fleet size and mix model: a multi-objective approach

We examine the interplay between the business and logistical aspects of a heterogeneous vehicle mix and fleet size problem using inputs from a dairy cooperative in India. Five objective functions have been modelled and simultaneously solved using a mixed-integer linear fuzzy goal programming method. These include net profit as a maximization function, and transportation cost, transportation time, lost sales due to non-service, and in-transit damage or loss as minimization functions. Our paper contributes to the literature by evaluating critical business objectives such as net profits, lost sales due to non-service, and in-transit loss in conjunction with the typical heterogeneous fleet size and mix optimization decisions. The paper proposes two different solution methods: the Competing and the Compensatory method, which may be viewed as two extreme ends of the solution spectrum. Under the Competing method, all five objectives are assumed to be equally important, while the Compensating method allows the optimal solution to endogenously attach priorities to the different objectives. The two provide very different solutions since the Compensatory method considers the synergies between the objectives while the Competing method ignores them. The sensitivity analysis in the paper will also aid to managerial decision-making by evaluating different priorities for the multiple objectives during different periods. Given the impreciseness in the goal definitions and incomplete information available to a decision-maker, our paper the strengthens vehicle fleet size and mix decision modelling problems by adding other managerial perspectives.

Coordinating supply and demand in ride-sourcing markets with pre-assigned pooling service and traffic congestion externality

This paper proposes an equilibrium model to describe a ride-sourcing market with both ride-pooling (RP) and non-pooling (NP) services considering traffic congestion externality. In particular, we develop a deductive model to approximate the pool-matching probability and passengers’ expected waiting time under a pre-assigned pool-matching mechanism with meeting points, which is being used in products like Uber Express Pool. Using the model, we derive the equilibrium properties and examine the optimal operating strategies for achieving two market scenarios, including the monopoly optimum and social optimum. In contrast to the traditional wisdom, we find that the market could exist in one or multiple equilibria, depending on the trip fare difference between RP and NP services. Additionally, we show that average sojourn time first decreases in the vehicle fleet size (when traffic congestion is mild) and then increases in the vehicle fleet size (when traffic congestion is heavy), exhibiting a “smiling curve”. It is found that the monopoly optimum solution is always located in the downward side of the “smiling curve”, which implies the ride-sourcing platform will self-regulate its fleet size to avoid heavy traffic congestion. We also discuss the impacts of potential labor supply and background traffic on the platform’s optimal operating strategy and its optimal profit. This study gains interesting managerial insights that help understand how ride-sourcing platforms determine optimal operating strategies for both RP and NP services by considering traffic congestion externality.

How Many Vehicles Do We Need? Fleet Sizing for Shared Autonomous Vehicles With Ridesharing

Fleet sizing is critical for shared autonomous vehicle(SAV) fleet management to reduce maintenance costs and traffic congestions. As the passenger demands are dynamic, how to make the demand-aware dynamic ridesharing and calculate the fleet size is an important and challenging problem. In this paper, we propose a minimum fleet sizing method called Fleet Sizing for demand-aware Dynamic Ridesharing (FSDR) to accurately determine the fleet size for ridesharing enabled SAV system. Specifically, the travel demands are first predicted by an ensemble method that takes account of temporal correlations between regions. Then a concept called demand utility is proposed to measure the travel demands when planning vehicle paths, and the ride-matching dispatches vehicles to high travel demand regions by maximizing the demand utility along the vehicle path. Based on the ride-matching result, the minimum fleet size is calculated based on a trip graph by the Hopcroft-Karp algorithm. FSDR is evaluated on two real GPS taxi trajectory datasets from Wuhan, China, and San Francisco, USA. The result validates that the proposed demand-aware ridesharing in FSDR can significantly reduce the fleet size compared to the existing ride-matching methods. Moreover, the result shows that by allowing ridesharing, the vehicle fleet size can be reduced by 30%.

