Frequent time window changing disruptions result in high secondary delivery rates in the last mile delivery. With the rapid growth of parcel volumes in online shopping, the time window changing disruptions could translate to substantial delivery cost-wastes. In recent years, customer pickup (CP), a new delivery mode that allows customers to pick up their parcels from shared delivery facilities, has provided a new way to deal with such disruptions. This study proposed a disruption recovery problem with time windows change in the last mile delivery in which customers can be served through home delivery (HD) or CP. A variant variable neighborhood descent (VVND) algorithm was presented to solve the problem. Computational experiments based on a set of instances were tested, and results were compared with other heuristics in the literature, which have affirmed the competitiveness of the model and algorithm.
The rapid e-commerce growth results in a fast increase of parcel delivery. According to the State Post Bureau of China, the parcel volume of online shopping of 3.67 billion in 2011 increased to 40.06 billion in 2017, with an average growth rate of more than 48% within six years. This increase of parcel volume also caused the increase of the one-time delivery failure rate. Many parcels failed to be delivered at the first attempt [
Previously, in terms of the last mile delivery, home delivery (HD) (that is, delivering parcels directly to customers’ homes or workplaces) was common. Recently, customer pickup (CP) has become widely popular, because it allows customers to pick up their parcels from shared delivery facilities (SDFs) near their homes or workplaces at their convenience. The SDFs widely used in more than 80 cities in China include the “CaiNiao” station established by Alibaba Company, “FengChao” established by SF-Express, and “Sposter” established by the China Post Group.
The rescheduling of delivery routes [
The rest of this paper is structured as follows. Section
One key issue related to our research was the shared delivery facilities (parcel lockers or shared reception boxes) in the last mile delivery. The SDF studies were categorized into two streams: case study and routing optimization.
The case studies analyzed the benefits of the SDFs in the last mile delivery by using survey data. Punakivi et al. [
The routing optimization focused on solving the SDF location and the delivery routing problem. Mainly, Deutsch et al. [
Another key issue related to our research is the disruption recovery problem (DRP), which is involved in multiple research areas, such as the passenger transport disruption recovery problem [
Existing literature on the DRP had produced effective solutions for various disruptions, especially the disruption that occurred in logistics. However, such literature mainly focused on the DRP in the HD mode, and no study on the disruption problem in the CP mode was available. This study explored the disruption recovery problem (DRP) with time windows change in the last mile delivery in the CP mode to solve the practical problem and bridge the gap in the literature.
A network without SDFs in the last mile delivery is described as follows.
Network and route without SDFs.
A network with SDFs in the last mile delivery is described as follows.
Network and route with SDFs.
Couriers depart from depots and deliver parcels according to the initial optimal solution. During delivery, couriers must adjust the delivery route to obtain a good solution when a disruption occurs (customers’ time windows changed). In this paper, the objective function is to minimize the cost related to customer satisfaction, route cost, and SDF opening cost.
Without losing generality, the following assumptions are made.
Table
Notions used in formulation.
Sets | |
---|---|
| Network, |
| Node set, |
| Depot set, |
| Customer set, |
| SDF set, |
| Arc set, |
| Delivery arc set, |
| Pickup arc set, |
| |
Parameters | |
| |
| Number of SDFs |
| Number of customers |
| Distance of |
| Travel time of |
| Pickup cost of |
| Pickup time of |
| Time window of customer |
| Unit opening cost of SDF |
| Large positive number |
| Sub-weight of delivery delay time |
| Sub-weight of pickup distance |
| Weight of pickup cost |
| Weight of routing cost |
| Weight of SDFs opening cost |
| Server radius of the SDFs |
| |
Decision variables | |
| |
| Binary variable, |
| Binary variable, |
| Integer variable, arrival time to node |
When a disruption occurs, the influence of customers and couriers is different.
Relationship between customer satisfaction and delivery delay time.
Relationship between customer satisfaction and pickup distance.
