# An Approximation Algorithm for a Task Allocation, Sequencing and Scheduling Problem involving a Human-Robot Team

## TL;DR

This paper introduces an approximation algorithm for optimizing task allocation, sequencing, and scheduling in human-robot teams, with proven performance bounds and computational validation.

## Contribution

It provides a novel approximation algorithm with specific ratios for human-robot task scheduling, addressing a complex combinatorial problem.

## Key findings

- Approximation ratios depend on team composition (humans and robots).
- Algorithm performance validated through computational experiments.
- Provides bounds for different team configurations.

## Abstract

This article presents an approximation algorithm for a task allocation, sequencing and scheduling problem involving a team of human operators and robots. Specifically, we present an algorithm with an approximation ratio as a function of the number of human operators ($m$) and the number of robots ($k$) in the team. The approximation ratios are $\frac{7}{2} -\frac{5}{2k}$, $\frac{5}{2} -\frac{1}{k}$ and $\frac{7}{2} -\frac{1}{k}$ when $m=1$, $m\geq k\geq 2$ and $k>m\geq 2$ respectively. We also present computational results to corroborate the performance of the proposed approximation algorithm.