The response surface method, which has not been applied in the field of logistics, is used to study the express storage and distribution system. The goal is to find out the key factors affecting “customer satisfaction” and “warehouse explosion” and determine the optimal parameters to minimize the operation time and congestion rate of the system. The Box–Behnken response surface method is used to optimize the factors such as sorting speed, distribution speed, sorting temporary storage capacity, and distribution temporary storage capacity in the system, and the logistics simulation software is used to verify the experiment. The predicted value is in good agreement with the measured value. The optimal parameters are sorting speed of 0.002 D/PCS, distribution speed of 31 M/

With the rapid development of information technology and the Internet plus, e-commerce is becoming the main force of China’s economic and social development. Not only many domestic e-commerce enterprises but also foreign e-commerce giants have set foot in the Chinese market, making consumers face more choices. In this context, “customer satisfaction” has become an important indicator to measure the development of e-commerce enterprises. Whether e-commerce enterprises can quickly respond to and meet customer needs to the greatest extent determines the survival of the competitiveness of enterprises and development in the highly competitive market.

As a service industry of e-commerce, logistics industry is an important link between e-commerce enterprises and customers. This service is the most direct feeling of customers, with “visualization”, and its service level directly affects customers’ evaluation of e-commerce enterprises. However, compared with the rapid development of e-commerce, the supporting warehousing and distribution operation, namely logistics express service, cannot fully keep up with its development. Especially when various platforms launch various preferential activities one after another, when the network transaction volume is huge and the package delivery volume is also huge, the “warehouse explosion event” often occurs, that is, in a short time, the pressure of the warehouse increases sharply and the distribution system also bears great pressure. In view of this phenomenon, by optimizing the express storage and distribution system, the “warehouse explosion event” can be reduced and the “customer satisfaction” can be improved.

At present, the research on the optimization of express storage and distribution at home and abroad is limited. Most scholars mainly use simulation or heuristic algorithms to study the optimization of storage and distribution. Li et al. [

Express warehousing and distribution system can simulate its composition, randomness and parameters through the simulation model, but the simulation operation is only the simulation of the real system and cannot get the optimal solution or the most satisfactory solution, so it needs to be combined with the optimization algorithm. The combination of the randomness of the system and the mathematical programming model will lead to a series of complex formulas, and the published models rarely consider the random factors. Response surface methodology (RSM) is a simulation optimization method. It can be easily combined with random factors and deterministic simulation problems. It is used to model and analyze the problem in which the response of interest is affected by multiple variables. Its ultimate purpose is to optimize the response. However, the literature on the application of response surface methodology in the field of logistics is basically blank. This paper studies the physical flow problem of express storage and distribution system based on response surface theory and discusses the feasibility of response surface method to study the logistics problem. The goal is to find out the key factors affecting “customer satisfaction” and “warehouse explosion” and determine the optimal parameters to minimize the operation time and congestion rate of the system.

Starting from the “warehouse explosion event,” this paper analyzes the relevant problems in the process of parcel distribution in various promotional activities and carries out simulation experiments on the sorting operation and subsequent delivery operation in the transit warehouse. In practice, the process of express warehousing and distribution is too cumbersome, and some operations do not affect the results of simulation experiments in this model. Therefore, the simulation model is simplified into the following links:

The parcel is delivered to the express company and enters the area to be sorted for sorting.

Input the package information and sort the packages intelligently according to different destinations.

After picking, the packages are transferred to the waiting area for distribution.

After the arrival of the delivery vehicle, the package shall be packaged and delivered according to the batch.

To be more in line with the actual model and not limit any other factors, only the impact of the storage capacity of the temporary storage area, the sorting operation of parcels and the later delivery operation on the logistics express service is considered, including the sorting speed, distribution speed, sorting temporary storage capacity, and distribution temporary storage capacity. The number

To simulate the express warehousing and distribution process, the logistics simulation software Flexsim is used to establish the simulation model of warehousing and distribution, as shown in Figure

Simulation model of express warehousing and distribution system.

The response surface methodology is based on a collection of sample points collected in a designated design space for a limited experimental design, and the fitted response variable replaces the real response surface. In engineering optimization design, the application of response surface methodology can not only get the relationship between response variables and factors but also get the optimization plan, that is, the optimal combination of factors so that the objective function can be optimized.

In the response surface method, to obtain a mathematical model representing the relationship between factors and response variables, first-order and second-order response surface models in the form of linear or quadratic polynomial functions are often used to approximate. Usually a low-order polynomial can satisfy engineering application requirements; if the response surface has strong nonlinearity, then high-order polynomials are required. When considering the cross-effects between random variables, polynomials with cross-terms can be used.

The basic form of the first-order response surface model is as follows:

The basic form of the second-order response surface model is as follows:

Among them,

Usually in the process of calculation, the first-order model is used first, the purpose of which is to guide the experimenter along the path to improve the system to the optimal nearby area quickly and effectively. Once the optimal area is found, a more refined model can be used (for example, the second-order model). Perform analysis to determine the best position throughout. Estimate the regression coefficient of the regression equation using the least square method. Construct a polynomial response surface model.

