# Location and Routing Planning Considering Electric Vehicles with Restricted Distance in Agriculture

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}, N

_{2}O, greenhouse gases (GHGs) [2], and negative externalities, including air pollution, noise, accidents, traffic congestions, climate change risk, and resource consumption [3]. According to Arias et al. (2018) [4], non-renewable energy sources that release GHGs account for 14% of global pollution. Thus, in the last decade, green logistics with green energy sources have received increased attention intending to minimize harmful effects on the environment. Electric vehicles (EVs) have become more attractive solutions to environmental problems via green technology. Many logistics companies have started projects for the implementation of EVs in their operations, such as UPS and DHL [5].

## 2. Literature Review

## 3. Problem Description and Mathematical Model

- The total cassavas at farms assigned to a collection center must not exceed the capacity of the collection center.
- Each farm must deliver all generated cassavas to a collection center.
- Each route begins at a collection center and ends at the same place.
- The total cassavas on EVs must not exceed their load capacity at any time.
- Each farm can be visited more than once if the cassavas exceed a vehicle’s capacity. Then, partial deliveries are allowed.
- The route range must not exceed a given distance.

- I
- set of cassava farms, I = {i1, i2, i3, …}

- S
_{ij} - the shipment cost per kilometer from node i to node j
- Q
_{i} - cassava amount of farm i (kg)
- D
_{ij} - distance from node i to node j (km)
- V
- EV load capacity (kg)
- H
_{j} - collection center capacity (kg)
- O
_{j} - opening cost if node j is selected to be collection center
- T
- maximum distance available for each EV
- F
- fixed cost per EV used. F is calculated by determining annual depreciation of EV divided by seasonal harvest period in one year (90 days). Then, the daily fixed cost per EV used is obtained.

- y
_{ij} - = 1 if farm i is allocated to collection center j and a partial shipment is needed= 0 otherwise
- x
_{ij} - = 1 if there is a transportation from farm i to farm j and the remain from partial shipment is routed= 0 otherwise
- z
_{j} - = 1 if collection center j is chosen= 0 otherwise
- n
_{i} - = number of partial shipments at farm i
- K
- = number of EVs used

- u
_{i} - cumulative cassava quantity in EV at farm i, used for sub-tour prevention
- m
_{j} - number of round transports using for routing at collection center j
- r
_{i} - remaining cassavas after partial shipment from farm i
- t
_{i} - cumulative distance at farm i

_{j}= 0, only one arc can be 1, otherwise, m

_{j}arcs are going into the depot j. Equation (6) is the connectivity equation which ensures that the vehicle must leave farm i after it has been visited. Equation (7) determines the route among the farms that are allocated to the same collection center. Equations (8) and (9) guarantee that the route length must not exceed the maximum distance allowed for each EV. Equations (10) and (11) specify that the load capacity of each EV must never be exceeded and deal with sub-tour prevention, respectively. Equation (12) limit the number of EVs used. Finally, Equation (13) defines the domain of decision variables.

## 4. Methodology

#### 4.1. Construct Initial Solution

#### 4.2. Destructive Degree

#### 4.3. Destroy Operators

#### 4.3.1. Random Elimination

#### 4.3.2. Worst Elimination

#### 4.3.3. Connected Elimination

#### 4.3.4. Depot Elimination

#### 4.3.5. Route Elimination

#### 4.4. Repair Operators

#### 4.4.1. Random Repairing

#### 4.4.2. Greedy Repairing

- Step 1: Randomly select a farm in the box;
- Step 2: Determine the objective value at each possible solution that this farm could be placed at;
- Step 3: Place the farm at the cheapest position;
- Step 4: Repeat the process until there are no farms left in the box.

