Approximation algorithms for Job Scheduling with reconfigurable resources

TL;DR

This paper addresses the MultiBot scheduling problem with reconfigurable resources, proposing a greedy approximation algorithm that guarantees a solution within 4/3 of the optimal, relevant for reconfigurable robot applications.

Contribution

It introduces the MultiBot problem, proves its NP-hardness, and provides a greedy approximation algorithm with a 4/3 ratio for resource-efficient scheduling.

Findings

The MultiBot problem is strongly NP-hard.

A greedy algorithm achieves a 4/3 approximation ratio.

The approach offers practical solutions for reconfigurable robot scheduling.

Abstract

We consider here the MultiBot problem for the scheduling and the resource parametrization of jobs related to the production or the transportation of different products inside a given time horizon. Those jobs must meet known in advance demands. The time horizon is divided into several discrete identical periods representing each the time needed to proceed a job. The objective is to find a parametrization and a schedule for the jobs in such a way they require as less resources as possible. Though this problem derived from the applicative context of reconfigurable robots, we focus here on fundamental issues. We show that the resulting strongly NP-hard Multibot problem may be handled in a greedy way with an approximation ratio of $\frac{4}{3}$.