Facility location, inventory control, and vehicle routes scheduling are three key issues to be settled in the design of logistics system for e-commerce. Due to the online shopping features of e-commerce, customer returns are becoming much more than traditional commerce. This paper studies a three-phase supply chain distribution system consisting of one supplier, a set of retailers, and a single type of product with continuous review (
With the booming development of e-commerce industry, especially that B2C online shopping has become a part of people’s daily life, returning goods is becoming more and more common. Studies show that there are more customer returns in e-commerce than in the traditional business, and the return rate sometimes can be up to 35% of the initial order in online selling [
Facility location, inventory control, and vehicle routes scheduling are three core issues to be settled in strategic/tactical and operational decision levels for logistics system in e-business. Previous work on these three areas is fruitful. In fact, there is a mutually dependent relationship among these problems. Comprehensive optimizing and logistics activities management should be based on this relationship [
Many researches concerning the IRP, LRP, and LIP are studied deeply and have made some abundant achievements. However, there are few researches on the integration of LIRP. Some researchers appeal to carry out research on LIRP [
Previous researches on reverse logistics mainly focus on independent activities about LIRP. Fleischmann et al. [
Li et al. [
In this paper, we develop a practical stochastic LIRP model considering returns in e-commerce and provide a pseudo-parallel genetic algorithm integrating simulated annealing (PPGASA). To our best knowledge, this work is the first step to introduce returns into the stochastic LIRP in e-commerce, which makes it become more practical. We also provide an effective algorithm named PPGASA to solve the model, which is based on pseudo-parallel genetic algorithm and simulated annealing. Results of numerical examples show that PPGASA outperforms genetic algorithm (GA) on optimal solution, computing time, and computing efficiency and stability.
The remainder of this paper is organized as follows. Section
Customer returns in e-commerce generally have a high integrity, which do not need to be repaired and can reenter the sales channels after a simple repackaging process [
Diagram of the LIRP network.
The supply chain in this study consists of one supplier, multiple MCs, multiple retailers, and a single type of product with continuous review
The objective of this problem is to determine the quantity, locations, order times, and order size of MCs and arrange the routes. The final target is to minimize the total cost and improve the efficiency of logistics operations. The involved decisions are as follows:
There is a single type of goods. The total demand on each route is less than or equal to the vehicle capacity. The vehicle type is homogeneous. Each route is served by one vehicle. Each route begins and ends at the same MC. The capacity of each MC is finite. The forward distribution and reverse collection service could be met at the same time. The daily demand and returns of each retailer are stochastic and obey the normal distribution. The returned goods without quality defect. Returned goods are processed and repackaged at MCs.
The cost of
The objective is to minimize the total cost of the system; we formulate the model
The objective function (
The abstract idea of solution approach is described as follows. Firstly, we derive optimal order times
In order to calculate the minimum of the objective function, make the following operation based on the model.
Constraints (
In order to obtain the economic order size and the optimal order time, we calculate the gradient of objective function (
We introduce the generalized Lagrange multiplier
Let
Putting
As we know, the VRP is an NP-hard problem. The LIRP containing the VRP is more complicated. It is generally believed that there is no complete, accurate, and efficient analytic algorithm to solve NP-hand problems. Note that bioinspired computation for solving optimization problems is widely applied; we design a hybrid algorithm based on PPGA and SA to solve the proposed model.
Although traditional genetic algorithm (GA) has strong global search ability in solving optimization problems, it has defects such as premature and weak local search ability. On the other hand, SA has strong local search ability without premature problem. Therefore, the combination of GA and SA can overcome the defects of each of the two methods, bring into play their respective advantages, and improve the solving efficiency. This hybrid algorithm is named pseudo-parallel genetic algorithm integrating simulated annealing (PPGASA).
Parallel genetic algorithm (PGA) can improve the operation speed of GA and maintain population diversity, inhibiting the occurrence of “premature” phenomenon. Generally, the PGA is executed on a parallel machine or a LAN. But a single processor machine is applicable if real-time requirements are not needed, which is so called pseudo-parallel genetic algorithm (PPGA) [
This study adopts the natural number coding method; using unrepeated
If
Select two parent individuals randomly from the population.