#### 4.4.3. Regret Repairing

#### 4.4.4. Route Repairing

#### 4.5. Weight Adjustment and Solution Acceptance Methods

- (1)
- Greedy Acceptance (GA)The solution s’ is only accepted if it is better than the incumbent solutions.
- (2)
- Simulated Annealing (SA)This method is motivated by a well-known metaheuristic, simulated annealing, which was first introduced by Metropolis et al. (1953) [47]. SA is the most widespread acceptance method used by ALNS algorithms. Every improving solution is accepted. Nevertheless, if Z(s’) > Z(s), s’ is accepted with a probability, as shown by Equation (14):$$p=ex{p}^{\frac{\left(Z\left(s\right)-Z\left(s\prime \right)\right)}{T}}$$
- (3)
- Threshold Acceptance (TA)The new solution s’ is accepted if Z(s’) – Z(s) < Th. Th is called the threshold, which is decreased at every iteration by factor α.
- (4)
- Old Bachelor Acceptance (OBA)The new solutions’ is accepted if Z Z(s’) − Z(s) < Th with a threshold Th, which is the same as in the TA method. Th is decreased by factor α if a new solution is accepted. On the contrary, Th is increased by factor β if a new solution is rejected.

## 5. Computational Results

^{®}version 19 software package was used for statistical tests, where the significance level was set to be equivalent to 0.05 for all tests.

^{®}are shown in Table 3. In this table, the numbers are p-values from the test. The signs $\le $, =, and $\ge $ specify that the solution is less than, equal to, or greater than the compared method.

^{®}are shown in Table 4. The results are used to examine if the proposed heuristics are different than those of compared methods. The results show that the lower bound solutions from Lingo are lower than the solutions from all proposed heuristics, however they take a long computational time. Comparing the proposed heuristics, ALNS-1 is worse than ALNS-2 and ALNS-4. The best algorithm here, similar to the medium-sized instance, is ALNS-4.

## 6. Conclusions and Future Works

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Instance Name | Lingo | ALNS-1 | ALNS-2 | ALNS-3 | ALNS-4 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Status | Cost (Baht) | Time (min) | Cost (Baht) | Time (min) | Cost (Baht) | Time (min) | Cost (Baht) | Time (mins) | Cost (Baht) | Time (min) | |

S1 | Opt. * | 52,643 | 0.12 | 52,643 | 0.22 | 52,643 | 0.19 | 52,643 | 0.24 | 52,643 | 0.22 |

S2 | Opt. | 52,863 | 0.13 | 52,863 | 0.20 | 52,863 | 0.25 | 52,863 | 0.23 | 52,863 | 0.24 |

S3 | Opt. | 53,603 | 0.11 | 53,603 | 0.19 | 53,603 | 0.19 | 53,603 | 0.18 | 53,603 | 0.28 |

S4 | Opt. | 55,976 | 0.14 | 55,976 | 0.17 | 55,976 | 0.24 | 55,976 | 0.21 | 55,976 | 0.25 |

S5 | Opt. | 54,716 | 0.15 | 54,716 | 0.22 | 54,716 | 0.25 | 54,716 | 0.25 | 54,716 | 0.23 |

S6 | Opt. | 103,451 | 0.16 | 103,451 | 0.26 | 103,451 | 0.23 | 103,451 | 0.24 | 103,451 | 0.22 |

S7 | Opt. | 105,644 | 0.14 | 105,644 | 0.25 | 105,644 | 0.24 | 105,644 | 0.19 | 105,644 | 0.21 |

S8 | Opt. | 107,809 | 0.18 | 107,809 | 0.23 | 107,809 | 0.21 | 107,809 | 0.18 | 107,809 | 0.22 |

Instance Name | Lingo | ALNS-1 | ALNS-2 | ALNS-3 | ALNS-4 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Status | Cost (Baht) | Time (min) | Cost (Baht) | Time (min) | Cost (Baht) | Time (min) | Cost (Baht) | Time (min) | Cost (Baht) | Time (min) | |

M1 | Best ** | 116,229 | 4320 | 12,742 | 2.22 | 111,812 | 2.28 | 112,742 | 2.51 | 111,812 | 2.58 |

M2 | Best | 108,869 | 4320 | 105,603 | 2.51 | 104,732 | 2.27 | 105,385 | 2.62 | 104,514 | 2.69 |

M3 | Best | 118,519 | 4320 | 114,963 | 2.13 | 114,015 | 2.31 | 114,963 | 2.61 | 113,778 | 2.62 |

M4 | Best | 116,957 | 4320 | 113,448 | 2.26 | 113,448 | 2.27 | 113,448 | 2.36 | 113,448 | 2.64 |

M5 | Best | 165,057 | 4320 | 160,105 | 2.21 | 158,785 | 2.73 | 159,775 | 2.53 | 158,455 | 2.32 |

