Two Multivehicle Routing Problems with Unit-Time Windows

TL;DR

This paper introduces approximation algorithms for two multivehicle routing problems with uniform time windows, focusing on maximizing visited locations and minimizing vehicles used, with proven approximation guarantees.

Contribution

It presents novel approximation algorithms for two related multivehicle routing problems with unit-time windows, including a constant-factor approximation for the first and a 6-approximation for the second on tree metrics.

Findings

Approximation algorithm achieves a constant factor for maximizing visits.

A 6-approximation algorithm is provided for minimizing vehicles on tree metrics.

Algorithms work under the assumption of uniform time windows.

Abstract

Two multivehicle routing problems are considered in the framework that a visit to a location must take place during a specific time window in order to be counted and all time windows are the same length. In the first problem, the goal is to visit as many locations as possible using a fixed number of vehicles. In the second, the goal is to visit all locations using the smallest number of vehicles possible. For the first problem, we present an approximation algorithm whose output path collects a reward within a constant factor of optimal for any fixed number of vehicles. For the second problem, our algorithm finds a 6-approximation to the problem on a tree metric, whenever a single vehicle could visit all locations during their time windows.