Reducing the Impact of Bounded Parametric Uncertainty on Hodgson's Scheduling Algorithm Using Interval Programming

Abstract

Input uncertainty is a major challenge to the decision-making process as it leads to output inaccuracy, which increases the cost and the risk. Bounded uncertainty is usually formulated as mathematical intervals as it provides the upper bound and the lower bound without any information between them such as probability distribution or membership function. The lack of descriptive function between the upper and lower bounds makes the probabilistic and fuzzy techniques not effective. This research aims to reduce the impact of bounded uncertainty on the final result of the scheduling objective function and algorithm. The premise of this research is that performing the calculations using uncertain values and then approximating the final result produces more accurate results than approximating the uncertain input values before performing the calculations. The proposed methodology was to extend the scheduling algorithm to be interval based through extending numerical arithmetic to interval arithmetic and extending Boolean logic to interval logic. The methodology is applied to Hodgson's scheduling algorithm, which is used to minimize the number of delayed tasks. The solution is implemented using a MATLAB toolbox named TORSCHE by slicing its code and extending it. The experiments used the aircraft landing data with bounded uncertainty, and it enhanced the accuracy of the results by 12% than using the averaging or midpoint approximation.