β - Robust Parallel Machine Scheduling with Uncertain Durations

Abstract

Uncertainty is a main characteristic of many real-world scheduling problems, and scheduling solutions should be robust against changes. In this paper, we consider parallel machines that the processing time of each task follows a normal distribution and total completion times as main optimization criterion. We propose a mixed-integer nonlinear programming (MINLP) model to minimize the risk of the completion time exceeding a fixed value. The objective is to find a β-robust schedule. Additionally, we use a proper approximation to convert the MINLP model to an integer programming one. The computational results on a small example are presented to demonstrate the effectiveness of the proposed approach. Furthermore, we compare and analyze the associated results of these models. Finally, the conclusion is provided.