The vehicle routing problem

Unmanned aerial vehicles, or drones, have the potential to significantly reduce the cost and time of making last-mile deliveries and responding to emergencies. Despite this potential, little work has gone into developing vehicle routing problems (VRPs) specifically for drone delivery scenarios. Existing VRPs are insufficient for planning drone deliveries: either multiple trips to the depot are not permitted, leading to solutions with excess drones, or the effect of battery and payload weight on energy consumption is not considered, leading to costly or infeasible routes. We propose two multitrip VRPs for drone delivery that address both issues. One minimizes costs subject to a delivery time limit, while the other minimizes the overall delivery time subject to a budget constraint. We mathematically derive and experimentally validate an energy consumption model for multirotor drones, demonstrating that energy consumption varies approximately linearly with payload and battery weight. We use this approximation to derive mixed integer linear programs for our VRPs. We propose a cost function that considers our energy consumption model and drone reuse, and apply it in a simulated annealing (SA) heuristic for finding suboptimal solutions to practical scenarios. To assist drone delivery practitioners with balancing cost and delivery time, the SA heuristic is used to show that the minimum cost has an inverse exponential relationship with the delivery time limit, and the minimum overall delivery time has an inverse exponential relationship with the budget. Numerical results confirm the importance of reusing drones and optimizing battery size in drone delivery VRPs.

Vehicle Routing Problems for Drone Delivery

Green Logistics has emerged as the new agenda item in supply chain management. The traditional objective of distribution management has been upgraded to minimizing system-wide costs related to economic and environmental issues. Reflecting the environmental sensitivity of vehicle routing problems (VRP), an extensive literature review of Green Vehicle Routing Problems (GVRP) is presented. We provide a classification of GVRP that categorizes GVRP into Green-VRP, Pollution Routing Problem, VRP in Reverse Logistics, and suggest research gaps between its state and richer models describing the complexity in real-world cases. The purpose is to review the most up-to-date state-of-the-art of GVRP, discuss how the traditional VRP variants can interact with GVRP and offer an insight into the next wave of research into GVRP. It is hoped that OR/MS researchers together with logistics practitioners can be inspired and cooperate to contribute to a sustainable industry.

Survey of Green Vehicle Routing Problem: Past and future trends

In this paper, we present a statistical criterion for accepting/rejecting the pairwise reciprocal comparison matrices in the analytic hierarchy process. We have studied the consistency in random matrices of different sizes. We do not agree with the traditional criterion of accepting matrices due to their inflexibility and because it is too restrictive when the size of the matrix increases. Our system is capable of adapting the acceptance requirements to different scopes and consistency necessities. The advantages of our consistency system are the introduction of adaptability in the acceptance criterion and the simplicity of the index we have used, the eigenvalue (λmax) and the simplicity of the criterion.

Consistency in the analytic hierarchy process: a new approach

Driven by new laws and regulations concerning the emission of greenhouse gases, carriers are starting to use electric vehicles for last-mile deliveries. The limited battery capacities of these vehicles necessitate visits to recharging stations during delivery tours of industry-typical length, which have to be considered in the route planning to avoid inefficient vehicle routes with long detours. We introduce the electric vehicle-routing problem with time windows and recharging stations E-VRPTW, which incorporates the possibility of recharging at any of the available stations using an appropriate recharging scheme. Furthermore, we consider limited vehicle freight capacities as well as customer time windows, which are the most important constraints in real-world logistics applications. As a solution method, we present a hybrid heuristic that combines a variable neighborhood search algorithm with a tabu search heuristic. Tests performed on newly designed instances for the E-VRPTW as well as on benchmark instances of related problems demonstrate the high performance of the heuristic proposed as well as the positive effect of the hybridization.

The Electric Vehicle-Routing Problem with Time Windows and Recharging Stations

A Green Vehicle Routing Problem (G-VRP) is formulated and solution techniques are developed to aid organizations with alternative fuel-powered vehicle fleets in overcoming difficulties that exist as a result of limited vehicle driving range in conjunction with limited refueling infrastructure The G-VRP is formulated as a mixed integer linear program Two construction heuristics, the Modified Clarke and Wright Savings heuristic and the Density-Based Clustering Algorithm, and a customized improvement technique, are developed Results of numerical experiments show that the heuristics perform well Moreover, problem feasibility depends on customer and station location configurations Implications of technology adoption on operations are discussed

A Green Vehicle Routing Problem

Bicycle-sharing programs have emerged around the world. Theoretically, the effect of bicycle sharing on more conventional transit modes can take a substitute or complementary form. On one hand, bicycle sharing could substitute for conventional transit as a convenient and sustainable travel option. On the other hand, bicycle sharing may complement such transit by seamlessly connecting transit stations with origins and destinations and thus increase accessibility. However, the questions of how and to what extent bicycle-sharing programs affect public transit ridership remain to be answered, despite the attempts of a few empirical and quantitative studies. This study examined the impact of the Capital Bikeshare (CaBi) program on Metrorail’s ridership in Washington, D.C. When CaBi trips were mapped, it was observed that Metrorail stations had been important origins and destinations for CaBi trips. Six of seven CaBi stations producing more than 500 trips were located close to Metrorail stations. This study con...

Bicycle sharing and public transit: does Capital Bikeshare affect Metrorail ridership in Washington, D.C.?

An experiment on the consistency of aggregated comparison matrices in AHP

The proliferation of micromobility, evolving from station-based to dockless bikeshare programs, has dramatically accelerated since 2017 with an influx of investment from the private sector to a new...

Exploratory Analysis of Real-Time E-Scooter Trip Data in Washington, D.C.:

The State of Maryland aims to double its transit ridership by the end of 2020. The Maryland Statewide Transportation Model (MSTM) has been used to analyze different policy options at a system-wide level. Direct ridership models (DRMs) estimate ridership as a function of station environment and transit service features rather than using mode-choice results from large-scale traditional models. They have been particularly favored for estimating the benefits of smart growth policies such as transit-oriented development (TOD) on transit ridership and can be used as complements to the traditional four-step models for analyzing smart-growth scenarios at a local level. They can also provide valuable information that a system-level analysis cannot provide. For example, DRMs can provide ridership estimate when densifying either households or employment at certain stations to test the effectiveness of TOD strategies at target stations. In this study, the authors developed DRMs of rail transit stations, namel...

Sevgi Erdogan

Papers

A Green Vehicle Routing Problem

Bicycle sharing and public transit: does Capital Bikeshare affect Metrorail ridership in Washington, D.C.?

An experiment on the consistency of aggregated comparison matrices in AHP

Exploratory Analysis of Real-Time E-Scooter Trip Data in Washington, D.C.:

How to Increase Rail Ridership in Maryland: Direct Ridership Models for Policy Guidance