# Shared bikes distribution vehicle routing problem with split delivery considering carbon emission

## TL;DR

This paper studies how to efficiently deliver shared bikes while minimizing carbon emissions and delivery costs, using a model and algorithm tested in a real-world example.

## Contribution

A novel model and genetic algorithm for shared bike distribution with split deliveries and carbon emission considerations.

## Key findings

- The model minimizes total carbon emission and delivery costs under split deliveries and vehicle load limits.
- A genetic algorithm (GA) was developed with a proven time complexity and approximate ratio bounds.
- An empirical example in Xi’an showed the GA’s approximation ratio was 3.52, indicating good performance.

## Abstract

The distribution of shared bikes is different from that of other goods. There are some demand stations which need a large number of shared bikes, such as bus stations, subway exits and business districts. The demand of these stations cannot be met in a single delivery, so the demand can be split into batches for distribution. Therefore, shared bikes need to be delivered from distribution centers to demand stations. However, these delivery vehicles generate carbon emissions during the process, which has an impact on environment. Thus, shared bikes distribution vehicle route selection with considering carbon emission under demand splitting is an important problem. The paper established a model for distribution vehicle route selection of shared bikes considering carbon emission which aims at minimization the sum of carbon emission cost and delivery cost, under demand splitting of the stations and delivery vehicles with load limit. Then an approximation algorithm GA is designed to solve it. The time complexity of GA was proved, and the upper and lower bounds of the approximate ratio of GA are discussed. Finally, an empirical example was facilitated by examining real shared bikes stations in the Yanta district of Xi’an, China, to verify the effectiveness of the model and algorithm. The approximation ratio of GA is 3.52 which shows that the approximate performance of the algorithm in the example is good. The results and conclusions yield a theoretical basis for decision-makers to optimize the delivery of shared bikes.