الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
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Abstract
The Vehicle Routing Problem (VRP) is one of the most studied problems in logistics. VRP aims to determine the optimal set of routes for a fleet of vehicles to deliver the required products to a group of customers geographically distributed in dispersed places. This type of problem is a combinatorial problem including permutations and combinations of routes. The number of solutions is a function of the size of problem (which number of customers in the present case). Therefore, reaching the all-possible solutions through the formation of all routes is difficult and it is called NP-Hard. The best option is to use meta-heuristic techniques and develop effective and efficient solution methodology to find solutions close to optimal. In the field of VRP, most of the researchers seeks to identify research goals that have multiple objectives to improve results. Recent research in the field of VRP seeks to reach a set of goals. Among these goals are reducing the total distances traveled by the fleet of vehicles, reducing the total cost of fleet of vehicles, and reaching the lowest possible energy consumption. Recent research also deals with the use of a heterogeneous transport fleet (HFVRP). Fleet heterogeneity considers vehicle capacity, energy consumption, diversity in items transported, and the type of vehicles (in terms of their use of diesel fuel, electricity, natural gas, or hydrogen in their operation).
The objective of the present research is to develop a mathematical model and solution methodology to determine the optimal routes of vehicles that serve a certain number of customers and yield near optimal fleet total fleet travel distance. Three types or vehicles fleets are under study which are pure CVs, pure EVs, and mixed fleet of diesel and electric vehicles. The idea behind using mixed fleet is to study the possibility of controlling the produced CO2 emissions by the fleet.
The problem incorporates a depot, batteries’ recharging stations and a number of customers located apart from each other. Roads connecting all customers and the depot are available. Each customer has pre-determined daily demand from a variety of commodities. A heterogeneous fleet of vehicles of different carrying capacities is available for delivering commodities to customers. Any vehicle starts its routing journey fully loaded and each customer is visited once during the shift. vehicle routes can serve any number of customers. The vehicles routes have no definite direction such that it may be clockwise or anticlockwise. Refuelling of CVs is made upon reaching the depot for loading. EV is visiting the nearest electrical charging stations or the depot for recharging. The number of CVs to EVs in the fleet vehicle type is decided according to permissible CO2 emission cap.
A mathematical model is designed to express the problem with an objective function of minimizing total fleet travel distance. The Genetic Algorithm (GA) is used to find a solution to the problem. The GA idea is to build and randomize feasible solutions and apply some changes with crossover and mutation operators, to improve the solutions.
The vehicle routing problem is then studied considering different vehicles parameters including vehicle type, speed, and capacity. Also, parameters related to customers such as number of customers and locations of charging stations are also considered in the study. CO2 emissions cap is considered as constraint to limit fleet emissions.
The output of applying GA as a solution methodology are concerned with total travel distance, total travel time, fleet size (CV – EV), number of routes, number of EVs recharging, and total travel emissions.
The results of the research have led to the following conclusions:
• The developed mathematical model and the solution methodology were tested and experimented by solving benchmark problems. The accuracy of the results proved to an acceptable degree as errors didn’t exceed 7.7%, and computational speed was small even with large size problems.
• Using high-capacity homogenous vehicles fleet, reduces the number of visits to the depot for commodities recharging and consequently reduces the total traveled distance and travel time.
• The required number of vehicles is not affected by an increase in vehicle capacity until reaching a certain capacity after which a DROP in the required number of vehicles takes place.
The number of electric vehicles visiting the depot or charging stations decreases with increasing vehicle capacity. However, the number of visits to the depot is higher for small vehicle capacities as compared to the number of visits to charging stations. This is because the small capacity vehicles obligatory should visit the depot more frequently for reloading of commodities.
Small capacity vehicles visit the depot more frequently than the large vehicles as the reloading frequency of commodities is higher than large capacity vehicles which adds extra travel distance. In the case of EVs, additional distances are added as the vehicles must travel to CSs for batteries recharging. This leads to the conclusion that electric vehicles fleet will have to travel greater distances as compared to that of CVs for the same vehicle capacity. Similarly, it can also be concluded that the small vehicles’ capacity, when compared to high vehicles’ capacities, require a higher number of routes and higher number of visits to depot leading to higher travel time.
Increasing the MDTR reduces the number of EV visits to CSs and the depot and consequently reduces the number of vehicles routes and total travel distance and time. For example, it was found that increasing battery life from 50km to 150km reduces the total travel distance by about 30%using 100-units vehicle. However, the number of routes does not change. On the other hand, increasing the MDTR, the number of vehicles needed to complete the service remains constant until certain value of MDTR after which the number of EVs decreases stepwise.
The reference CO2 emissions of a fleet (Emission Cap) in the present study is determined by calculating the total emissions produced by a pure CVs fleet from solving the current VRP. To reduce the total emissions to a certain limit, EVs are introduced to join the present CVs fleet. It was found that if emissions are equal to zero, the fleet is pure EVs, if it is equal to 1, the fleet is pure CVs. In between these values, the number of EVs at zero ratio decreases linearly until the ratio of one where the number of EVs is zero. In contrast, the number of CVs in the mixed fleet remains almost constant for the remaining range of emissions ratios. The use of constant number of CVs within the mixed fleet means that the number of EVs increases with decreasing emission ratio and EVs should make higher number of routes.