# Joint Inventory Replenishment Planning of an E-Commerce Distribution System with Distribution Centers at Producers’ Locations

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}emission released by transportation. The joint replenishments of multiple products are constrained by a maximum joint replenishment quantity. Trans-shipments happen among different distribution centers. The considered problem seeks to find the replenishment quantities of products among stocks, which can minimize the total replenishment cost of the system, and is formulated as a novel mathematical model. The effectiveness of our proposed model is validated by computational experiments based on Alibaba’s data. The results indicate that PDCs and trans-shipments can bring about lower replenishment costs if a common service level of the system is given.

## 1. Introduction

- The joint replenishment of products with distribution centers at the producers’ locations for a three-echelon distribution system is studied.
- Each replenishment is constrained by a maximum joint replenishment quantity.
- Horizontal and vertical replenishments of products are allowed for each stock.

_{2}emissions.

## 2. Problem Description

## 3. Models and Analysis

#### 3.1. Models

**Indices**

**Main Parameters**

_{t}: target common service level of the inventory system, $0\le {\alpha}_{t}\le 1$

_{t}

**Variables**

_{2}emissions are also reduced. This will contribute to the distribution process of the CE concept.

_{t}may not always be achieved. In order to always achieve α

_{t}, we can define the following parameter $s{c}_{ij}^{e}$ and the decision variable ${q}_{ij}^{}$, and replace constraint (6) with constraint (10). If the sum of the required replenishment quantities of all products is larger than the maximum joint replenishment quantity, ${q}_{ij}^{}\ge 0$. Thus, all ${q}_{ij}^{}$ must be finished using external freight capacity, where a greater replenishment cost must be paid. Then, objective function (1) can be revised to Equation (11).

#### 3.2. Analysis

## 4. Results

_{t}is set to 92% (Case 1), 95% (Case 2), and 98% (Case 3). The corresponding ${z}_{{\alpha}_{t}}$ is set to 1.41 (Case 1), 1.65 (Case 2), and 2.06 (Case 3), respectively. Furthermore, there are fifteen stocks that include four suppliers, one PDC, four CDCs, and six FDCs in the distribution system, where four products are replenished.

_{2}emissions and the wastages of commodities.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**A three-echelon distribution system of Alibaba. CDC, central distribution center; FDC, front distribution center.

**Figure 3.**A multiple-echelon distribution system with producers’ distribution center (PDC) in Alibaba.

**Figure 8.**Total replenishment cost reduction percentage of the system by adding horizontal replenishment.

**Figure 9.**Total replenishment cost reduction percentage of the system by increasing the maximum joint replenishment quantities.

