S M Nazmuz Sakib Hydro-Weighted Distributionally Robust Supply Chains for Water-Scarce Regions: The Sakib Principle, Sakib Number, Sakib Frontier and Sakib Constant

We propose a guardian framework for designing and operating water-scarce supply chains that (i) scales distributional robustness by geospatial water stress (Aqueduct 4.0), (ii) routs flows via entropic optimal transport with basin water budgets (Sinkhorn), and (iii) embeds queue-aware water metrics at processors. Within this framework we formalize the S M Nazmuz Sakib Hydro-Robustness Principle (Sakib Principle) and three decision primitives: the Sakib Number δ ⋆ (the knee of the hydro-robustness frontier), the Sakib Frontier (cost-water trade-off curve under hydro-weighted robustness), and the Sakib Constant κ S (frontier curvature at δ ⋆). The framework is intended for calibration with external datasets-WRI Aqueduct (baseline water stress), WaterStat/Water Footprint data for products and countries, USDA NASS (IWMS 2023), and EPA ECHO (U.S. facilities)-to ensure transparency and replicability. We detail computational formulations (KL-DRO duals, Sinkhorn routing), an empirical protocol (joins, ablations, cross-region tests), and diagnostics (WCR, HRFC, WAU) to guide robust water-aware decisions.