# Collaborative Optimization of Vehicle and Crew Scheduling for a Mixed Fleet with Electric and Conventional Buses

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. Literature Review

- 1.
- Two-phase sequence method

- 2.
- Collaborative scheduling method

#### 1.3. Contributions

## 2. Methodology

#### 2.1. Notation Definition

#### 2.2. Vehicle Scheduling (Upper Layer)

#### 2.2.1. Objective Functions

#### 2.2.2. Constraints

_{hj}are departure times specified in the timetables for service trips i and j run by CB h; ${t}_{hi}$ is the travel time of CB h on service trip i, h; ${T}_{ki}$ and ${T}_{kj}$ are departure times specified in the timetables for service trips i and j run by EB k; ${t}_{ki}$ is the travel time of EB k on the service trip i, h; ${t}_{kr}$ is the charging time of EB k on charging trip r, h; ${t}_{r}^{\mathrm{min}}$ is the minimum charging time of EB k, h; and ${W}_{ki}^{end}$ is the remaining battery power when EB k ends the service trip i, kWh.

#### 2.3. Crew Scheduling (Lower Layer)

#### 2.3.1. Objective Functions

#### 2.3.2. Constraints

#### 2.4. Solution Algorithm

_{p}, and the maximum number of iterations Maxgen.

## 3. Case Study

#### 3.1. Scenario Description

_{1}= 100% and the lower limit ${\delta}_{2}$ = 20%. The energy consumption rate of EB is 1.2 kWh/km; hence, the energy consumption of each service trip ${w}_{kj}$ = 33.6 kWh, and the energy consumption of returning from the departure station to the depot ${W}_{ki}^{depot}$ = 6 kWh. Electric bus charging power b = 120 kW, minimum charging time ${t}_{r}^{\mathrm{min}}$ = 0.15 h. Refer to the TOU power price of general industry to determine the unit electricity price of EB charging ${E}_{q}$, as shown in Table 2. The night electricity price ${E}_{night}^{\prime}$ = ${E}_{6}$ = 0.369 RMB/kWh. The average travel time of the bus ${t}_{hi}={t}_{ki}=$ 1.7 h, including the running time on the route ${t}_{hi}^{\prime}$ = ${t}_{ki}^{\prime}$ = 1 h, the total docking time at the stations ${t}_{hi}^{\u2033}$ = ${t}_{ki}^{\u2033}$ = 0.5 h, and the dwell time at the departure station is 0.2 h.

#### 3.2. Results

#### 3.3. Analysis

- (i)
- Vehicle- and charging-scheduling scheme

- (ii)
- Crew scheduling

## 4. Conclusions

- (i)
- The collaborative optimization method of vehicle scheduling and crew scheduling established for the mixed fleet can ensure the specificity of drivers and buses, and it also arranges the charging plan during valley-peak periods to ensure service integrity and save the operation cost of the bus route.
- (ii)
- The utilization intensity of EBs is greater than that of CBs, which is reflected in that not only is the number of service trips allocated each day significantly larger than that of CBs, but also the idle time is less than that of CBs. In the vehicle-scheduling process of the mixed fleet, CBs supplement EBs, and the service trip is allocated only when the number of EBs is insufficient.
- (iii)
- In the collaborating process of vehicle scheduling and driver scheduling for the mixed fleet, drivers can use the dwell time at the departure station, the idle time between adjacent service trips, and the charging time of EB to allow for reasonable rest. In this way, fatigue driving can be effectively avoided.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Notation | Description |
---|---|

${x}_{kij}$ | 1 if service trips i and j are adjacent trips run by EB k; 0 otherwise |

${x}_{hij}$ | 1 if service trips i and j are adjacent trips run by CB h; 0 otherwise |

${y}_{gki}$ | 1 if the driver g drives EB k to complete the service trip i; 0 otherwise |

${y}_{ghi}$ | 1 if the driver g drives CB h to complete the service trip i; 0 otherwise |

${\theta}_{kr}$ | 1 if EB k is charged during charging trip r; 0 otherwise |

${\gamma}_{gij}$ | 1 if driver g continuously performs driving trips i and j; 0 otherwise |

