Single machine scheduling problems with uncertain parameters and the OWA criterion

TL;DR

This paper introduces a framework for solving single machine scheduling problems under uncertainty using the OWA criterion, which generalizes traditional decision-making criteria and accounts for decision makers' risk attitudes.

Contribution

It proposes a general approach for applying the OWA operator to single machine scheduling with uncertain parameters, extending robust scheduling methods.

Findings

Positive computational results for certain problem classes

Negative computational results indicating complexity issues

Framework accommodates various decision maker risk preferences

Abstract

In this paper a class of single machine scheduling problems is discussed. It is assumed that job parameters, such as processing times, due dates, or weights are uncertain and their values are specified in the form of a discrete scenario set. The Ordered Weighted Averaging (OWA) aggregation operator is used to choose an optimal schedule. The OWA operator generalizes traditional criteria in decision making under uncertainty, such as the maximum, average, median or Hurwicz criterion. It also allows us to extend the robust approach to scheduling by taking into account various attitudes of decision makers towards the risk. In this paper a general framework for solving single machine scheduling problems with the OWA criterion is proposed and some positive and negative computational results for two basic single machine scheduling problems are provided.