Generate two random cut points to represent the mapped segments.
Exchange the segments of the two parent individuals to produce two new individuals.
Determine the mapping relations between two segments.
Legalize two new individuals with mapping relationship through repair strategy.
Select one parent individual randomly from the population.
Generate two random numbers to represent the mutation points.
Swap the positions of these two mutation points to produce a new individual.
Compared with other mutations, studies show that convergence rate of this method has a greater advantage in control population. It can effectively prevent premature convergence of GA and avoid the occurrence of local optimal solution.
We calculate the fitness function values using the initializing population, sort the individuals by descending of the fitness function values, and then divide the population equally into two groups. The one with larger values is called successful subgroup, and the other one is called unsuccessful subgroup. In order to maintain the independent evolution of the two subgroups and balance the overall exploring ability and the convergence speed, information exchange should occur only in the appropriate stages. After
Select the individual
Select randomly individual
If
Select the individual
Select randomly individual
If
In this paper, the termination condition is that the fitness has reached a plateau such that successive
The pseudocodes of HGSAA are shown in Pseudocode
[ [ [
An example is used to illustrate the proposed heuristic method. The data of
Based on Matlab 7.0 platform, we programmed the PPGASA and then run it 30 times on a computer (CPU: Intel Core i3-2130 @ 3.4 GHz, RAM: 2.85 GB DDR, OS: Windows 7).
In this subsection, we will discuss five parameters’ impact on the PPGASA. The performances of PPGASA vary with the different values of these parameters, which are shown in Tables
The results with different
|
Cost | CPU time | ||||||
---|---|---|---|---|---|---|---|---|
Range | Mean | Standard deviation | Coefficient of variation | Range |
Mean |
Standard deviation | Coefficient of variation | |
0.0001 | 1.28 | 2.17 | 0.34 | 0.27 | 0.76 | 1.46 | 0.17 | 0.28 |
0.0005 | 0.99 | 1.65 | 0.27 | 0.16 | 0.86 | 1.60 | 0.25 | 0.15 |
0.001 | 1.60 | 2.15 | 0.52 | 0.33 | 1.34 | 1.54 | 0.21 | 0.30 |
0.005 | 1.30 | 2.1 | 0.40 | 0.30 | 0.86 | 1.53 | 0.17 | 0.27 |
The results with different
|
Cost | CPU time | ||||||
---|---|---|---|---|---|---|---|---|
Range | Mean | Standard deviation | Coefficient of variation | Range | Mean | Standard deviation | Coefficient of variation | |
0.1 | 2.70 | 1.97 | 0.65 | 0.33 | 4.26 | 2.92 | 1.13 | 0.39 |
0.4 | 2.26 | 2.18 | 0.65 | 0.30 | 2.01 | 1.42 | 0.57 | 0.40 |
0.7 | 2.91 | 2.17 | 0.84 | 0.39 | 1.34 | 1.42 | 0.42 | 0.30 |
0.9 | 0.99 | 1.65 | 0.27 | 0.16 | 0.86 | 1.60 | 0.25 | 0.15 |
The results with different
|
Cost | CPU time | ||||||
---|---|---|---|---|---|---|---|---|
Range | Mean | Standard |
Coefficient of variation | Range | Mean | Standard |
Coefficient of variation | |
10 | 1.23 | 1.70 | 0.52 | 0.31 | 0.43 | 0.75 | 0.12 | 0.16 |
