A concise guide to existing and emerging vehicle routing problem variants

Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem variants with different attributes. In this article, we provide a concise overview of existing and emerging problem variants. Models are typically refined along three lines: considering more relevant objectives and performance metrics, integrating vehicle routing evaluations with other tactical decisions, and capturing fine-grained yet essential aspects of modern supply chains. We organize the main problem attributes within this structured framework. We discuss recent research directions and pinpoint current shortcomings, recent successes, and emerging challenges.

A concise guide to existing and emerging vehicle routing problem variants.

https://hal.archives-ouvertes.fr/hal-01807145/document

The role of operational research in green freight transportation

When planning routes for fleets of electric commercial vehicles, it is necessary to precisely predict the energy required to drive and plan for charging whenever needed, in order to manage their driving range limitations. Although there are several energy estimation models available in the literature, so far integration with Vehicle Routing Problems has been limited and without demonstrated accuracy. This paper introduces the Two-stage Electric Vehicle Routing Problem (2sEVRP) that incorporates improved energy consumption estimation by considering detailed topography and speed profiles. First, a method to calculate energy cost coefficients for the road network is outlined. Since the driving cycle is unknown, the model generates an approximation based on a linear function of mass, as the latter is only determined while routing. These coefficients embed information about topography, speed, powertrain efficiency and the effect of acceleration and braking at traffic lights and intersections. Secondly, an integrated two-stage approach is described, which finds the best paths between pairs of destinations and then finds the best routes including battery and time-window constraints. Energy consumption is used as objective function including payload and auxiliary systems. The road cost coefficients are aggregated to generate the path cost coefficients that are used in the routing problem. In this way it is possible to get a proper approximation of the complete driving cycle for the routes and accurate energy consumption estimation. Lastly, numerical experiments are shown based on the road network from Gothenburg-Sweden. Energy estimation is compared with real consumption data from an all-electric bus from a public transport route and with high-fidelity vehicle simulations. Routing experiments focus on trucks for urban distribution of goods. The results indicate that time and energy estimations are significantly more precise than existing methods. Consequently the planned routes are expected to be feasible in terms of energy demand and that charging stops are properly included when necessary.

Energy consumption estimation integrated into the Electric Vehicle Routing Problem

Electric Vehicle Routing Problem with Time-Dependent Waiting Times at Recharging Stations

Conventionally, vehicle routing problems are defined on a network in which the customer locations and arcs are given. Typically, these arcs somehow represent the distances or expected travel time derived from the underlying road network. When executed, the quality of the solutions obtained from the vehicle routing problem depends largely on the quality of the road network representation. This paper explicitly considers path selection in the road network as an integrated decision in the time-dependent vehicle routing problem, denoted as path flexibility (PF). This means that any arc between two customer nodes has multiple corresponding paths in the road network (geographical graph). Hence, the decisions to make are involving not only the routing decision but also the path selection decision depending upon the departure time at the customers and the congestion levels in the relevant road network. The corresponding routing problem is a time-dependent vehicle routing problem with path flexibility (TDVRP–PF). We formulate the TDVRP–PF models under deterministic and stochastic traffic conditions. We derive important insights, relationships, and solution structures. Based on a representative testbed of instances (inspired on the road network of Beijing), significant savings are obtained in terms of cost and fuel consumption, by explicitly considering path flexibility. Having both path flexibility and time-dependent travel time seems to be a good representation of a wide range of stochasticity and dynamics in the travel time, and path flexibility serves as a natural recourse under stochastic conditions. Exploiting this observation, we employ a Route-Path approximation method generating near-optimal solutions for the TDVRP–PF under stochastic traffic conditions.

Jean-Philippe Gross

Papers

Time-dependent vehicle routing problem with path flexibility