# Research on the Modeling of Automatic Pricing and Replenishment Strategies for Perishable Goods with Time-Varying Deterioration Rates

^{*}

## Abstract

**:**

## 1. Introduction

- (a)
- Ensure that the market demand for various categories of vegetable commodities is met;
- (b)
- A correction of the shelf life is made in consideration of the damage;
- (c)
- The average order quantity of each single product is greater than 2.5 kg;
- (d)
- The total gain is maximized.

## 2. Related Models

#### 2.1. Model 1: SVR Model

#### 2.2. Model 2: Long Short-Term Memory (LSTM) Model

#### 2.3. Model 3: Time Series (ARIMA)

## 3. Results

#### 3.1. Data Processing

_{ij}represents the Euclidean distance. W represents the weight. D represents the square distance from the current coordinates. T represents the total number of axes, and P represents the number of current axes.

#### 3.2. Model 1—Solving Process

- (a)
- In the SVR model, the loss is calculated if and only if the absolute value of the difference between and f(x) and y is greater than ε, whereas in the general linear model, the loss is calculated as long as f(x) and y are not equal.
- (b)
- The optimization methods of the two models are different. In the SVR model, the model is optimized by maximizing the width of the spaced band and minimizing the loss, while in the general linear regression model, the model is optimized by the average value after gradient descent.

#### 3.3. Model 2—Solving Process

^{.}

#### 3.4. Model 3—Solving Process

#### 3.5. Final Results

- Understanding the distribution: The histogram can clearly show the distribution of the average revenue of each item. By looking at the shape of the histogram, it is possible to understand the concentrated trend in the average return, the extent of the dispersion, and whether there are outliers.
- Identifying the median and mean: The central trend in the histogram can help identify the mean and median. This can be very helpful in understanding overall trends and evaluating the performance of the product portfolio.
- Outliers found: The tail of the histogram (long tail or short tail) may indicate the presence of outliers. Outliers can be extreme positive or negative gains, and with histograms; these extremes can be more easily identified.
- Comparing different items: In case of a histogram of multiple items, one can conveniently compare the average revenue distribution between the items. This can help find the best- or worst-performing pieces, as well as understand the differences between different pieces.

- (a)
- Market demand, which mainly includes the market demand for individual products;
- (b)
- Consumer feedback and evaluation data;
- (c)
- Supply chain data, including seasonal items, transportation time, delivery costs, etc.;
- (d)
- Loss data, which includes items that may have been discounted but not sold.

#### 3.6. Advantages of the Model

- (1)
- The model does not add too many prior assumptions to the original data, nor does it add or delete too many factors to the original data after thorough data preprocessing and outlier detection and confirmation. This ensures the diversity and authenticity of the data, so that deeper features can be obtained from the data and the accuracy of subsequent tasks can be guaranteed.
- (2)
- The model does not rely on artificial feature engineering, which ensures the transferability and robustness of the model.
- (3)
- The model abandons the linear fitting scheme such as least squares. Instead, it seeks a fitting model based on machine learning, which can obtain better results in nonlinear cases.
- (4)
- The model optimizes the backpack problem through the greedy strategy and obtains a quantitative category replenishment volume and pricing strategy, which appropriately fulfills the requirements.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 13.**The relationship between the total sales volume of each category and the cost-plus pricing.

**Figure 14.**SVR non-parametric regression fitting of each category’s data. (Blue scatters: These scatters represent the raw data of the first set of data; Orange scatters: These scatters represent data predicted using the support vector regression model).

Category | Correlation Coefficient |
---|---|

Aquatic rhizomes | −0.198 |

Flowers and leaves | 0.185 |

Broccoli | 0.136 |

Eggplant | 0.057 |

Peppers | 0.272 |

Edible fungi | −0.090 |

Date | Numeric Value |
---|---|

1 July | 0.175 |

2 July | 0.127 |

3 July | 0.110 |

4 July | 0.130 |

5 July | 0.143 |

6 July | 0.159 |

7 July | 0.155 |

The Expected Sales Volume | The Markup Rate |
---|---|

<20 kg | 150% |

<50 kg | 130% |

Else | 120% |

Category | Cost |
---|---|

Aquatic rhizomes | 11.22 yuan |

Flowers and leaves | 5.44 yuan |

Broccoli | 7.57 yuan |

Eggplant | 5.17 yuan |

Peppers | 7.61 yuan |

Edible fungi | 7.20 yuan |

Date | Flowers and Leaves | Broccoli | Aquatic Rhizome Species | Eggplant | Peppers | Edible Fungi |
---|---|---|---|---|---|---|

1 July | 152.9374 | 19.79373 | 20.42285 | 23.27763 | 95.03952 | 54.13958 |

2 July | 110.9889 | 14.36459 | 14.82115 | 16.89291 | 68.97154 | 39.28986 |

3 July | 96.13208 | 12.44177 | 12.83722 | 14.63165 | 59.73913 | 34.03059 |

4 July | 113.6106 | 14.70391 | 15.17126 | 17.29195 | 70.60079 | 40.21979 |

5 July | 124.9717 | 16.1743 | 16.68839 | 19.02115 | 77.66087 | 44.23977 |

6 July | 138.9546 | 17.98401 | 18.55562 | 21.14939 | 86.3502 | 49.18967 |

7 July | 135.4588 | 17.53159 | 18.08881 | 20.61733 | 84.17786 | 47.9522 |

Date | Flowers and Leaves | Broccoli | Aquatic Rhizome Species | Eggplant | Peppers | Edible Fungi |
---|---|---|---|---|---|---|

1 July | 0.641624 | 0.48805 | 0.491309 | 0.573781 | 0.64409 | 0.584361 |

2 July | 0.64675 | 0.512502 | 0.524329 | 0.573377 | 0.60185 | 0.598898 |

3 July | 0.629628 | 0.522525 | 0.537349 | 0.576475 | 0.596621 | 0.598996 |

4 July | 0.645114 | 0.510706 | 0.522049 | 0.572993 | 0.602605 | 0.598604 |

5 July | 0.64025 | 0.503097 | 0.512382 | 0.571804 | 0.607352 | 0.596339 |

6 July | 0.638909 | 0.494664 | 0.501243 | 0.571689 | 0.620462 | 0.591398 |

7 July | 0.638808 | 0.496633 | 0.503928 | 0.57154 | 0.616203 | 0.592846 |

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**MDPI and ACS Style**

Gu, A.; Yan, Z.; Zhang, X.; Xiang, Y.
Research on the Modeling of Automatic Pricing and Replenishment Strategies for Perishable Goods with Time-Varying Deterioration Rates. *Axioms* **2024**, *13*, 62.
https://doi.org/10.3390/axioms13010062

**AMA Style**

Gu A, Yan Z, Zhang X, Xiang Y.
Research on the Modeling of Automatic Pricing and Replenishment Strategies for Perishable Goods with Time-Varying Deterioration Rates. *Axioms*. 2024; 13(1):62.
https://doi.org/10.3390/axioms13010062

**Chicago/Turabian Style**

Gu, Aihua, Zhongzhen Yan, Xixi Zhang, and Yongsheng Xiang.
2024. "Research on the Modeling of Automatic Pricing and Replenishment Strategies for Perishable Goods with Time-Varying Deterioration Rates" *Axioms* 13, no. 1: 62.
https://doi.org/10.3390/axioms13010062