A Decision System for Routing Problems and Rescheduling Issues Using Unmanned Aerial Vehicles
Abstract
:1. Introduction
2. Problem Description of This Study
3. Mathematical Model of This Study
3.1. Symbols
3.2. Hypothesis
- There is only one UAV involved;
- The operating time of the UAV is inversely proportional to the load weight; the heavier the load weight of the UAV, the shorter the operating time;
- The service time that the UAV spends on each customer will not be a focus;
- The delivery route is fixed;
- The impact of weather, buildings, or UAV malfunctions on the operating route and speed of the unmanned vehicle will not be considered;
- Once the load weight of the UAV is confirmed in the distribution center, the operating time will be confirmed, and will not increase due to the real-time decreasing load weight during delivery;
- The speed is constant; it will not change due to load requests, number of requests, or operating time;
- The UAV can serve many customers; each customer, however, can only be served once;
- The locations of the UAV and customer are known;
- We assume that the UAV is departing from the logistics center;
- Customer requirements will not change and are known;
- The UAV will return to the logistics center after delivery;
- The load weight carried is inversely proportional to the greatest load weight of the UAV;
- The UAV which departs from the logistics center is completely in-tact, everything runs well, and the UAV comes with a full tank of gas/fully charged battery.
3.3. Decision of the Heuristic Algorithm
- Generate random feasible routes.
- Process reproduction on the selected shorter routes.
- Pair individuals, chose two nodes randomly, and check the existence of the travel route. A certain subsequent route can be reversed to achieve the result of mutation if nodes conflict.
- Generate a new plan (offspring Routes + mutation Routes).
- Determine that the vehicle still has space for rush requests if the solution of the match state were satisfied; scheduling should be ended if the vehicle does not have the capacity for new requests.
- Compute the algorithm to increase revenue and consider customer reception for early or late delivery.
- Establish corresponding feasible routes for every possible backup schedule.
- Apply the optimal cost computed in model control of the real-time state as the initial price and calculate every feasible route. If no optimal solution can be computed, recalculate again using the rush request step of the real-time state model evolution.
- Select the best solution, with minimum operating and delay costs.
4. Case Study
4.1. The Result of the Study
4.2. Sensitivity Analysis
- The logistics service providers decided to increase the weight of customer satisfaction to achieve the least missed time windows. Because the time window of the request around the logistics center does not have a fixed changing trend, the shortest route distance will constantly fluctuate.
- While increasing the weight of the shortest route can decrease the missed time windows, it will lower the profit at the same time. The logistics service providers will only receive a new request that is near the logistic center.
- The profit and total route distance increase along with the increased missed time window weight. This is mean that the logistics service provider can receive the new request when the customer can accept a delay in their request.
5. Conclusions and Recommendation
Author Contributions
Funding
Conflicts of Interest
Appendix A. Random Table of the Weight of the Demand
