Measure-theoretic decision optimization for uncertainty-aware resource planning in industrial systems

Abstract

In terms of large-scale industrial resource management, various factors have been shown to affect performance, including changes in market demand, disruptions in supply chains, and energy distribution. These circumstances cannot be captured completely using conventional finite-scenario appraisals because there is no scenario tree that can guarantee performance with respect to probability distributions that occur outside of sampled scenarios. Thus, model applications are limited follow a measure-theoretic and use the concept of Radon probability measures, which allows one to represent operational uncertainties as well as those of the environment in case of the need to. Consequently, the resource allocation model becomes much more efficient, as well as infinitely dimensional and managed with measures. The performance of the program is attained via the minimax approach. The use of mass-transport duality makes it easy to transform the worst-case expected revenue value into the convex problem. In addition, its efficiency is supported by the application of generalized Karush-Kuhn-Tucker conditions that have been derived directly from the theory of measures. The boundedness of multipliers has been justified, as well. Finally, the methods of empirical moment-matching atomic measures and projected-gradient minimax interior-point are very promising, making it possible for the program to become less complicated in terms of numerical validation.