Sensitivity and Stability Analysis for Resource Allocation under Stochastic Perturbations

Author(s)	Saksham Bhardwaj, Anirudha Anil Gaikwad, Nupur Garg, Hiten Chadha
Country	India
Abstract	Optimal resource allocation is sensitive to system parameters, however, in real-world settings, these parameters are affected by stochastic perturbations which leads to unpredictable fluctuations in allocation results. Current approaches either rely on deterministic assumptions or repeated optimization under uncertainty, making them computationally expensive and less practical. In this work, we develop a sensitivity and stability analysis framework for resource allocation by leveraging Karush-Kuhn-Tucker (KKT) conditions and the implicit function theorem. Our analysis shows that allocation deviations scale linearly with the magnitude of perturbation, while remaining bounded with high probability. Our proposed framework offers an efficient alternative for analyzing allocation robustness without repeatedly solving the optimization problem.
Keywords	Resource Allocation, Sensitivity Analysis, Stability Analysis, Stochastic Perturbations, KKT Conditions, Implicit Function Theorem, Convex Optimization, Probabilistic Bounds, Constraint Switching, Robust Optimization, Monte Carlo Simulation
Field	Computer > Data / Information
Published In	Volume 8, Issue 3, May-June 2026
Published On	2026-05-09

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