03 47 43 73 86 | 36 96 47 36 61 | 46 98 63 71 62 | 33 26 16 80 45 | 60 11 14 10 95 |
97 74 24 67 62 | 42 81 14 57 20 | 42 53 32 37 32 | 27 07 36 07 51 | 24 51 79 89 73 |
16 76 62 27 66 | 56 50 26 71 07 | 32 90 79 78 53 | 13 55 38 58 59 | 88 97 54 14 10 |
12 56 85 99 26 | 96 96 68 27 31 | 05 03 72 93 15 | 57 12 10 14 21 | 88 26 49 81 76 |
55 59 56 35 64 | 38 51 82 46 22 | 31 62 43 09 90 | 06 18 44 32 53 | 23 83 01 30 30 |
16 22 77 94 39 | 49 54 43 54 82 | 17 37 93 23 78 | 87 35 20 96 43 | 84 26 34 91 64 |
84 42 17 53 31 | 57 24 55 06 88 | 77 04 74 17 67 | 21 76 33 50 25 | 83 92 12 06 76 |
63 01 63 78 59 | 16 95 55 67 19 | 98 10 50 71 75 | 12 86 73 58 07 | 44 39 52 38 79 |
33 21 12 34 29 | 78 64 56 07 82 | 52 42 07 44 38 | 15 51 00 13 42 | 99 66 02 79 54 |
57 60 86 32 44 | 09 47 27 96 54 | 49 17 46 09 62 | 90 52 84 77 27 | 08 02 73 43 28 |
18 18 07 92 45 | 44 17 16 58 09 | 79 83 86 19 62 | 06 76 50 03 10 | 55 23 64 05 05 |
26 62 38 97 75 | 84 16 07 44 99 | 83 11 46 32 24 | 20 14 85 88 45 | 10 93 72 88 71 |
23 42 40 64 74 | 82 97 77 77 81 | 07 45 32 14 08 | 32 98 94 07 72 | 93 85 79 10 75 |
52 36 28 19 95 | 50 92 26 11 97 | 00 56 76 31 38 | 80 22 02 53 53 | 86 60 42 04 53 |
37 85 94 35 12 | 83 39 50 08 30 | 42 34 07 96 88 | 54 42 06 87 98 | 35 85 29 48 39 |
70 29 !7 12 13 | 40 33 20 38 26 | 13 89 51 03 74 | 17 76 37 13 04 | 07 74 21 19 30 |
56 62 18 37 35 | 96 83 50 87 75 | 97 12 55 93 47 | 70 33 24 03 54 | 97 77 46 44 80 |
99 49 57 22 77 | 88 42 95 45 72 | 16 64 36 16 00 | 04 43 18 66 79 | 94 77 21 21 90 |
16 08 15 04 72 | 33 27 14 34 09 | 45 59 34 68 49 | 12 72 07 31 45 | 99 27 72 95 14 |
31 16 93 32 43 | 50 27 89 87 19 | 20 15 37 00 49 | 52 85 66 60 44 | 38 68 88 11 80 |
68 34 30 13 70 | 55 74 30 77 40 | 44 22 78 84 26 | 04 33 46 09 52 | 68 07 97 06 57 |
74 57 25 65 76 | 59 29 97 68 60 | 71 91 38 67 54 | 13 58 18 24 76 | 15 54 55 95 52 |
27 42 37 86 53 | 48 55 90 65 72 | 96 57 69 36 10 | 96 46 92 42 45 | 97 60 49 04 91 |
00 39 68 29 61 | 66 37 32 20 30 | 77 84 57 03 29 | 10 15 65 04 26 | 11 04 96 67 24 |
29 94 98 94 24 | 68 49 69 10 82 | 53 75 91 93 30 | 34 25 20 57 27 | 40 48 73 51 92 |
16 90 82 66 59 | 83 62 64 11 12 | 67 19 00 71 74 | 60 47 21 29 68 | 02 02 37 03 31 |
11 27 94 75 06 | 06 09 19 74 66 | 02 94 37 34 02 | 76 70 90 30 86 | 38 45 94 30 38 |
35 24 10 16 20 | 33 32 51 26 38 | 79 78 45 04 91 | 16 92 53 56 16 | 02 75 50 95 98 |
38 23 16 86 38 | 42 38 97 01 50 | 87 75 66 81 41 | 10 01 74 91 62 | 48 51 84 08 32 |
31 96 25 91 47 | 96 44 33 49 13 | 34 86 82 53 91 | 00 52 43 48 85 | 27 55 26 89 62 |
Appendix B. The Example (Customer Demand) of This Study
!! n20w20.001 | ||||||
CUST NO. | XCOORD | YCOORD | DEMAND | READY TIME | DUE DATE | SERVICE TIME |
1 | 16.00 | 23.00 | 0.00 | 0.00 | 408.00 | 0.00 |
2 | 22.00 | 4.00 | 0.00 | 62.00 | 68.00 | 0.00 |
3 | 12.00 | 6.00 | 0.00 | 181.00 | 205.00 | 0.00 |
4 | 47.00 | 38.00 | 0.00 | 306.00 | 324.00 | 0.00 |
5 | 11.00 | 29.00 | 0.00 | 214.00 | 217.00 | 0.00 |
6 | 25.00 | 5.00 | 0.00 | 51.00 | 61.00 | 0.00 |
7 | 22.00 | 31.00 | 0.00 | 102.00 | 129.00 | 0.00 |
8 | 0.00 | 16.00 | 0.00 | 175.00 | 186.00 | 0.00 |
9 | 37.00 | 3.00 | 0.00 | 250.00 | 263.00 | 0.00 |
10 | 31.00 | 19.00 | 0.00 | 3.00 | 23.00 | 0.00 |
11 | 38.00 | 12.00 | 0.00 | 21.00 | 49.00 | 0.00 |
12 | 36.00 | 1.00 | 0.00 | 79.00 | 90.00 | 0.00 |
13 | 38.00 | 14.00 | 0.00 | 78.00 | 96.00 | 0.00 |
14 | 4.00 | 50.00 | 0.00 | 140.00 | 154.00 | 0.00 |
15 | 5.00 | 4.00 | 0.00 | 354.00 | 386.00 | 0.00 |
16 | 16.00 | 3.00 | 0.00 | 42.00 | 63.00 | 0.00 |
17 | 25.00 | 25.00 | 0.00 | 2.00 | 13.00 | 0.00 |
18 | 31.00 | 15.00 | 0.00 | 24.00 | 42.00 | 0.00 |