Drone-based delivery: a concurrent heuristic approach using a genetic algorithm

PurposeThe purpose of this study is to solve NP-Hard drone routing problem for the last-mile distribution. This is suitable for the multi-drones parcel delivery for the various items from a warehouse to many locations.Design/methodology/approachThis study conducts as a mission assignment of the single location per flight with the constraint satisfactions such as various payloads in weight, drone speeds, flight times and coverage distances. A genetic algorithm is modified as the concurrent heuristics approach (GCH), which has the knapsack problem dealing initialization, gene elitism (crossover) and gene replacement (mutation). Those proposed operators can reduce the execution time consuming and enhance the routing assignment of multiple drones. The evaluation value of the routing assignment can be calculated from the chromosome/individual representation by applying the proposed concurrent fitness.FindingsThis study optimizes the total traveling time to accomplish the distribution. GCH is flexible and can provide a result according to the first-come-first-served, demanded weight or distance priority.Originality/valueGCH is an alternative option, which differs from conventional vehicle routing researches. Such researches (traveling time optimization) attempt to minimize the total traveling time, distance or the number of vehicles by assuming all vehicles have the same traveling speed; therefore, a specific vehicle assignment to a location is neglected. Moreover, the main drawback is those concepts can lead the repeated selection of best quality vehicles concerning the speed without considering the vehicle fleet size and coverage distance while this study defines the various speeds for the vehicles. Unlike those, the concurrent concept ensures a faster delivery accomplishment by sharing the work load with all participant vehicles concerning to their different capabilities. If the concurrent assignment is applied to the drone delivery effectively, the entire delivery can be accomplished relatively faster than the traveling time optimization.

Optimizing Customized Transit Service considering Stochastic Bus Arrival Time

The introduction of customized bus (CB) service intends to expand and elevate existing transit service, which offers an efficient and sustainable alternative to serve commuters. A probabilistic model is proposed to optimize CB service with mixed vehicle sizes in an urban setting considering stochastic bus arrival time and spatiotemporal demand, which minimizes total cost subject to bus capacity and time window constraints. The studied optimization problem is combinatorial with many decision variables including vehicle assignment, bus routes, timetables, and fleet size. A heuristic algorithm is developed, which integrates a hybrid genetic algorithm (HGA) and adaptive destroy-and-repair (ADAR) method. The efficiency of HGA-ADAR is demonstrated through numerical comparisons to the solutions obtained by LINGO and HGA. Numerical instances are carried out, and the results suggested that the probabilistic model considering stochastic bus arrival time is valuable and can dramatically reduce the total cost and early and late arrival penalties. A case study is conducted in which the proposed model is applied to optimize a real-world CB service in Xi’an, China. The relationship between decision variables and model parameters is explored. The impacts of time window and variance of bus arrival time, which significantly affect service reliability, are analysed.

Pareto-efficient solutions and regulations of congested ride-sourcing markets with heterogeneous demand and supply

Ride-sourcing services have experienced dramatic growth over the past decade but aroused debates on whether and how the government should regulate the ride-sourcing platform. To tackle this critical issue, this paper investigates the regulatory outcomes of various representative government regulations, including price-cap regulation, vehicle fleet size control, wage (per-order) regulation, income (hourly earnings) regulation, car utilization rate regulation, commission charge regulation, etc. In particular, we try to answer two key questions: (1) whether a regulation leads to a Pareto-efficient outcome; (2) what are the impacts of the regulations on the platform’s decisions and the resulting realized passenger demand and driver supply. By conducting theoretical and numerical studies, we offer some interesting and useful managerial insights for the government in designing appropriate regulations. Notably, some prevailing regulations, such as fleet size control and wage regulation, fail to achieve a Pareto-efficient outcome, while the maximum commission regulation and minimum service level (demand) regulation can achieve Pareto-efficient outcomes in markets with homogeneous drivers and mild traffic congestion. In addition, drivers’ heterogeneity and traffic congestion substantially affect the regulatory outcomes of various regulations. For example, in markets with homogeneous drivers, the income regulation does not take effect, while in markets with heterogeneous drivers, the income regulation does influence the platform’s decisions but still cannot achieve a Pareto-efficient outcome. We also show that the government acts quite differently under mild or heavy traffic congestion: it tends to encourage more drivers to participate in the market by a minimum fleet size regulation when traffic congestion is light, but restrain the vehicle fleet size by a maximum fleet size regulation when traffic congestion is severe.