The cost related to service satisfaction can be formulated as Formula (
On the basis of the above statements, the model for the proposed problem can be stated as follows:
which is subject to
Objective function (
For the disruption recovery problem, the algorithm should focus not only on solution accuracy, but also on solution speed. If the solution time is too long, then the solution may have been infeasible. The variable neighborhood descent (VND) has been successfully applied for solving hard combinatorial optimization problems, and it particularly performs well for solving LRPs [
A mixed encoding scheme is designed to represent a solution. In the encoding scheme, two sections are shown in Figure
Encoding scheme for the solution of Figure
First section
Second section
The steps of the Randomly select Reallocate the customers within the service radius of the SDFs. Randomly insert the SDFs into the route.
The steps of Randomly select Delete the SDFs from the delivery route. Randomly insert the customers of the SDFs into the delivery route.
Figure
Illustration of the
Case (a): If the selected node is a customer (in the route or SDF), then it can be reinserted to the route or the SDF.
Case (b): If the selected node is a SDF, then it can be only reinserted to route.
Figure
Insertion move operator.
Case (a)
Case (b)
2-opt move operator.
In the network with time windows, partial arcs are disconnected due to the time window constraints, which can be used to calculate each node location range (LR) in the route. By using LR, partial useless exchange can be reduced.
Figure
Improved 2-Opt algorithm.
The proposed algorithm is compiled with C++ and runs on PC with an Intel i5-7500 3.40 GHz CPU, 8.00GB RAM.
The test dataset consists of 100 customers (an instance n100w60.004 proposed by Dumas et al. [
Time windows change.
Customer no. | Status | Time window | Customer no. | Status | Time window | ||
---|---|---|---|---|---|---|---|
| | | | ||||
6 | Old TW | 627 | 664 | 43 | Old TW | 382 | 413 |
New TW | 50 | 100 | New TW | 30 | 80 | ||
10 | Old TW | 460 | 499 | 47 | Old TW | 34 | 122 |
New TW | 100 | 150 | New TW | 500 | 540 | ||
13 | Old TW | 21 | 67 | 53 | Old TW | 0 | 68 |
New TW | 400 | 440 | New TW | 600 | 668 | ||
27 | Old TW | 145 | 233 | 62 | Old TW | 510 | 574 |
New TW | 350 | 400 | New TW | 110 | 170 | ||
34 | Old TW | 725 | 795 | 70 | Old TW | 37 | 128 |
New TW | 200 | 260 | New TW | 700 | 758 |
The parameters are the same as the above tests:
Optimal solution of customer assignment.
SDF no. | Customer no. | SDF no. | Customer no. |
---|---|---|---|
102 | 13,62,76,89 | 107 | / |
103 | 28,43,45,53,59 | 108 | 4 |
104 | 12,18,24,33,68 | 109 | 26,34,37 |
105 | 63,97 | 110 | / |
106 | 14 |
Optimal solution of delivery route.
1-94-58-42-98-82-103-9-39-75-35-50-84-41-5-102-80-25-55-66-11-95-23-6-96-31-67-109-30-100-2-21-81-79-108-10-17-61-38-92-86-57-15-36-19-85-77-60-20-104-69-44-48-64-40-52-72-73-7-32-87-29-90-22-65-51-56-49-46-91-54-71-74-10678-105-27-93-3-99-16-8-88-83-47-101-70 |
This study reports the comparisons of the reschedule route in the CP mode (RRCP) with the original delivery route (ODR) and the reschedule route in the HD mode (RRHD), where Difference = RRCP – RRHD and GAP = (RRHD - RRCP) / RRHD
Comparison of the three schemes.
Item | ODR | RRHD | RRCP | Difference | GAP(%) |
---|---|---|---|---|---|
Delay time | 53000 | 521 | 17 | −504 | 96.74% |
Pickup cost | 0 | 0 | 169 | +169 | – |
Opening cost | 0 | 0 | 105 | +105 | – |
Route cost | 764 | 703 | 442 | −261 | 37.13% |
Total cost | 53764 | 1224 | 733 | −491 | 40.08% |
CPU Time (S) | 0 | 21 | 22 |
Compared with the RRHD, the RRCP increases the pickup cost and SDF opening cost by providing customer pickup services, but the total cost is reduced by 40.08%. The delay time is reduced from 521 to 17 or 96.74%; route cost is reduced from 703 to 442 or 37.13%. As carbon emission is closely related to delivery route distance, the proposed model can help effectively reduce carbon emission.
