Integrating Public Transport in Sustainable Last-mile Delivery: Column Generation Approaches

This repository contains the instances and the solutions presented in the following paper:

@article{delle_donne_et_al,
    title={Integrating Public Transport in Sustainable Last-mile Delivery: Column Generation Approaches},
    author={{Delle Donne}, Diego and Santini, Alberto and Archetti, Claudia},
    year=2025,
    doi={10.1016/j.ejor.2024.12.047},
    url={https://www.sciencedirect.com/science/article/pii/S0377221724009901}
}

You can also cite this repository through Zenodo:

@misc{delle_donne_et_al_instances,
    title={{Instances and Results for the Paper ``Integrating Public Transport in Sustainable Last-mile Delivery: Column Generation Approaches''}},
    author={{Delle Donne}, Diego and Santini, Alberto and Archetti, Claudia},
    year=2024,
    doi={10.5281/zenodo.10493847},
    url={https://github.com/alberto-santini/public-transport-lmd}
}

Datasets

The repository contains two datasets:

• Instances in folder mandal_and_archetti are from the following paper and are used for comparison with the method proposed by the paper's authors.

@misc{mandal_archetti,
    title={A Decomposition Approach to Last Mile Delivery Using Public Transportation Systems}, 
    author={Minakshi Punam Mandal and Claudia Archetti},
    year={2023},
    eprint={2306.04219},
    archivePrefix={arXiv},
    primaryClass={math.OC}
}

• Instances in folder delle_donne_et_al were generated specifically for our paper. We used them as a testbed for our algorithms and to test the effectiveness of the approaches we proposed.

Results

Results are provided in the .csv format. File delle_donne_instances.csv constains the results for the instances of folder delle_donne_et_al. File mandal_instances.csv contains the results for the instances of folder mandal_et_archetti.

Instance format

Each instance is described by three files.

The .city file

The .city file describes the characteristics of stops, customers, and transit lines.

Stops

Lines starting with S describe stops. Each line describes a stop, and contains:

• The name (field name).
• The capacity (field capS).
• Field capI can be ignored.
• Field capO can be ignored.
• Field cost can be ignored.
• The x coordinate (field x).
• The y coordinate (field y).
• The service time (field Ts).
• The maximum wait time of a parcel (field Wmax).

Consolidation and Distribution Centre

Lines starting with O describe the Consolidation and Distribution Centre (CDC). In our instances, there is only one CDC, and it is decribed by:

• Its name (field name).
• Its x coordinate (field x).
• Its y coordinate (field y).

The line following the CDC description lists all stops that can be reached from it. By definition, these are the in-stops; all other stops are out-stops.

Customers

Lines starting with D describe customers. Each customer has the following associated fields:

• The name (field name).
• The x coordinate (field x).
• Its y coordinate (field y).

The line following each customer description lists which out-stops can be used to serve the customer.

Public Transport Lines

Lines starting with F describe public transport lines. Each public transport line is described by the following data:

• The name (field name).
• The fleet name (field fleetname). It can be ignored.
• The vehicle capacity (field cap).
• Field cost can be ignored.
• The time when the first vehicle of the line reaches the first stop in its sequence (field first_bus).
• The interval between two consecutive buses of the line (field frequency).
• The number of daily runs (field nBuses).

The line following each public transport line's description is the sequence of visited stops. To compute the bus arrival times at the stops, consider a speed equal to 0.2 times the euclidean distance between successive stops.

The .demands file

The .demands file gives further informations about the clients. The first field of each line is the customer's name; the second is the customer's demand; the third and fourth field are the start and end time of the customer's time window.

The .params file

The .params file contains other instance information. Field Lmax is the maximum duration of a courier's route. Field maxTrucks is the truck fleet size. Field maxFreightersPerStop is the number of couriers available at each out-stop. Field trucksCap is the truck's capacity. Field freighterCap is the courier's capacity.