OCB | the operation cost of CBs |

OEB | the operation cost of EBs |

MCB | the carbon emission of the mixed fleet |

CP | the driver’s one-day wage |

${S}^{2}$ | the variance of the number of possible vehicle swaps of drivers |

${G}^{\prime}$ | the number of drivers required for daily operations |

${N}_{g}$ | the number of buses that driver g needs to drive every day |

${F}_{h}$ | the fuel cost per mileage |

${M}_{h}$ | the average carbon emission per kilometer |

${L}_{0}$ | the trip length |

${T}_{hi}$$\text{}({T}_{hj}$) | departure times of service trips i (j) run by CB h |

${T}_{ki}$$\text{}({T}_{kj}$) | departure times of service trips i (j) run by EB k |

${t}_{hi}$$\text{}({t}_{hj}$) | the travel time of CB h on service trip i (j) |

${t}_{ki}$$\text{}({t}_{kj}$) | the travel time of EB k on the service trip i (j) |

${t}_{hi}^{\prime}$ | the effective working hours of CB h on driving trip i |

${t}_{ki}^{\prime}$ | the effective working hours of EB k on driving trip i |

${t}_{hi}^{\u2033}$ | dwell times of CB h on service trip i |

${t}_{ki}^{\u2033}$ | dwell times of EB k on service trip i |

${t}_{kr}$ | the charging time of EB k on charging trip r |

${E}_{q}$ | the unit electricity price of charging in the period q |

${W}_{k}^{rated}$ | the rated battery capacity of EB k |

${W}_{kj}^{end}$ | the remaining battery power when EB k ends the service trip j |

${w}_{kj}$ | the energy consumption of EB k on the service trip j |

${\delta}_{2}$ | the lower limit of the battery state of charge (SOC) |

${\delta}_{1}$ | the upper limit of the battery state of charge (SOC) |

${\zeta}_{1}$ | the maximum time that the driver shall drive continuously |

${\zeta}_{2}$ | the minimum rest time after continuous driving |

${\zeta}_{3}$ | the maximum time that the driver work overtime |

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i | ${\mathit{T}}_{\mathit{h}\mathit{i}}/{\mathit{T}}_{\mathit{k}\mathit{i}}$ | i | ${\mathit{T}}_{\mathit{h}\mathit{i}}/{\mathit{T}}_{\mathit{k}\mathit{i}}$ | i | ${\mathit{T}}_{\mathit{h}\mathit{i}}/{\mathit{T}}_{\mathit{k}\mathit{i}}$ | i | ${\mathit{T}}_{\mathit{h}\mathit{i}}/{\mathit{T}}_{\mathit{k}\mathit{i}}$ |
---|---|---|---|---|---|---|---|

1 | 05:50 | 18 | 08:37 | 35 | 11:42 | 52 | 15:18 |

2 | 06:03 | 19 | 08:49 | 36 | 11:57 | 53 | 15:29 |

3 | 06:16 | 20 | 09:01 | 37 | 12:12 | 54 | 15:40 |

4 | 06:28 | 21 | 09:08 | 38 | 12:26 | 55 | 15:51 |

5 | 06:39 | 22 | 09:15 | 39 | 12:41 | 56 | 16:04 |

6 | 06:47 | 23 | 09:24 | 40 | 12:56 | 57 | 16:12 |

7 | 06:56 | 24 | 09:33 | 41 | 13:10 | 58 | 16:23 |

8 | 07:05 | 25 | 09:42 | 42 | 13:19 | 59 | 16:36 |

9 | 07:14 | 26 | 10:00 | 43 | 13:33 | 60 | 16:54 |

10 | 07:23 | 27 | 10:04 | 44 | 13:44 | 61 | 17:08 |

11 | 07:32 | 28 | 10:09 | 45 | 13:57 | 62 | 17:24 |

12 | 07:41 | 29 | 10:14 | 46 | 14:08 | 63 | 17:39 |

13 | 07:53 | 30 | 10:27 | 47 | 14:19 | 64 | 17:57 |

14 | 08:00 | 31 | 10:42 | 48 | 14:31 | 65 | 18:10 |

15 | 08:10 | 32 | 10:57 | 49 | 14:43 | 66 | 18:20 |

16 | 08:18 | 33 | 11:12 | 50 | 14:57 | 67 | 18:39 |

17 | 08:30 | 34 | 11:26 | 51 | 15:07 | 68 | 19:00 |

q | Period Starting Time | Period Ending Time | ${\mathit{E}}_{\mathit{q}}$ (RMB/kWh) |
---|---|---|---|