To gain additional insights, a sensitive analysis is conducted to show how the acceptable distance
Results of sensitive analysis of
Item | | |||||||
---|---|---|---|---|---|---|---|---|
0 | 5 | 10 | 15 | 20 | 30 | 40 | 50 | |
Delay time | 521 | 197 | 97 | 17 | 17 | 17 | 17 | 17 |
Pickup cost | 0 | 41 | 97 | 169 | 169 | 169 | 169 | 169 |
Opening cost | 0 | 60 | 80 | 105 | 105 | 105 | 105 | 105 |
Route cost | 703 | 647 | 552 | 442 | 442 | 442 | 442 | 442 |
Total cost | 1224 | 944 | 826 | 733 | 733 | 733 | 733 | 733 |
Sensitive analysis of
From the sensitive analysis, we can see that when
For the evaluation of the performance of the proposed algorithm, tests based on the benchmark instance proposed by Dumas et al. [
Table
Comparison between SA and the proposed method.
No. | N | M | SA | VVND | GAP(%) | ||
---|---|---|---|---|---|---|---|
Obj | Time | Obj | Time | ||||
1 | 20 | 1 | | 0.003 | | 0.002 | 0.00 |
2 | 20 | 2 | | 0.008 | | 0.005 | 0.00 |
3 | 20 | 3 | | 0.015 | | 0.017 | 0.00 |
4 | 20 | 4 | | 0.027 | | 0.029 | 0.00 |
5 | 20 | 5 | | 0.036 | | 0.053 | 0.00 |
6 | 40 | 1 | | 0.046 | | 0.013 | 0.00 |
7 | 40 | 3 | 430 | 0.180 | | 0.089 | 2.09 |
8 | 40 | 5 | 385 | 0.358 | | 0.293 | 4.42 |
9 | 40 | 7 | 326 | 0.651 | | 0.772 | 0.00 |
10 | 40 | 9 | 326 | 0.957 | | 1.107 | 1.23 |
11 | 60 | 1 | | 0.180 | | 0.042 | 0.00 |
12 | 60 | 4 | 532 | 0.920 | | 0.523 | 5.45 |
13 | 60 | 7 | 455 | 2.155 | | 1.301 | 1.32 |
14 | 60 | 10 | 440 | 3.580 | | 2.726 | 0.68 |
15 | 60 | 13 | 440 | 5.628 | | 4.802 | 0.68 |
16 | 100 | 1 | 629 | 1.111 | | 0.178 | 0.32 |
17 | 100 | 5 | 562 | 7.030 | | 2.647 | 1.96 |
18 | 100 | 10 | 561 | 15.604 | | 10.473 | 4.81 |
19 | 100 | 15 | 530 | 28.451 | | 26.282 | 0.38 |
20 | 100 | 20 | 530 | 42.368 | | 42.486 | 1.51 |
21 | 150 | 1 | 810 | 4.753 | | 0.590 | 1.11 |
22 | 150 | 6 | 800 | 28.851 | | 17.938 | 5.13 |
23 | 150 | 12 | 735 | 67.610 | | 47.126 | 4.08 |
24 | 150 | 18 | 732 | 115.203 | | 76.767 | 5.74 |
25 | 150 | 24 | 720 | 169.527 | | 146.271 | 5.83 |
AVG | 490.68 | 19.81 | 479.28 | 15.30 | 1.87 |
Table
Table
Comparison between HD and the proposed method.