To calculate the accuracy of the results, it is necessary to determine the accuracy of the fitting equation. It is usually determined in the form of variance.

The fitting accuracy of the model is usually evaluated by

There are many response surface experimental design methods. The commonly used methods are central composite design (CCD), D-optimal design (DoD), Box–Behnken design (BBD), and so on. [

BBD [

This paper selects the parcel warehousing volume of the sorting center of an express company in November 2020 for analysis, as shown in Figure

Parcel warehousing volume of sorting center of an express company in November 2020.

The Box–Behnken response surface methodology was used to design the experiment with 4 factors and 3 levels, with sorting speed (A), distribution speed (B), sorting temporary storage capacity (C) and distribution temporary storage capacity (

Factors and levels.

Factor | Variable | Level | ||
---|---|---|---|---|

−1 | 0 | 1 | ||

Sorting speed (D/PCS) | A | 0.001 | 0.0055 | 0.01 |

Delivery speed (M/ | B | 20 | 30 | 40 |

Capacity of sorting temporary storage area (PCS) | C | 200 | 400 | 600 |

Distribution staging area capacity (PCS) | D | 200 | 300 | 400 |

Experimental scheme and results.

Experiment number | A | B | C | D | Operation time ( | Blockage rate (%) |
---|---|---|---|---|---|---|

1 | 0.001 | 20 | 400 | 300 | 32.12 | 12.4 |

2 | 0.0055 | 30 | 200 | 400 | 30.59 | 29.6 |

3 | 0.01 | 30 | 200 | 300 | 40.51 | 67.7 |

4 | 0.01 | 30 | 600 | 300 | 40.51 | 53.8 |

5 | 0.001 | 30 | 600 | 300 | 30.18 | 0 |

6 | 0.01 | 30 | 400 | 200 | 40.51 | 60.8 |

7 | 0.01 | 40 | 400 | 300 | 40.31 | 61.1 |

8 | 0.001 | 30 | 200 | 300 | 30.18 | 9.1 |

9 | 0.0055 | 40 | 200 | 300 | 30.43 | 29.7 |

10 | 0.001 | 40 | 400 | 300 | 30.02 | 0 |

11 | 0.0055 | 20 | 400 | 400 | 31.9 | 17.1 |

12 | 0.0055 | 30 | 400 | 300 | 30.59 | 17.9 |

13 | 0.0055 | 40 | 400 | 400 | 30.43 | 18 |

14 | 0.0055 | 30 | 600 | 400 | 30.59 | 1.1 |

15 | 0.0055 | 30 | 400 | 300 | 30.59 | 17.9 |

16 | 0.0055 | 30 | 600 | 200 | 30.59 | 1.1 |

17 | 0.0055 | 40 | 600 | 300 | 30.43 | 1.2 |

18 | 0.0055 | 30 | 400 | 300 | 30.59 | 17.9 |

19 | 0.0055 | 20 | 400 | 200 | 31.9 | 31 |

20 | 0.0055 | 30 | 200 | 200 | 30.59 | 29.6 |

21 | 0.0055 | 20 | 600 | 300 | 31.9 | 1.1 |

22 | 0.0055 | 40 | 400 | 200 | 30.43 | 18 |

23 | 0.0055 | 30 | 400 | 300 | 30.59 | 17.9 |

24 | 0.0055 | 20 | 200 | 300 | 31.9 | 45.2 |

25 | 0.001 | 30 | 400 | 200 | 30.18 | 1 |

26 | 0.0055 | 30 | 400 | 300 | 30.59 | 17.9 |

27 | 0.001 | 30 | 400 | 400 | 30.18 | 0 |

28 | 0.01 | 20 | 400 | 300 | 40.43 | 60.9 |

29 | 0.01 | 30 | 400 | 400 | 40.51 | 60.8 |

Using Design-Expert12.0 software to regression fit the operation time (_{1}) and blockage rate (_{2}) in Table

Table

Results of analysis of variance.