M6 | Best | 163,300 | 4320 | 158,401 | 2.34 | 157,095 | 2.57 | 158,074 | 2.38 | 156,768 | 2.77 |

M7 | Best | 167,665 | 4320 | 162,635 | 2.31 | 161,294 | 2.78 | 162,300 | 2.44 | 161,294 | 2.44 |

M8 | Best | 169,725 | 4320 | 164,633 | 2.27 | 163,275 | 2.62 | 164,294 | 2.51 | 163,275 | 2.41 |

Instance Name | Lingo | ALNS-1 | ALNS-2 | ALNS-3 | ALNS-4 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Status | Cost (Baht) | Time (min) | Cost (Baht) | Time (min) | Cost (Baht) | Time (min) | Cost (Baht) | Time (min) | Cost (Baht) | Time (min) | |

L1 | LB *** | 172,727 | 7200 | 186,200 | 5.82 | 184,991 | 6.71 | 186,200 | 6.31 | 184,991 | 6.72 |

L2 | LB | 175,367 | 7200 | 189,046 | 5.42 | 187,818 | 5.32 | 189,046 | 5.45 | 187,643 | 6.66 |

L3 | LB | 175,017 | 7200 | 188,668 | 5.58 | 187,443 | 5.77 | 188,143 | 6.76 | 187,268 | 6.51 |

L4 | LB | 183,455 | 7200 | 197,764 | 5.71 | 196,480 | 5.44 | 197,214 | 6.32 | 196,297 | 6.11 |

L5 | LB | 192,638 | 7200 | 207,664 | 6.67 | 206,315 | 6.58 | 207,664 | 6.88 | 206,315 | 6.44 |

L6 | LB | 271,964 | 7200 | 293,177 | 6.66 | 291,273 | 6.62 | 292,361 | 6.62 | 291,273 | 7.71 |

L7 | LB | 276,329 | 7200 | 297,883 | 6.22 | 295,948 | 7.38 | 297,883 | 7.71 | 295,948 | 7.34 |

Case study | LB | 476,548 | 7200 | 513,719 | 13.55 | 510,383 | 15.66 | 512,289 | 15.39 | 509,906 | 15.30 |

Instance | ALNS-1 | ALNS-2 | ALNS-3 | ALNS-4 |
---|---|---|---|---|

M1 | −3.09% | −3.95% | −3.09% | −3.95% |

M2 | −3.09% | −3.95% | −3.31% | −4.17% |

M3 | −3.09% | −3.95% | −3.09% | −4.17% |

M4 | −3.09% | -3.09% | −3.09% | −3.09% |

M5 | −3.09% | −3.95% | −3.31% | −4.17% |

M6 | −3.09% | −3.95% | −3.31% | −4.17% |

M7 | −3.09% | −3.95% | −3.31% | −3.95% |

M8 | −3.09% | −3.95% | −3.31% | −3.95% |

Average | −3.09% | −3.84% | −3.23% | −3.95% |

L1 | 7.24% | 6.63% | 7.24% | 6.63% |

L2 | 7.24% | 6.63% | 7.24% | 6.54% |

L3 | 7.24% | 6.63% | 6.98% | 6.54% |

L4 | 7.24% | 6.63% | 6.98% | 6.54% |

L5 | 7.24% | 6.63% | 7.24% | 6.63% |

L6 | 7.24% | 6.63% | 6.98% | 6.63% |

L7 | 7.24% | 6.63% | 7.24% | 6.63% |

Case study | 7.24% | 6.63% | 6.98% | 6.54% |

Average | 7.24% | 6.63% | 7.11% | 6.59% |

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**Figure 7.**The depot elimination operator. (

**a**) The current solution. (

**b**) The selected depot is closed. (

**c**) All farms are moved to the farm box.

Small Instance Name | Number of Farms | Total Cassava (kg) | Medium Instance Name | Number of Farms | Total Cassava (kg) | Large Instance Name | Number of Farms | Total Cassava (kg) |
---|---|---|---|---|---|---|---|---|