No. | N | M | HD | Proposed method | GAP | ||||
---|---|---|---|---|---|---|---|---|---|
Total | Total | Route | Delay | Pickup | Opening | (%) | |||
1 | 20 | 1 | 335 | 289 | 263 | 0 | 16 | 10 | 13.73 |
2 | 20 | 2 | 335 | 261 | 211 | 0 | 35 | 15 | 22.09 |
3 | 20 | 3 | 335 | 251 | 177 | 0 | 54 | 20 | 25.07 |
4 | 20 | 4 | 335 | 238 | 216 | 0 | 12 | 10 | 28.96 |
5 | 20 | 5 | 335 | 228 | 195 | 0 | 23 | 10 | 31.94 |
6 | 40 | 1 | 494 | 477 | 477 | 0 | 0 | 0 | 3.44 |
7 | 40 | 3 | 494 | 421 | 352 | 0 | 49 | 20 | 14.78 |
8 | 40 | 5 | 494 | 368 | 277 | 0 | 66 | 25 | 25.51 |
9 | 40 | 7 | 494 | 326 | 253 | 0 | 48 | 25 | 34.01 |
10 | 40 | 9 | 494 | 322 | 253 | 0 | 44 | 25 | 34.82 |
11 | 60 | 1 | 609 | 580 | 561 | 0 | 14 | 5 | 4.76 |
12 | 60 | 4 | 609 | 503 | 386 | 0 | 72 | 45 | 17.41 |
13 | 60 | 7 | 609 | 449 | 331 | 0 | 63 | 55 | 26.27 |
14 | 60 | 10 | 609 | 437 | 334 | 0 | 53 | 50 | 28.24 |
15 | 60 | 13 | 609 | 437 | 334 | 0 | 53 | 50 | 28.24 |
16 | 100 | 1 | 655 | 627 | 587 | 0 | 25 | 15 | 4.27 |
17 | 100 | 5 | 655 | 551 | 489 | 0 | 37 | 25 | 15.88 |
18 | 100 | 10 | 655 | 534 | 454 | 0 | 45 | 35 | 18.47 |
19 | 100 | 15 | 655 | 528 | 447 | 0 | 46 | 35 | 19.39 |
20 | 100 | 20 | 655 | 522 | 447 | 0 | 40 | 35 | 20.31 |
21 | 150 | 1 | 859 | 801 | 747 | 0 | 39 | 15 | 6.75 |
22 | 150 | 6 | 859 | 759 | 577 | 0 | 112 | 70 | 11.64 |
23 | 150 | 12 | 859 | 705 | 541 | 0 | 94 | 70 | 17.93 |
24 | 150 | 18 | 859 | 690 | 597 | 0 | 53 | 40 | 19.67 |
25 | 150 | 24 | 859 | 678 | 504 | 0 | 89 | 85 | 21.07 |
AVG | 590 | 479 | 19.79 |
Table
This study proposed a disruption recovery problem with time window changes in the last mile delivery of online shopping. One characteristic of the problem is that the delivery route could be rescheduled by using SDFs when time window changing disruptions occurred during the delivery process. The VVND algorithm was presented, which included a 2-opt algorithm improved by LR to speed up its convergence, to solve this problem. The proposed method and algorithm were tested on a set of instances. The results corroborated that the proposed method could quickly recover the delivery and reduce the total delivery cost when time window changing disruptions occurred in the last mile delivery. Meanwhile, the proposed algorithm had an evident competitiveness compared with other heuristics, and the total delivery cost could be reduced by approximately 3% to 34% with the increasing number of SDFs compared with the solution of the HD mode.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This work was supported by the National Science and Technology Support Program of China (Grant Nos. 71331002, 71502047, 71601061, and 71771077); the Ministry of Chinese Education, Humanities and Social Sciences project (Grant No. 17YJA630037); the National Key R&D Program of China (No. 2016YFC0803203); the Fundamental Research Funds for the Central Universities project (Grant No. JS2017HGXJ0044); the “Double-First Class” Construct Project (Grant No. 45000-411104/005); and the Natural Science Foundation of Anhui Province in China (Grant No. 1808085QG229).