19 | 36.00 | 14.00 | 0.00 | 20.00 | 33.00 | 0.00 |
20 | 28.00 | 16.00 | 0.00 | 9.00 | 21.00 | 0.00 |
21 | 20.00 | 35.00 | 0.00 | 275.00 | 300.00 | 0.00 |
999 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
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Category | Subcategory | Authors |
---|---|---|
heuristic algorithm | particle swarm optimization (PSO) | Khosiawan et al. [4] |
tabu search | Zhen et al. [8] | |
genetic-sweep algorithm | Euchi and Sadok [13] | |
mixed-integer linear programming | Ozkan and Atli [14] | |
swarm intelligence | Schwarzrock et al. [11] | |
Game theory | Gigante et al. [15] |
Dimension | Factors | Authors |
---|---|---|
Operation time | Customer due date, customer service time, processing time, setup time, release date, ready time, and idle time | Chen et al. [16], Dewa et al. [17] |
Organization | Leadership, development process of the system, and governance | Barmponuakis et al. [18], Eichleay et al. [10] |
UAVs | Robust wireless communication, three-dimensional trajectory data, precise UAV control, weather conditions, air traffic control, fuel consumption, and service range, socio-technical | Khosiawan et al. [4], Thibbotuwawa et al. [9], Dingil et al. [3] |
Decision Variable | Description |
---|---|
The binary variable of 0 or 1 0: other situations, 1: unmanned vehicle i travels from j to jk | |
Parameter definition | |
The weight of logistics service provider’s profit | |
The weight of the total distance | |
The weight of penalty | |
Unmanned vehicles with different models and capacities, i = 1…, D; we assumed that it was only one in this study | |
j | Customer in match state, j = 1…, C |
jk | Customer in the real-time state, jk = 1…, C |
Customer number (a big constant); we assumed that it was 999 in this study | |
Delivery price (Fees charged by logistics service providers to customers) | |
The capacity of unmanned vehicles i | |
Fixed travel cost of unmanned vehicles i | |
Variable travel cost of unmanned vehicles i | |
The initial time of unmanned vehicle i; we assumed that it was 0 in this study | |
Maximum travel time of unmanned vehicle i | |
Customer j’s requirement | |
Customer’s rush requirements in real-time | |
The load of the unmanned vehicle is inversely proportional to the flight time | |
Unit distance from the customer in real-time state | |
The unit distance required speed of unmanned vehicle i | |
The early fees of an unmanned vehicle arriving before the start of customer j’s time window | |
The delay fees of an unmanned vehicle arriving after the end of customer j’s time window | |
The fees of the unmanned vehicle | |
Total operating time of unmanned vehicle i | |
The time arrived the customer in the real-time state of the unmanned vehicle (a-arrive) | |
Time window lower limit of customer in real-time state | |
Time window upper limit of the customer in the real-time state (b-begin; e-end) |
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Lin, I.-C.; Lin, T.-H.; Chang, S.-H. A Decision System for Routing Problems and Rescheduling Issues Using Unmanned Aerial Vehicles. Appl. Sci. 2022, 12, 6140. https://doi.org/10.3390/app12126140
Lin I-C, Lin T-H, Chang S-H. A Decision System for Routing Problems and Rescheduling Issues Using Unmanned Aerial Vehicles. Applied Sciences. 2022; 12(12):6140. https://doi.org/10.3390/app12126140
Chicago/Turabian StyleLin, I-Ching, Tsan-Hwan Lin, and Sheng-Hung Chang. 2022. "A Decision System for Routing Problems and Rescheduling Issues Using Unmanned Aerial Vehicles" Applied Sciences 12, no. 12: 6140. https://doi.org/10.3390/app12126140