Cost | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

CWP | 36,932.1 | 36,438.9 | 38,743.4 | 36,687 | 36,694.8 | 38,981.4 | 38,405.2 | 37,720.3 | 39,171.6 | 36,551.8 |

CNP | 47,488.2 | 46,279.3 | 47,337.7 | 44,500.3 | 45,612.4 | 48,169 | 47,169.6 | 49,363.6 | 48,132.6 | 44,959.1 |

CRP | 22.2% | 21.3% | 18.2% | 17.6% | 19.6% | 19.1% | 18.6% | 23.6% | 18.6% | 18.7% |

Cost | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

CWP | 40,171.2 | 39,868 | 41,947.5 | 40,177.8 | 39,944.6 | 42,756.5 | 42,120.1 | 41,385.9 | 42,933.6 | 40,458.6 |

CNP | 52,539.5 | 51,436.3 | 51,884.2 | 49,376.5 | 50,592 | 53,740.9 | 52,634.3 | 55,105.8 | 53,614.9 | 50,808.2 |

CRP | 23.5% | 22.5% | 19.2% | 18.6% | 21% | 20.4% | 20% | 24.9% | 19.9% | 20.4% |

Cost | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

CWP | 46,143 | 46,255.7 | 48,003.3 | 46,669.3 | 42,999.3 | 49,850.3 | 48,983.6 | 48,274.1 | 50,156.5 | 47,779.5 |

CNP | 61,841.9 | 61,126.8 | 60,545.1 | 58,576.4 | 59,750.3 | 64,237.2 | 62,942.1 | 65,762 | 64,448.9 | 61,811.9 |

CRP | 25.4% | 24.3% | 20.7% | 20.3% | 28% | 22.4% | 22.2% | 26.6% | 22.2% | 22.7% |

Cost | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

CWH | 16,693.5 | 20,031.4 | 6824.78 | 5929 | 12,192.4 | 17,757.1 | 12,449.3 | 8698.53 | 12,497.5 | 3816.82 |

CNH | 19,380.2 | 21,781.6 | 9928.04 | 8492.26 | 16,383.1 | 20,753.5 | 15,644.3 | 12,099.8 | 16,682.9 | 7135.07 |

CRH | 13.9% | 8% | 31.3% | 30.2% | 25.6% | 14.4% | 20.4% | 28.1% | 25.1% | 46.5% |

Cost | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

CWH | 18,465.2 | 22,007.6 | 7222.13 | 6636.09 | 13,622.1 | 19,720.1 | 13,876.2 | 9931.27 | 14,125.2 | 4397.65 |

CNH | 21,119.6 | 23,742.4 | 10,646.3 | 9322.92 | 17,788.7 | 22,697 | 17,110.5 | 13,337.3 | 18,270.5 | 8018.24 |

CRH | 12.6% | 7.3% | 32.2% | 28.8% | 23.4% | 13.1% | 18.9% | 25.5% | 22.7% | 45.2% |

Cost | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

CWH | 21,504.6 | 25,420.5 | 7957.23 | 7865.67 | 16,074.5 | 23,095.5 | 16,320.2 | 12,119.2 | 16,913.7 | 5818 |

CNH | 24,118.3 | 27,157.6 | 11,879.3 | 10,766.3 | 20,190.3 | 26,021 | 19,625.1 | 15,454.3 | 20,986.8 | 9542.25 |

CRH | 10.8% | 6.4% | 33% | 26.9% | 20.4% | 11.2% | 16.8% | 21.6% | 19.4% | 39% |

Cost | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

MR1 | 36,421.6 | 35,687.7 | 37,834.3 | 35,792.5 | 36,111.8 | 37,972.8 | 37,521.1 | 36,871 | 38,592.4 | 35,933.4 |

MR2 | 35,294.6 | 34,505.8 | 35,504.4 | 34,595.3 | 34,662.5 | 36,114.6 | 35,738.5 | 35,438.4 | 36,866.6 | 34,859.5 |

MR3 | 34,796 | 34,198.4 | 34,961.8 | 34,252 | 34,502.2 | 35,891.8 | 35,347.4 | 34,995.1 | 36,183.1 | 34,358 |

CRM | 4.5% | 4.2% | 7.6% | 4.3% | 4.5% | 5.5% | 5.8% | 5.1% | 6.2% | 4.4% |

Cost | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

MR1 | 39,639.7 | 38,911.5 | 41,035.3 | 39,091.4 | 39,298.9 | 41,742.1 | 41,207.7 | 40,534.7 | 42,306.3 | 39,603.5 |

MR2 | 38,141.6 | 37,344.7 | 38,381.7 | 37,419.7 | 37,632.2 | 39,304.4 | 38,976.3 | 38,603.5 | 40,408.6 | 38,196 |

MR3 | 37,543.8 | 37,003.1 | 37,568.1 | 37,074.2 | 37,273.7 | 39,000.3 | 38,439.7 | 37,975.1 | 39,525.8 | 37,658.7 |

CRM | 5.3% | 4.9% | 8.4% | 5.2% | 5.2% | 6.6% | 6.7% | 6.3% | 6.6% | 4.9% |

Cost | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

MR1 | 45,165.2 | 44,773.4 | 46,510 | 45,052.3 | 44,849.2 | 48,209.7 | 47,556.2 | 46,844.2 | 48,729.4 | 46,280.2 |

MR2 | 43,365.9 | 42,222.7 | 43,325.6 | 42,247.3 | 42,793 | 44,798.1 | 44,526.5 | 44,045.7 | 46,486.9 | 43,935.5 |

MR3 | 42,308.9 | 41,811.2 | 42,033 | 41,896.8 | 42,119.2 | 44,353.2 | 43,745.4 | 43,142.1 | 45,314.7 | 43,287.9 |

CRM | 6.3% | 6.6% | 9.6% | 7% | 6.1% | 8% | 8% | 7.9% | 7% | 6.5% |

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**MDPI and ACS Style**

Dai, B.; Li, F.
Joint Inventory Replenishment Planning of an E-Commerce Distribution System with Distribution Centers at Producers’ Locations. *Logistics* **2021**, *5*, 45.
https://doi.org/10.3390/logistics5030045

**AMA Style**

Dai B, Li F.
Joint Inventory Replenishment Planning of an E-Commerce Distribution System with Distribution Centers at Producers’ Locations. *Logistics*. 2021; 5(3):45.
https://doi.org/10.3390/logistics5030045

**Chicago/Turabian Style**

Dai, Bo, and Fenfen Li.
2021. "Joint Inventory Replenishment Planning of an E-Commerce Distribution System with Distribution Centers at Producers’ Locations" *Logistics* 5, no. 3: 45.
https://doi.org/10.3390/logistics5030045