# Approximation results for makespan minimization with budgeted uncertainty

## TL;DR

This paper develops approximation algorithms for minimizing makespan under processing time uncertainty, providing an EPTAS for identical machines and bounds for unrelated machines.

## Contribution

It introduces an EPTAS for makespan minimization with uncertainty on identical machines and analyzes approximation bounds for unrelated machines.

## Key findings

- EPTAS achieved for identical machines
- 3-approximation algorithm for unrelated machines
- Inapproximability ratio of 2−ε for unrelated machines

## Abstract

We study approximation algorithms for the problem of minimizing the makespan on a set of machines with uncertainty on the processing times of jobs. In the model we consider, which goes back to~\cite{BertsimasS03}, once the schedule is defined an adversary can pick a scenario where deviation is added to some of the jobs' processing times. Given only the maximal cardinality of these jobs, and the magnitude of potential deviation for each job, the goal is to optimize the worst-case scenario. We consider both the cases of identical and unrelated machines. Our main result is an EPTAS for the case of identical machines. We also provide a $3$-approximation algorithm and an inapproximability ratio of $2-\epsilon$ for the case of unrelated machines