A nonlinear optimization and simulation framework for sustainable waqf allocation across Makkah, Madinah, and Qassim under Saudi vision 2030

Abstract

Abstract Waqf (Islamic endowment) is a vital socioeconomic instrument whose contemporary effectiveness depends on efficient, transparent, and mathematically grounded and optimization-consistent management. Aligned with Saudi Vision 2030, this study develops a nonlinear welfare optimization and stochastic simulation framework for sustainable Waqf allocation across Makkah, Madinah, and Qassim in the sectors of education, healthcare, and housing. The model formulates a strictly concave logarithmic social welfare function subject to affine feasibility constraints, ensuring global optimality and uniqueness of the solution under Karush–Kuhn–Tucker (KKT) conditions. Regional allocations are endogenously optimized, while sectoral distributions follow normalized policy-determined priority weights reflecting institutional development objectives. MATLAB-based analyses integrate deterministic nonlinear optimization, sector-weight sensitivity testing, and truncated Monte Carlo stochastic perturbations to evaluate robustness under funding uncertainty. A dynamic 2025–2035 demographic simulation incorporates the closed-form population growth model to ensure intertemporal allocation consistency. By integrating Cash Waqf Linked Sukuk mechanisms, digital governance platforms, and KPI-based performance monitoring, the framework enhances social welfare, regional equity, and financial transparency. The proposed model provides policymakers with a reproducible, globally optimal, and risk-aware decision-support system for sustainable Islamic endowment management.