Risk averse single machine scheduling - complexity and approximation

TL;DR

This paper investigates the complexity and approximation of single machine scheduling problems under uncertainty, using risk measures like VaR and CVaR, and provides new and strengthened complexity results.

Contribution

It introduces new complexity results for risk-averse scheduling problems and enhances existing complexity findings in the context of uncertain processing times and due dates.

Findings

New complexity results for risk-averse scheduling problems

Strengthened existing complexity results

Analysis of scheduling under uncertainty with risk criteria

Abstract

In this paper a class of single machine scheduling problems is considered. It is assumed that job processing times and due dates can be uncertain and they are specified in the form of discrete scenario set. A probability distribution in the scenario set is known. In order to choose a schedule some risk criteria such as the value at risk (VaR) an conditional value at risk (CVaR) are used. Various positive and negative complexity results are provided for basic single machine scheduling problems. In this paper new complexity results are shown and some known complexity results are strengthen.