Extended Time Dependent Vehicle Routing Problem for Joint Task Allocation and Path Planning in Shared Space

Abstract

We address the joint task allocation and path planning problem whereby an operator with a fleet of vehicles must assign multiple tasks to each vehicle, while ensuring collision-free paths for them such that the total travel cost is minimized. Instead of sequentially solving the task allocation problem first, and then resolving all predicted collisions, i.e. conflicts between vehicles, we propose a novel method that solves in a simultaneous way task allocation and multi-agent path planning. Specifically, we introduce an extension of the Time Dependent Vehicle Routing Problem (TDVRP) whereby we propose to integrate conflicts information into a time dependent cost function used in the task allocation resolution. We compare our approach to two baseline approaches that both use a standard Capacitated VRP (CVRP) solver, a “one-shot” method and a “multi-shot” method. We perform simulations on benchmark realistic warehouse scenarios and the obtained results show that our proposed approach is able to generate improvements in the solutions costs compared to the baseline approaches.