15 | 1.21 | 1.72 | 0.46 | 0.27 | 0.39 | 0.39 | 0.16 | 0.14 |
20 | 0.99 | 1.65 | 0.27 | 0.16 | 0.86 | 1.60 | 0.25 | 0.15 |
30 | 1.18 | 1.86 | 0.37 | 0.20 | 2.53 | 2.55 | 0.67 | 0.26 |
The results with different
|
Cost | CPU time | ||||||
---|---|---|---|---|---|---|---|---|
Range | Mean | Standard |
Coefficient of variation | Range | Mean | Standard |
Coefficient of variation | |
10 | 1.96 | 2.12 | 0.72 | 0.34 | 0.72 | 1.50 | 0.42 | 0.28 |
40 | 2.05 | 2.09 | 0.61 | 0.29 | 0.78 | 1.59 | 0.47 | 0.29 |
70 | 1.10 | 1.98 | 0.58 | 0.29 | 0.92 | 1.54 | 0.39 | 0.27 |
100 | 0.99 | 1.65 | 0.27 | 0.16 | 0.86 | 1.60 | 0.25 | 0.15 |
The results with different
|
Cost | CPU time | ||||||
---|---|---|---|---|---|---|---|---|
Range | Mean | Standard |
Coefficient of variation | Range | Mean | Standard |
Coefficient of variation | |
0.1 | 1.56 | 1.98 | 0.68 | 0.35 | 0.77 | 1.57 | 0.43 | 0.27 |
0.4 | 1.68 | 1.93 | 0.61 | 0.32 | 1.53 | 1.58 | 0.38 | 0.24 |
0.7 | 1.60 | 2.13 | 0.73 | 0.34 | 0.59 | 1.51 | 0.44 | 0.29 |
0.9 | 0.99 | 1.65 | 0.27 | 0.16 | 0.86 | 1.60 | 0.25 | 0.15 |
Figures
Optimization results on different values
Optimization results on different values
Optimization results on different values
Optimization results on different values
Optimization results on different values
For getting the results of the instance, we run another 100 times on the same computer. One of the minimum values of objective function in the 100 experiments is 963850. Table
Solution of instance
MC | Routing number | Routing | Order times | Order interval |
Order quantity | Safety stock |
---|---|---|---|---|---|---|
|
|
|
32 | 9 | 656 | 630 |
|
||||||
|
|
|
31 | 10 | 590 | 610 |
|
||||||
|
|
|
53 | 6 | 702 | 744 |
|
|
31 | 10 | 387 | 400 | |
|
||||||
|
|
|
46 | 7 | 613 | 658 |
|
|
35 | 9 | 531 | 558 | |
|
||||||
|
|
|
40 | 8 | 555 | 592 |
|
|
35 | 9 | 253 | 144 |
Topological structure of the network.
For comparison, GA is programmed by Matlab 7.0 as well, and the instance
Trends of optimal objective function value by GA.
Trends of optimal objective function value by PPGASA.
The fluctuation cure of optimal objective function values obtained from the 100 times experiments is shown in Figures
The fluctuation curve of optimal objective function value by PPGASA.
The fluctuation curve of optimal objective function value by GA.
The optimal objective function value and the CPU time of these two algorithms are shown in Table
Statistical results of optimal objective function value of two algorithms (cost: yuan, CPU time: second).
Algorithm | Mean | Standard deviation | Coefficient of variation | Significance test | ||
---|---|---|---|---|---|---|
|
|
|||||
Cost | PPGASA | 1650568 | 271320 | 0.16 | −9.144 | 0.000 |
GA | 2134686 | 454600 | 0.21 | |||
|
||||||
CPU time | PPGASA | 1.60 | 0.25 | 0.15 | 6.826 | 0.000 |
GA | 1.38 | 0.25 | 0.18 |
In this section, a series of experiments are given to show that PPGASA is more efficient and stable than GA. Similar with Section
Each instance was calculated 100 times by PPGASA and GA, respectively; the results are shown in Tables
Optimal objective function values of two algorithms (yuan).
