Fourth party logistics (4PL) has been receiving great attention and studied by researchers. This paper studies multipoint to multipoint 4PL system routing optimization with reliability constraints. Objective factors which cause disturbances of transportation time are taken into consideration. The mathematical model of the multipoint to multipoint multitask routing optimization in 4PL system with reliability constraints is set up. To solve the model, a Messy Genetic Algorithm (Messy GA) with double arrays encoding method is designed. The experimental result is compared with the Enumeration Algorithm (EA), and it shows that this algorithm can find the satisfactory solution and is a powerful optimization method for solving the problem.
With the rapid development of global economy, trade between enterprises grows remarkably. Hence the ability to integrate supply chain for logistics companies has to increase. They are eager to a logistics company that owns strong comprehensive strength to provide scheme for the whole supply chain and be able to meet multiproduct distribution services from different production places to different demand places. Then, the fourth party logistics (4PL) appeared [
Many researchers have studied the 4PL and it has received increasing attention [
Multipoint to multipoint and multitask problem in 4PL system with route selection and 3PL supplier’s selection integrated is considered in this paper. It is a complex system. We take objective factors that cause disturbances of transportation time into consideration, and the mathematical model is set up. Our goal is minimizing the total cost in this multitask problem, and all tasks must satisfy reliability constraints that customer required. Because the multipoint to multipoint 4PL system routing problem is NP-hard two algorithms are designed: Messy Genetic Algorithm (Messy GA) and Enumeration Algorithm (EA). The algorithm is coded in Matlab 7.0 and run on a Core 2 2.83 GHz computer. The comparisons in simulation testify the algorithms’ effectiveness.
We use a straightforward way to describe the 4PL logistics system, which is multigraph. It can easily tell us all information needed clearly, as Figure
Directed graph with 8 nodes.
The route of 4PL system is composed of cities and 3PL providers. It forms a parallel system. According to reliability theory, the reliability of 4PL system can be calculated by continued multiplication of the reliability of 3PL. Here, each 3PL is seen as a logistics unit. In this paper, the transportation time of the 3PL providers is uncertain and has normal distribution. Hence, the time reliability of logistics unit can be defined as the probability of the goods delivered in a timely manner. It can be calculated by the following formula:
Another important influence factor of reliability is transportation cost. It can be calculated by the following formula:
Here the reliability of logistics unit function is given as follows:
The reliability of 4PL system can be calculated by the following formula:
There is not only one task between the supply and demand nodes. Each path on the 4PL system cannot be reused. The transportation time of 3PL providers is uncertain and has normal distribution. It is independent from each other.
Variables and parameters are defined as follows:
The mathematical model for 4PL system routing optimization with reliability constraints can be described as follows:
The multipoint to multipoint 4PL system routing optimization is a typical NP-hard problem. According to the characteristics of the model, a Messy Genetic Algorithm (Messy GA) with double arrays encoding method is designed. In the following, we first describe the Messy GA in detail and then introduce an Enumeration Algorithm (EA), which is used to check the quality of the solutions obtained by the Messy GA.
According to the characteristics of the model, a Messy GA with double arrays encoding method is designed. Messy GA differ from normal genetic algorithms in that they allow variable-length strings. The detailed description of the process can be written as below.
The values of
Crossover operation.
To check the quality of the solutions obtained by the Messy GA, the Enumeration Algorithm (EA) is used. Because the solution space is very large, the EA is described as follows.
Assume that a 4PL company undertakes a transnational transportation. In this transportation, we need to transport 3 tons of food and 5 tons of coal from the supply nodes
The algorithm is coded in Matlab 7.0 and run on a Core 2 2.83 GHz computer [
The node and arc data are given in Tables
The data of nodes for the 8-node problem.
Node | Cost (1000 dollars) | Capacity (ton) |
---|---|---|
|
5 | 9 |
|
4 | 8 |
|
3 | 10 |
|
6 | 12 |
|
4 | 9 |
|
3 | 8 |
|
2 | 10 |
|
2 | 12 |
The data of arcs for the 8-node problem.
|
|
|
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|---|---|
1 | 3 | 1 | 18 | 12 |
|
24 | 0.88493 | 0.945959 | 0.915445 |
2 | 18 | 10 |
|
24 | 0.908789 | 0.945959 | 0.927374 | ||
|
|||||||||
2 | 3 | 1 | 18 | 11 |
|
24 | 0.841345 | 0.945959 | 0.893652 |
2 | 18 | 12 |
|
24 | 0.878327 | 0.945959 | 0.912143 | ||
4 | 1 | 17 | 10 |
|
24 | 0.933193 | 0.942873 | 0.938033 | |
2 | 20 | 12 |
|
24 | 0.873451 | 0.951229 | 0.91234 | ||
|
|||||||||
3 | 5 | 1 | 18 | 9 |
|
24 | 0.788145 | 0.945959 | 0.867052 |
2 | 17 | 10 |
|
36 | 0.99617 | 0.942873 | 0.969521 | ||
|
|||||||||
4 | 5 | 1 | 18 | 15 |
|
36 | 0.941958 | 0.945959 | 0.943959 |
2 | 12 | 12 |
|
18 | 0.933193 | 0.920044 | 0.926619 | ||
6 | 1 | 13 | 14 |
|
18 | 0.959941 | 0.925961 | 0.942951 | |
2 | 16 | 13 |
|
18 | 0.99379 | 0.939413 | 0.966602 | ||
|
|||||||||
5 | 7 | 1 | 17 | 11 |
|
18 | 0.841345 | 0.942873 | 0.892109 |
2 | 10 | 14 |
|
20 | 0.88493 | 0.904837 | 0.894884 | ||
8 | 1 | 12 | 16 |
|
20 | 0.990185 | 0.920044 | 0.955115 | |
2 | 12 | 17 |
|
20 | 0.959941 | 0.920044 | 0.939993 | ||
|
|||||||||
6 | 8 | 1 | 15 | 10 |
|
24 | 0.945201 | 0.935507 | 0.940354 |
2 | 10 | 9 |
|
24 | 0.99702 | 0.904837 | 0.950929 |
The experimental results are shown in Table
Comparison of two algorithms.
Algorithm | Total cost (1000 dollars) | Optimal route | Reliability of the route | Run time (second) |
---|---|---|---|---|
Messy GA | 357 |
|
0.859 (FOOD) | <1 |
|
0.862 (COAL) | |||
|
||||
EA | 357 |
|
0.859 (FOOD) | 5689 |
|
0.862 (COAL) |
The 4PL company needs to transport food and coal from supply nodes to demand nodes with the reliability not less than 0.85. From Table
The routing optimization in 4PL system is one of the most important problems in supply chain optimization. This study set up the mathematical model of the multipoint to multipoint 4PL system routing optimization with reliability constraints based on the reliability theory. The Messy GA and the EA are proposed to solve the model. Numerical experiments are carried out to investigate the performance of the proposed Messy GA. The experiment results show that the Messy GA can obtain the same best result as the EA.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This paper is supported by the Science and Technology Support Program of Liaoning Province (no. 2013216015) and the Science and Technology Support Program of Shenyang (no. F13-051-2-00 and no. F14-231-1-24).