Investigating the Recoverable Robust Single Machine Scheduling Problem Under Interval Uncertainty

TL;DR

This paper studies a robust scheduling problem for a single machine under interval uncertainty, proposing complexity results, an approximation algorithm, and computational experiments to evaluate different solution approaches.

Contribution

It introduces a 2-approximation algorithm and analyzes complexity for special cases of the recoverable robust single machine scheduling problem.

Findings

The approximation algorithm achieves a 2-approximation ratio.

The mixed-integer programming formulation performs well in experiments.

The greedy heuristic is computationally efficient and effective.

Abstract

We investigate the recoverable robust single machine scheduling problem under interval uncertainty. In this setting, jobs have first-stage processing times p and second-stage processing times q and we aim to find a first-stage and second-stage schedule with a minimum combined sum of completion times, such that at least Delta jobs share the same position in both schedules. We provide positive complexity results for some important special cases of this problem, as well as derive a 2-approximation algorithm to the full problem. Computational experiments examine the performance of an exact mixed-integer programming formulation and the approximation algorithm, and demonstrate the strength of a proposed polynomial time greedy heuristic.