Single machine scheduling problems with uncertain parameters and the OWA criterion

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 used 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 a 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.