S1 | 4 | 12,978 | M1 | 15 | 41,530 | L1 | 25 | 64,111 |

S2 | 4 | 11,923 | M2 | 15 | 38,154 | L2 | 25 | 63,900 |

S3 | 5 | 16,210 | M3 | 16 | 41,872 | L3 | 28 | 64,077 |

S4 | 6 | 20,692 | M4 | 17 | 47,938 | L4 | 30 | 67,218 |

S5 | 7 | 22,688 | M5 | 18 | 50,526 | L5 | 30 | 66,320 |

S6 | 8 | 29,770 | M6 | 19 | 51,356 | L6 | 35 | 73,872 |

S7 | 9 | 32,776 | M7 | 19 | 51,773 | L7 | 40 | 81,096 |

S8 | 10 | 35,485 | M8 | 20 | 50,358 | Case study | 86 | 185,675 |

Algorithm Name | Acceptance Method Used |
---|---|

ALNS-1 | Greedy Acceptance (GA) |

ALNS-2 | Simulated Annealing (SA) |

ALNS-3 | Threshold Acceptance (TA) |

ALNS-4 | Old Bachelor Acceptance (OBA) |

Method | ALNS-1 | ALNS-2 | ALNS-3 | ALNS-4 |
---|---|---|---|---|

Lingo | $\ge $(0.014) | $\ge $(0.014) | $\ge $(0.014) | $\ge $(0.014) |

ALNS-1 | - | $\ge $(0.022) | =(0.059) | $\ge $(0.022) |

ALNS-2 | - | - | $\le $(0.022) | =(0.100) |

ALNS-3 | - | - | - | $\ge $(0.022) |

ALNS-4 | - | - | - | - |

Method | ALNS-1 | ALNS-2 | ALNS-3 | ALNS-4 |
---|---|---|---|---|

Lingo | $\le $(0.014) | $\le $(0.014) | $\le $(0.014) | $\le $(0.014) |

ALNS-1 | - | $\ge $(0.014) | =(0.100) | $\ge $(0.014) |

ALNS-2 | - | - | $\le $(0.014) | $\ge $(0.014) |

ALNS-3 | - | - | - | $\ge $(0.014) |

ALNS-4 | - | - | - | - |

Medium-Size Instance | ALNS-1 | ALNS-2 | ALNS-3 | ALNS-4 |

Average | −3.09% | −3.84% | −3.23% | −3.95% |

Large-Size Instance | ALNS-1 | ALNS-2 | ALNS-3 | ALNS-4 |

Average | 7.24% | 6.63% | 7.11% | 6.59% |

Instance | Vehicles Capacity | BKS | MACO (Ting and Chen, 2013) | %dev | ALNS (Hemmelmayr et al., 2012) | %dev | ALNS-4 (Our Approach, 2020) | %dev |
---|---|---|---|---|---|---|---|---|

Total Cost | Best Solution | Best Solution | Best Solution | |||||

Gaskell67-21 × 5 | 6000 | 424.90 | 424.90 | 0.00% | 424.90 | 0.00% | 424.90 | 0.00% |

Gaskell67-22 × 5 | 4500 | 585.11 | 585.10 | 0.00% | 585.11 | 0.00% | 585.10 | 0.00% |

Gaskell67-29 × 5 | 4500 | 512.10 | 512.10 | 0.00% | 512.10 | 0.00% | 512.10 | 0.00% |

Gaskell67-32 × 5a | 8000 | 562.22 | 562.22 | 0.00% | 562.22 | 0.00% | 562.22 | 0.00% |

Gaskell67-32 × 5b | 11,000 | 504.33 | 504.33 | 0.00% | 504.33 | 0.00% | 504.33 | 0.00% |

Gaskell67-36 × 5 | 250 | 460.37 | 464.37 | 0.86% | 460.37 | 0.00% | 464.81 | 0.96% |

Christofides69-50 × 5 | 160 | 565.60 | 565.62 | 0.00% | 565.60 | 0.00% | 565.62 | 0.00% |

Christofides69-75 × 10 | 140 | 844.40 | 844.88 | 0.06% | 853.47 | 1.07% | 850.48 | 0.71% |

Christofides69-100 × 10 | 200 | 833.43 | 836.75 | 0.40% | 833.43 | 0.00% | 833.43 | 0.00% |

