On Solving Non-preemptive Mixed-criticality Match-up Scheduling Problem with Two and Three Criticality Levels

TL;DR

This paper addresses the NP-hard problem of scheduling mixed-criticality tasks with uncertain processing times on a single machine, proposing exact algorithms for two and three criticality levels and analyzing their approximability.

Contribution

It introduces efficient exact algorithms for two and three criticality levels in mixed-criticality scheduling and analyzes the problem's approximability.

Findings

Algorithms successfully solve instances with up to 200 tasks.

The problem is approximable within a constant factor.

Efficient solutions are derived from the structure of F-shaped tasks.

Abstract

In this paper, we study an NP-hard problem of a single machine scheduling minimizing the makespan, where the mixed-critical tasks with an uncertain processing time are scheduled. We show the derivation of F-shaped tasks from the probability distribution function of the processing time, then we study the structure of problems with two and three criticality levels for which we propose efficient exact algorithms and we present computational experiments for instances with up to 200 tasks. Moreover, we show that the considered problem is approximable within a constant multiplicative factor.