1 | 7:00 | 10:00 | 0.832 |

2 | 10:00 | 15:00 | 1.322 |

3 | 15:00 | 18:00 | 0.832 |

4 | 18:00 | 21:00 | 1.322 |

5 | 21:00 | 23:00 | 0.832 |

6 | 23:00 | 7:00 | 0.369 |

k | Departure Time of the First Service Trip | End Time of the Last Service Trip | Total Idle Time (min) | Total Service Time (min) | Number of Service Trips |
---|---|---|---|---|---|

1 | 5:50 | 19:39 | 83 | 714 | 7 |

2 | 6:03 | 19:52 | 111 | 714 | 7 |

3 | 6:16 | 20:02 | 98 | 714 | 7 |

4 | 6:28 | 20:21 | 107 | 714 | 7 |

5 | 6:39 | 20:42 | 115 | 714 | 7 |

6 | 6:47 | 18:36 | 71 | 612 | 6 |

7 | 6:56 | 16:25 | 59 | 510 | 5 |

8 | 7:05 | 16:39 | 64 | 510 | 5 |

9 | 7:14 | 17:46 | 122 | 510 | 5 |

h | Departure Time of the First Service Trip | End Time of the Last Service Trip | Total Idle Time (min) | Total Service Time (min) | Number of Service Trips |
---|---|---|---|---|---|

1 | 7:23 | 18:50 | 279 | 408 | 4 |

2 | 7:32 | 19:06 | 286 | 408 | 4 |

3 | 8:10 | 19:21 | 263 | 408 | 4 |

k | Departure Time of the Charging | End Time of the Charging | Charging Time (min) | Idle Time until Next Service Trip (min) |
---|---|---|---|---|

1 | 15:01 | 15:33 | 32 | 6 |

2 | 15:15 | 15:47 | 32 | 4 |

3 | 15:26 | 15:58 | 32 | 14 |

4 | 15:39 | 16:11 | 32 | 12 |

5 | 15:50 | 16:22 | 32 | 14 |

6 | 16:13 | 16:28 | 15 | 26 |

g | Check-in Time | Check-out Time | Total Effective Working Time (min) | Total Rest Time (min) | On-Duty Time (min) |
---|---|---|---|---|---|

1 | 5:50 | 19:39 | 420 | 187 | 817 |

2 | 6:03 | 19:52 | 420 | 187 | 817 |

3 | 6:16 | 20:02 | 420 | 184 | 814 |

4 | 6:28 | 20:21 | 420 | 191 | 821 |

5 | 6:39 | 20:42 | 420 | 201 | 831 |

6 | 6:47 | 18:36 | 360 | 157 | 697 |

7 | 6:56 | 16:25 | 300 | 107 | 557 |

8 | 7:05 | 16:39 | 300 | 112 | 562 |

9 | 7:14 | 17:46 | 300 | 170 | 620 |

g | First Check-in Time | First Check-out Time | Second Check-in Time | Second Check-out Time | Total Effective Working Time (min) | Total Rest Time (min) | On-Duty Time (min) |
---|---|---|---|---|---|---|---|

10 | 7:23 | 10:57 | 15:07 | 18:50 | 240 | 53 | 413 |

11 | 7:32 | 11:06 | 15:18 | 19:06 | 240 | 58 | 418 |

12 | 8:10 | 11:51 | 15:29 | 19:21 | 240 | 69 | 429 |

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## Share and Cite

**MDPI and ACS Style**

Wang, J.; Wang, H.; Chang, A.; Song, C.
Collaborative Optimization of Vehicle and Crew Scheduling for a Mixed Fleet with Electric and Conventional Buses. *Sustainability* **2022**, *14*, 3627.
https://doi.org/10.3390/su14063627

**AMA Style**

Wang J, Wang H, Chang A, Song C.
Collaborative Optimization of Vehicle and Crew Scheduling for a Mixed Fleet with Electric and Conventional Buses. *Sustainability*. 2022; 14(6):3627.
https://doi.org/10.3390/su14063627

**Chicago/Turabian Style**

Wang, Jing, Heqi Wang, Ande Chang, and Chen Song.
2022. "Collaborative Optimization of Vehicle and Crew Scheduling for a Mixed Fleet with Electric and Conventional Buses" *Sustainability* 14, no. 6: 3627.
https://doi.org/10.3390/su14063627