# A Sustainable Two-Echelon Logistics Model with Shipment Consolidation

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## Abstract

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## 1. Introduction

## 2. Literature Review

#### 2.1. Multi-Product Pickup and Delivery with Location-Routing and Direct Shipment vs. Shipment Consolidation

#### 2.2. Sustainable Models

#### 2.3. Research Questions and Contribution

**RQ1:**How can all the possible vehicle capacity be utilised in last mile distribution in order to reduce the number of dispatched vehicles, and the on-road time of the vehicles?**RQ2:**How can the emissions and pollutants produced by the vehicles be reduced?

## 3. Problem Statement and Mathematical Model

#### 3.1. Problem Statement and Network Description

#### 3.2. Model Assumptions

- Each node must belong to one of the following sets: distribution centre node, pickup node (Supplier), or delivery node (End user) [11].
- All the requests for the delivery must be satisfied by either direct shipments or transportation from distribution centres.
- There is a limit on the capacity of the products for each supplier.
- All distribution centres must be provided by vehicles to be able to perform any transportation processes.
- For the delivery and pick up, a fleet of homogeneous vehicles must perform all the delivery processes.
- After finishing each delivery, all the vehicles that are responsible for either pick up or delivery must return to the distribution centre.
- Vehicles can visit pick up nodes more than one time, but delivery nodes are not allowed to be visited more than one time.

#### 3.3. Linear Programming Transportation Model

#### 3.4. Distribution Centre Locations

#### 3.5. Cost Analysis

## 4. Case Study and Results

#### 4.1. The Consolidated Model

#### 4.2. The Non-Consolidated Model

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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DC | Plant 1 | Plant 2 | |
---|---|---|---|

DC 1 | Demanded quantity per week | 4500 cartons | 1500 cartons |

Relative location | 65 Km N. West | 63.37 Km S. East | |

DC 2 | Demanded quantity per week | 1000 cartons | 2000 cartons |

Relative location | 65 Km N. West | 63.37 Km S. East | |

DC 3 | Demanded quantity per week | 1500 cartons | 1500 cartons |

Relative location | 65 Km N. West | 63.37 Km S. East |

DC | Plant 1 | Plant 2 |
---|---|---|

DC 1 | 125 | 49.6 |

DC 2 | 79 | 89.5 |

DC 3 | 106 | 74.3 |

DC | DP1 | DP2 | DP3 | DP4 | DP5 | DP6 | DP7 |
---|---|---|---|---|---|---|---|

DC 1 | 177 | 165 | 165 | - | - | - | - |

DC 2 | - | - | - | 103 | 95.1 | - | - |

DC 3 | - | - | - | - | - | 124 | 119 |

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**MDPI and ACS Style**

Mostafa, N.A.; Eldebaiky, O.
A Sustainable Two-Echelon Logistics Model with Shipment Consolidation. *Logistics* **2023**, *7*, 18.
https://doi.org/10.3390/logistics7010018

**AMA Style**

Mostafa NA, Eldebaiky O.
A Sustainable Two-Echelon Logistics Model with Shipment Consolidation. *Logistics*. 2023; 7(1):18.
https://doi.org/10.3390/logistics7010018

**Chicago/Turabian Style**

Mostafa, Noha A., and Omar Eldebaiky.
2023. "A Sustainable Two-Echelon Logistics Model with Shipment Consolidation" *Logistics* 7, no. 1: 18.
https://doi.org/10.3390/logistics7010018