# An analytical bound on the fleet size in vehicle routing problems: a dynamic programming approach

arXiv: https://arxiv.org/abs/1905.05557 · HTML: https://mlsanity.com/paper/1905.05557/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2019.

## Built on by (most cited first, 1 of 1)

- [Learn to Solve Vehicle Routing Problems ASAP: A Neural Optimization Approach for Time-Constrained Vehicle Routing Problems with Finite Vehicle Fleet](https://mlsanity.com/paper/2411.04777/) (2024)

## Abstract (arXiv)

We present an analytical upper bound on the number of required vehicles for vehicle routing problems with split deliveries and any number of capacitated depots. We show that a fleet size greater than the proposed bound is not achievable based on a set of common assumptions. This property of the upper bound is proved through a dynamic programming approach. We also discuss the validity of the bound for a wide variety of routing problems with or without split deliveries.