Introduction to stochastic programming

The amount of pollution emitted by a vehicle depends on its load and speed, among other factors. This paper presents the Pollution-Routing Problem (PRP), an extension of the classical Vehicle Routing Problem (VRP) with a broader and more comprehensive objective function that accounts not just for the travel distance, but also for the amount of greenhouse emissions, fuel, travel times and their costs. Mathematical models are described for the PRP with or without time windows and computational experiments are performed on realistic instances. The paper sheds light on the tradeoffs between various parameters such as vehicle load, speed and total cost, and offers insight on economies of ‘environmental-friendly’ vehicle routing. The results suggest that, contrary to the VRP, the PRP is significantly more difficult to solve to optimality but has the potential of yielding savings in total cost.

The Pollution-Routing Problem

The vehicle routing problem

Personnel scheduling: A literature review

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

Due to the growing concern over environmental issues, regardless of whether companies are going to voluntarily incorporate green policies in practice, or will be forced to do so in the context of new legislation, change is foreseen in the future of transportation management. Assigning and scheduling vehicles to service a pre-determined set of clients is a common distribution problem. Accounting for time-dependent travel times between customers, we present a model that considers travel time, fuel, and CO2 emissions costs. Specifically, we propose a framework for modeling CO2 emissions in a time-dependent vehicle routing context. The model is solved via a tabu search procedure. As the amount of CO2 emissions is correlated with vehicle speed, our model considers limiting vehicle speed as part of the optimization. The emissions per kilometer as a function of speed are minimized at a unique speed. However, we show that in a time-dependent environment this speed is sub-optimal in terms of total emissions. This occurs if vehicles are able to avoid running into congestion periods where they incur high emissions. Clearly, considering this trade-off in the vehicle routing problem has great practical potential. In the same line, we construct bounds on the total amount of emissions to be saved by making use of the standard VRP solutions. As fuel consumption is correlated with CO2 emissions, we show that reducing emissions leads to reducing costs. For a number of experimental settings, we show that limiting vehicle speeds is desired from a total cost perspective. This namely stems from the trade-off between fuel and travel time costs.

Analysis of travel times and CO2 emissions in time-dependent vehicle routing

The use of electric vehicles for goods distribution opens up a wide range of research problems. Battery electric vehicles (BEVs) operate on batteries that have a limited life, as well as specific charging and discharging patterns which need to be considered in the context of their use for goods distribution. While many transportation problems associated with the integration of freight electric vehicles in distribution management problems have been investigated, there is room for further research on specifically how to model battery degradation and behaviour in such problems. The aim of this paper is to provide tractable models for transportation scientists that will allow predicting the lifetime degradation and instantaneous charging and discharging behaviour of BEV batteries.

Battery degradation and behaviour for electric vehicles: Review and numerical analyses of several models

Since the mid-2000s, electric vehicles have gained popularity in several countries even though their market share is still relatively low. However, most gains have been made in the area of passenger vehicles and most technical and scientific studies have been devoted to this case. By contrast, the potential of electric vehicular technology for goods distribution has received less attention. The issues related to the use of electric vehicles for goods distribution reveal a wide range of relevant research problems. The aims of this survey paper are to provide transportation researchers an overview of the technological and marketing background needed to conduct research in this area, to present a survey of the existing research in this field, and to offer perspectives for future research.

50th Anniversary Invited Article-Goods Distribution with Electric Vehicles: Review and Research Perspectives

Thirty years of heterogeneous vehicle routing

This paper introduces the fleet size and mix pollution-routing problem which extends the pollution-routing problem by considering a heterogeneous vehicle fleet. The main objective is to minimize the sum of vehicle fixed costs and routing cost, where the latter can be defined with respect to the cost of fuel and CO emissions, and driver cost. Solving this problem poses several methodological challenges. To this end, we have developed a powerful metaheuristic which was successfully applied to a large pool of realistic benchmark instances. Several analyses were conducted to shed light on the trade-offs between various performance indicators, including capacity utilization, fuel and emissions and costs pertaining to vehicle acquisition, fuel consumption and drivers. The analyses also quantify the benefits of using a heterogeneous fleet over a homogeneous one. Full text available at: http://www.sciencedirect.com/science/article/pii/S0191261514001623

/pdf/the-fleet-size-and-mix-pollution-routing-problem-3q7fi2llxx.pdf

Ola Jabali

Papers

Analysis of travel times and CO2 emissions in time-dependent vehicle routing

Battery degradation and behaviour for electric vehicles: Review and numerical analyses of several models

50th Anniversary Invited Article-Goods Distribution with Electric Vehicles: Review and Research Perspectives

Thirty years of heterogeneous vehicle routing

The fleet size and mix pollution-routing problem