The robust single machine scheduling problem with uncertain release and processing times

TL;DR

This paper addresses the challenge of creating robust schedules for a single machine with uncertain release and processing times, proposing heuristics to optimize total flow time under worst-case scenarios.

Contribution

It introduces a robust scheduling framework considering uncertainties in release and processing times, and develops heuristics to generate effective solutions.

Findings

Heuristics outperform baseline methods in robustness.

Robust schedules significantly reduce worst-case total flow time.

Complexity increases with non-zero release times.

Abstract

In this work, we study the single machine scheduling problem with uncertain release times and processing times of jobs. We adopt a robust scheduling approach, in which the measure of robustness to be minimized for a given sequence of jobs is the worst-case objective function value from the set of all possible realizations of release and processing times. The objective function value is the total flow time of all jobs. We discuss some important properties of robust schedules for zero and non-zero release times, and illustrate the added complexity in robust scheduling given non-zero release times. We propose heuristics based on variable neighborhood search and iterated local search to solve the problem and generate robust schedules. The algorithms are tested and their solution performance is compared with optimal solutions or lower bounds through numerical experiments based on synthetic data.