Source | Sum of squares | d | Mean square | |||
---|---|---|---|---|---|---|

Operation time | Model | 456.83 | 14 | 32.63 | 539.35 | <0.0001 |

299.20 | 1 | 299.20 | 4945.46 | <0.0001 | ||

5.47 | 1 | 5.47 | 90.37 | <0.0001 | ||

0.0000 | 1 | 0.0000 | 0.0000 | 1.0000 | ||

0.0000 | 1 | 0.0000 | 0.0000 | 1.0000 | ||

AB | 0.9801 | 1 | 0.9801 | 16.20 | 0.0013 | |

AC | 0.0000 | 1 | 0.0000 | 0.0000 | 1.0000 | |

AD | 0.0000 | 1 | 0.0000 | 0.0000 | 1.0000 | |

BC | 0.0000 | 1 | 0.0000 | 0.0000 | 1.0000 | |

BD | 0.0000 | 1 | 0.0000 | 0.0000 | 1.0000 | |

CD | 0.0000 | 1 | 0.0000 | 0.0000 | 1.0000 | |

^{2} | 142.58 | 1 | 142.58 | 2356.63 | <0.0001 | |

^{2} | 1.68 | 1 | 1.68 | 27.70 | 0.0001 | |

^{2} | 0.0072 | 1 | 0.0072 | 0.1191 | 0.7351 | |

^{2} | 0.0072 | 1 | 0.0072 | 0.1191 | 0.7351 | |

Residual | 0.8470 | 14 | 0.0605 | |||

Lack of fit | 0.8470 | 10 | 0.0847 | |||

Pure error | 0.0000 | 4 | 0.0000 | |||

Cor total | 457.68 | 28 | ||||

Blockage rate | Model | 13455.10 | 14 | 961.08 | 34.10 | <0.0001 |

9781.23 | 1 | 9781.23 | 347.04 | <0.0001 | ||

131.34 | 1 | 131.34 | 4.66 | 0.0487 | ||

1940.56 | 1 | 1940.56 | 68.85 | <0.0001 | ||

18.50 | 1 | 18.50 | 0.6564 | 0.4314 | ||

AB | 39.69 | 1 | 39.69 | 1.41 | 0.2551 | |

AC | 5.76 | 1 | 5.76 | 0.2044 | 0.6581 | |

AD | 0.2500 | 1 | 0.2500 | 0.0089 | 0.9263 | |

BC | 60.84 | 1 | 60.84 | 2.16 | 0.1639 | |

BD | 48.30 | 1 | 48.30 | 1.71 | 0.2116 | |

CD | 0.0000 | 1 | 0.0000 | 0.0000 | 1.0000 | |

^{2} | 1284.25 | 1 | 1284.25 | 45.57 | <0.0001 | |

^{2} | 43.29 | 1 | 43.29 | 1.54 | 0.2356 | |

^{2} | 3.45 | 1 | 3.45 | 0.1224 | 0.7317 | |

^{2} | 4.87 | 1 | 4.87 | 0.1729 | 0.6839 | |

Residual | 394.58 | 14 | 28.18 | |||

Lack of fit | 394.58 | 10 | 39.46 | |||

Pure error | 0.0000 | 4 | 0.0000 | |||

Cor total | 13849.68 | 28 |

The correlation coefficient

The variance analysis of the model shows that the ^{2}, and B^{2} are less than 0.01, indicating that these five items have highly significant effects, while the ^{2} in the blockage rate model are the model items with highly significant impact, B is the model item with significant impact, which has significant impact on the blockage rate, while the remaining items are nonsignificant items, which have no significant impact on the blockage rate.

The residual is the difference between the observed value and the predicted value of the regression model. In the absence of experimental outliers, the residual should conform to the normal distribution. It can be seen from Figures

Normal plot of residuals (operation time).

Normal plot of residuals (blockage rate).

Figure

Predicted vs. actual of operation time.

Predicted vs. actual blockage rate.

By looking at the results of analysis of variance, it can be inferred from the value of

It can be seen from Figures

Response surface and contour of the interaction between sorting speed and distribution speed on operation time.

Response surface and contour diagram of the influence of the interaction between sorting speed and sorting temporary storage capacity on blockage rate.

Based on the above response surface model analysis, the quadratic regression equation of the comprehensive index is solved using the Design-Expert12.0 software. The optimal parameters are A (sorting speed) 0.002 D/PCS, B (distribution speed) 31.167 M/

To test the prediction results, it is necessary to verify the optimal parameters of the prediction. To facilitate the actual operation, some validation parameters are corrected to the distribution speed of 31 M/

In this study, the optimal parameters of the express storage and distribution system are sorting speed of 0.002D/PCS, distribution speed of 31 M/

Owing to the difference of facilities and operating conditions, different simulation models of express warehousing and the distribution system will be produced. This paper studies the sorting operation and subsequent delivery operation in the transfer warehouse and the simulation model established under the ideal hypothesis state to determine the relevant parameters of the optimal express warehousing and distribution system to improve the consumer satisfaction index based on shortening working hours and reduce the congestion rate index based on the arrival congestion rate of packages.

The Box–Behnken response surface methodology is an optimization method integrating experimental design and mathematical modeling. It can effectively reduce the number of tests and shorten the experimental cycle. The analysis results are intuitive and clear, and the interaction between various factors can be investigated. The response surface method not only establishes the prediction model but also tests the adaptability of the model, the significance of the model and coefficient, analysis of variance and model diagnosis. In this paper, the parameters of express storage and distribution system are optimized by the Box–Behnken response surface methodology and the simulation experiment is carried out by Flexsim software. The optimization results and simulation results show that the deviation between the predicted value and the actual value is within 5%, indicating that the correlation is good and the response surface methodology optimization of express storage and distribution system parameters is reasonable and feasible.

The labeled dataset used to support the findings of this study is available from the corresponding author upon request.

The authors declare no conflicts of interest.

This work was supported by the