Optimal fleet size for a shared demand-responsive transport system with human-driven vs automated vehicles: A total cost minimization approach

Vehicle automation is expected to reduce the cost of shared demand-responsive transport (DRT) services. In this context, questions regarding the conditions under which fixed-route public transport can be replaced with shared on-demand services have emerged. The expected increase in competitiveness between fixed-route and on-demand services requires the development of frameworks that enable the analysis of transportation costs of alternative modes. In this research, we develop a total cost minimization model for demand-responsive door-to-door shared transportation services, including operator and user costs. Optimization variables are vehicle size and fleet size for operation with human-driven and automated vehicles. A hybrid approach is used in which the relevant variables are analytically and numerically modeled, using data from a large-scale agent-based simulation applied to the city of Munich. We compare the case in which all trip requests must be served with the case in which request rejections are allowed, based on waiting and travel times. Different demand levels and alternative scenarios for vehicle automation are analyzed. The results indicate that the performance of door-to-door on-demand shared systems depends on the operational scheme selected. For the DRT setup and vehicle assignment strategy studied, we find that if the system is forced to have no trip rejections, economies of scale are not present, and the high user costs hinder the system’s competitiveness even under the assumption of automated vehicles. In contrast, in a system that allows for trip rejections, economies of scale are present, and vehicle automation can especially reduce operator costs, increasing the system’s competitiveness against other transportation modes. Therefore, in our setting, the efficiency of the demand-responsive service depends on the ability to reject customers, which is against the spirit of a truly public transportation service. On scenario analysis, we show that a theoretical improvement in the performance of the real-time vehicle assignment strategy can significantly reduce total cost, with economies of scale under no-rejection operation. Future research needs to address whether the actual application of more complex vehicle assignment strategies can indeed make DRT systems more cost competitive while serving all trip requests.

Optimizing Vehicle Fleet and Assignment for Concentrating Solar Power Plant Heliostat Washing

Concentrating solar power central-receiver plants use thousands of sun-tracking mirrors, i.e., heliostats, to reflect sunlight to a central receiver, which collects and uses the heat to generate electricity. Over time, soiling reduces the reflectivity of the heliostats and, therefore, the efficiency of the system. Current industry practice sends vehicles to wash heliostats in an ad hoc fashion. We present a mixed-integer nonlinear program that determines wash vehicle fleet size, mix, and assignment of wash crews to heliostats to minimize the sum of (i) the revenues lost due to heliostat soiling, (ii) the costs of hiring wash crews and operating the vehicles, and (iii) the costs of purchasing wash vehicles. We establish conditions for convexity of the objective function, and then propose a decomposition method that enables near-optimal solutions to the wash vehicle fleet sizing and assignment problem on the order of a couple of minutes. These solutions yield hundreds of thousands of dollars in savings per year over current industry practices.

Vehicle scheduling for on-demand vehicle fleets in macroscopic travel demand models

The planning of on-demand services requires the formation of vehicle schedules consisting of service trips and empty trips. This paper presents an algorithm for building vehicle schedules that uses time-dependent demand matrices (= service trips) as input and determines time-dependent empty trip matrices and the number of required vehicles as a result. The presented approach is intended for long-term, strategic transport planning. For this purpose, it provides planners with an estimate of vehicle fleet size and distance travelled by on-demand services. The algorithm can be applied to integer and non-integer demand matrices and is therefore particularly suitable for macroscopic travel demand models. Two case studies illustrate potential applications of the algorithm and feature that on-demand services can be considered in macroscopic travel demand models.