Perl83-55 × 15 | 120 | 1112.06 | 1112.58 | 0.05% | * | * | * | * |

Perl83-85 × 7 | 160 | 1622.50 | 1623.14 | 0.04% | * | * | * | * |

Min92-27 × 5 | 2500 | 3062.02 | * | * | 3062.02 | 0.00% | 3067.46 | 0.18% |

Min92-134 × 8 | 850 | 5709.00 | 5709.00 | 0.00% | 5712.99 | 0.07% | 5712.99 | 0.07% |

Daskin95-88 × 8 | 9,000,000 | 355.78 | 355.78 | 0.00% | 355.78 | 0.00% | 355.78 | 0.00% |

Daskin95-150 × 10 | 8,000,000 | 43,919.90 | 44,131.02 | 0.48% | 44,309.20 | 0.89% | 44,096.49 | 0.40% |

Average | 0.13% | 0.13% | 0.16% | 0.18% | ||||

Number of testing instances | 14 | 13 | 13 | |||||

Number of BKS | 8 | 10 | 8 | |||||

Percentage of finding BKS | 57.14% | 76.92% | 61.54% |

Routing No. | Opened Location | Transportation Route | Distance (km) | Total Cost (Baht) |
---|---|---|---|---|

1 | 4 | 4–1– 4 | 146 | 51,840 |

2 | 4–1–7–10–20– 4 | 577 | 3780 | |

3 | 4–2– 21–39– 4 | 576 | 3775 | |

4 | 13 | 13–15– 13 | 132 | 51,777 |

5 | 13– 15–14–13 | 583 | 3807 | |

6 | 13–44–12–13 | 578 | 3784 | |

7 | 13–18–16–22–13 | 514 | 3496 | |

8 | 19 | 19–17–41–40–19 | 563 | 53,717 |

9 | 19–23–27–28–19 | 575 | 3771 | |

10 | 19–28–31–29–19 | 593 | 3852 | |

11 | 19–3– 8–9–19 | 573 | 3762 | |

12 | 42 | 42–45–86–32–35–42 | 570 | 53,748 |

13 | 42–34–33–24–42 | 533 | 3582 | |

14 | 42–43–37–26–42 | 544 | 3631 | |

15 | 42–25–38–45–42 | 524 | 3541 | |

16 | 46 | 46–47–46 | 151 | 51,863 |

17 | 46–47–46–50–46 | 551 | 3663 | |

18 | 46–49–48–46 | 583 | 3807 | |

19 | 49–56–57–58–49 | 581 | 3798 | |

20 | 55 | 55–36–84–55 | 590 | 53,838 |

21 | 55–83–82–55 | 542 | 3622 | |

22 | 55–81–85–55 | 561 | 3708 | |

23 | 72 | 72–76–53–6–72 | 562 | 53,712 |

24 | 72–59–60–61–72 | 564 | 3721 | |

25 | 72–63–69–71–72 | 555 | 3681 | |

26 | 72–5–62–68–74–72 | 583 | 3807 | |

27 | 80 | 80–77–75–52–11–80 | 570 | 53,748 |

28 | 80–54–51–70–80 | 583 | 3807 | |

29 | 80–64–65–66–80 | 578 | 3784 | |

30 | 80–73–67–80 | 561 | 3708 | |

31 | 80–78–79–80 | 578 | 3784 | |

Total cost | 509,906 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Theeraviriya, C.; Sirirak, W.; Praseeratasang, N.
Location and Routing Planning Considering Electric Vehicles with Restricted Distance in Agriculture. *World Electr. Veh. J.* **2020**, *11*, 61.
https://doi.org/10.3390/wevj11040061

**AMA Style**

Theeraviriya C, Sirirak W, Praseeratasang N.
Location and Routing Planning Considering Electric Vehicles with Restricted Distance in Agriculture. *World Electric Vehicle Journal*. 2020; 11(4):61.
https://doi.org/10.3390/wevj11040061

**Chicago/Turabian Style**

Theeraviriya, Chalermchat, Worapot Sirirak, and Natthanan Praseeratasang.
2020. "Location and Routing Planning Considering Electric Vehicles with Restricted Distance in Agriculture" *World Electric Vehicle Journal* 11, no. 4: 61.
https://doi.org/10.3390/wevj11040061