# Migrating towards Using Electric Vehicles in Campus-Proposed Methods for Fleet Optimization

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## Abstract

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## 1. Introduction

## 2. Literature Review

#### 2.1. Electric Vehicles

#### 2.2. EV Benefits Compared to CV

_{x}), carbon monoxide (CO), carbon dioxide (CO

_{2}), and other pollutants. The emissions can either affect the environment directly through diminished air quality and climate change or be precursors to species of concern, which are formed in the atmosphere. The former includes carbon monoxide (CO), and the latter includes volatile organic compounds (VOCs) and nitrogen oxides (NO

_{x}) which are precursors to the photochemical formation of ozone and PM [18]. Diesel vehicles have different emission characteristics than gasoline vehicles, e.g., NO

_{x}emission levels are higher for diesel vehicles [19].

#### 2.3. Fleet Optimization Models

- ${F}_{j}$ = Fixed cost associated with owning a vehicle of type j for T periods.
- ${f}_{j}$ = Fixed cost associated with hiring a vehicle a vehicle of type j for one period.
- ${V}_{j}$ = Variable cost of an owned vehicle of type j.
- ${v}_{j}$ = Variable cost of a hired vehicle of type j.
- ${x}_{j}$. = Number of owned vehicles of type j.
- ${y}_{jt}$ = Number of hired vehicles of type j in period t.
- ${z}_{jt}$ = Distance travelled by owned vehicle of type j in period t.
- ${w}_{jt}$ = Distance travelled by hired vehicle of type j in period t.

- F = Fixed cost/day of a company-owned vehicle.
- V = Variable cost/day of a company-owned vehicle.
- H = Hiring cost/vehicle per day.
- Y = Number of working days in a year.
- N = Number of vehicles in the fleet.
- ${X}_{r}$ = Number of loads carried by company vehicles on days when demand is ${d}_{r}$.
- ${h}_{r}$ = Number of loads carried by hired vehicles on days when demand is ${d}_{r}$.

- M = Number of vehicle types.
- N = Number of periods in the time horizon.
- ${\alpha}_{i}$ = Fixed cost per period of a type-i vehicle.
- ${\beta}_{i}$ = Variable cost per period of a type-i vehicle.
- ${\gamma}_{i}$ = Hiring cost per period of a type-i vehicle.
- ${\theta}_{ijk}$ = Probability that k type-i vehicles will be required during period j.
- ${N}_{i}$ = Maximum number of type-i vehicles required during a single period.
- ${P}_{max}$ = Maximum fleet size.

- L = Length of planning horizon in years.
- ${A}_{i}$ = Cost of acquiring a new bus in year i.
- ${a}_{i}$ = Number of new buses acquired at the beginning of year i.
- ${n}_{ij}$ = Number of buses j years old operated during year i.
- ${m}_{ij}$ = Number of route kilometers travelled by a bus j years old in year i.
- ${C}_{ij}\left({m}_{ij}\right)$ = Cost of operating a bus j years old in year i for ${m}_{ij}$ kilometers (for discounting purposes, operating costs incurred during the year are treated as occurring at the beginning of the year).

^{2}= 0.92 (total trip mileage by length of trip). Service level and fleet utilization metrics were used to assess the motor pool’s service capability [41]. A different study pointed out that increasing the fleet reduces the number of unsatisfied requests, but increases the fixed investment in the motor pool. Additionally, they found that the peak for checking out vehicles is early in the week and that the demand decreases later in the week. The check-out duration followed an exponential distribution [42].

## 3. Fleet Description and Usage

## 4. Cost Assumption

#### 4.1. Fixed Costs

#### 4.2. Variable Costs

#### 4.3. Break-Even Point

## 5. EV Fleet Size and Composition Optimization

#### 5.1. Fleet Size Optimization

#### 5.2. Fleet Composition Optimization

#### 5.2.1. Nomenclature

Decision variables | |

${P}_{k}$ | The number of k-type vehicle |

${A}_{k}$ | The estimated life for k-type vehicles |

Fixed costs | |

${\alpha}_{k}$ | The purchase price of k-type vehicle |

${\beta}_{k}$ | The incentive of k-type vehicle |

${\gamma}_{k}$ | The vehicle purchase tax rate of k-type vehicle |

Variable costs | |

${N}_{ik}$ | The number of k-type vehicle in year i |

$T{M}_{ik}$ | The travel mileage of k-type vehicle in year i |

${\delta}_{ik}$ | The insurance costs per year of k-type vehicles in year i |

${m}_{ik}$ | The maintenance costs per mile of k-type vehicles in year i |

$f{c}_{ik}$ | The fuel costs per mile of k-type vehicle in year i |

${\omega}_{ik}$ | The annual registration fee of k-type vehicle in year i |

Resale value | |

${S}_{ik}$ | The number of k-type sold vehicle in year i |

${\phi}_{ik}$ | The resale value of k-type vehicles in year i |

R | The break-even point |

#### 5.2.2. Optimization Model

## 6. Results

#### 6.1. Optimized Fleet Size

#### 6.2. Optimized Fleet Composition

#### 6.3. Detailed Breakdown Costs

#### 6.4. Sensitivity Analysis

## 7. Conclusions

## Author Contributions

## Conflicts of Interest

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**Figure 7.**Detailed break-down cost elements of (

**a**) CV (conventional vehicle) and (

**b**) EV (electric vehicle) per year.

Assumptions | 20,000 miles Per Year, Gasoline Price: $3.25/gal, Electricity Price: $0.10/kWh (10 Years, 5% Discount Rate) | |||
---|---|---|---|---|

EV (Chevrolet Volt) | CV (Dodge Avenger) | |||

No Subsidy | Subsidy (TN) | Subsidy | - | |

MSRP ($) | 34,095 | 19,900 | ||

Subsidy ($) | 0 | 2500 | 7500 | 0 |

Tax and registration (7%) ($) | 2387 | 2212 | 1862 | 2464 |

Total purchase price ($) | 36,482 | 33,807 | 28,457 | 21,293 |

Fuel cost/year ($) | 666.67 | 2600.00 | ||

Maintenance costs ($) | 200 ($0.01/mile) | 1600 ($0.08/mile) | ||

Depreciations | Data from Kelly Blue Book | |||

BEP (years) | 4.56 | 3.75 | 2.15 | - |

Number of Vehicles | Travel Mileage Per Year | Years Need to be Operated | Total Costs/Vehicle/Year (Resale Value Included) | |
---|---|---|---|---|

EVs | 7 | 10,218 miles | 4.5 | $6062 |

Gasoline Vehicles | 44 | 20,193 miles | 3 | $10,116 |

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Yoon, T.; Cherry, C.R.
Migrating towards Using Electric Vehicles in Campus-Proposed Methods for Fleet Optimization. *Sustainability* **2018**, *10*, 285.
https://doi.org/10.3390/su10020285

**AMA Style**

Yoon T, Cherry CR.
Migrating towards Using Electric Vehicles in Campus-Proposed Methods for Fleet Optimization. *Sustainability*. 2018; 10(2):285.
https://doi.org/10.3390/su10020285

**Chicago/Turabian Style**

Yoon, Taekwan, and Christopher R. Cherry.
2018. "Migrating towards Using Electric Vehicles in Campus-Proposed Methods for Fleet Optimization" *Sustainability* 10, no. 2: 285.
https://doi.org/10.3390/su10020285