Instance name | Algorithm | Mean | Standard deviation | Coefficient of variation | Significance test | |
---|---|---|---|---|---|---|
|
|
|||||
|
PPGASA | 27274.15 | 3072.70 | 0.1127 | −15.71 | 0.000 |
GA | 59644.00 | 20373.95 | 0.3416 | |||
|
||||||
|
PPGASA | 176597.12 | 51842.11 | 0.2936 | −2.069 | 0.040 |
GA | 193606.40 | 63820.20 | 0.3296 | |||
|
||||||
|
PPGASA | 1532353.00 | 240454.91 | 0.1569 | −24.268 | 0.000 |
GA | 3266300.00 | 672809.81 | 0.2060 | |||
|
||||||
|
PPGASA | 4368430.00 | 336908.31 | 0.0771 | −3.877 | 0.000 |
GA | 4571132.00 | 399811.55 | 0.0874 | |||
|
||||||
|
PPGASA | 5653803.00 | 481169.53 | 0.0851 | −2.113 | 0.036 |
GA | 58256800.00 | 655839.90 | 0.0113 | |||
|
||||||
|
PPGASA | 6095438.00 | 219212.14 | 0.0360 | −3.388 | 0.001 |
GA | 6221775.00 | 301680.88 | 0.0485 | |||
|
||||||
|
PPGASA | 6848350.00 | 617689.91 | 0.0902 | −3.391 | 0.001 |
GA | 7179759.00 | 757338.00 | 0.1055 |
CPU time of two algorithms (seconds).
Instance name | Algorithm | Mean | Standard deviation | Coefficient of variation | significance test | |
---|---|---|---|---|---|---|
|
|
|||||
|
PPGASA | 0.5325 | 0.0931 | 0.1748 | −2.488 | 0.014 |
GA | 0.5712 | 0.1243 | 0.2176 | |||
|
||||||
|
PPGASA | 1.3804 | 0.2670 | 0.1934 | −3.158 | 0.002 |
GA | 1.5322 | 0.3996 | 0.2608 | |||
|
||||||
|
PPGASA | 1.8469 | 0.2226 | 0.1205 | −4.704 | 0.000 |
GA | 2.0334 | 0.3282 | 0.1614 | |||
|
||||||
|
PPGASA | 3.8288 | 0.2372 | 0.0620 | −5.766 | 0.000 |
GA | 4.1037 | 0.4135 | 0.1008 | |||
|
||||||
|
PPGASA | 8.2635 | 1.6029 | 0.1940 | −10.607 | 0.000 |
GA | 11.5331 | 2.6330 | 0.2283 | |||
|
||||||
|
PPGASA | 9.3730 | 0.9723 | 0.1037 | −5.326 | 0.000 |
GA | 10.4171 | 1.7021 | 0.1634 | |||
|
||||||
|
PPGASA | 10.3791 | 1.5966 | 0.1538 | −13.805 | 0.000 |
GA | 14.4457 | 2.4756 | 0.1714 |
Tables
Observe from Tables
There exists a higher return rate in e-commerce than in traditional business. Generally, the returned goods have no quality defect and have great integrity. Just after a simple repackaging process, the returned goods can reenter the sales channels, which put forward high requirements to the logistics system that support the operation of e-commerce. In this paper, we formulate the stochastic LIRP model with returns in e-commerce and provide an effective heuristic algorithm named PPGASA to solve it. The main contributions are summarized as follows. We establish a stochastic LIRP model considering no quality defects returns in e-commerce to minimize the total cost of both forward and reverse logistics networks. It is very useful to help managers make the right decisions for e-commerce operations. The stochastic LIRP model with returns is a NP-hand problem and very hard to be solved by traditional methods. A heuristic algorithm named PPGASA based on PPGA and SA is designed to solve our model. Results of experimental data show that PPGASA outperforms GA on optimal solution, computing time, and computing stability. PPGASA is an excellent choice to solve the proposed LIRP model effectively.
While our model and approach increase the threshold of existing literature in this topic, we recognize a number of ways our research could be embellished by. Some extensions can be done in further work. Considering the variety of the types of goods, the multiple products model should be proposed. In reality, decision makers are always in front of imprecise and vague operational conditions [
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China (nos. 71171093, 71471073, and 71101061) and the Fundamental Research Funds for the Central Universities of China (nos. CCNU13A05049, CCNU14Z016, and CCNU14A05049).