A Hybrid Analytical, Numerical, and Machine Learning Framework for Health Management, Resource Allocation, Operational Efficiency, Risk Forecasting, and Strategic Decision-Making in Nepal

Abstract

We consider the problem of optimal health resource allocation in a setting where disease dynamics are governed by compartmental epidemiological models, demand is predicted by black-box machine learning forecasts, and resource deployment is constrained by geography, budget, and infrastructure fragility. This problem arises concretely in Nepal, where mountainous topography, climate-sensitive disease outbreaks, and decentralized governance create a decision environment too complex for siloed methodologies [1,2,3]. We pose the following question: Given that disease dynamics follow SEIR processes, demand is predicted by non-linear ML models, and resources are constrained by road networks and budget, what is the optimal allocation policy, and can we bound its suboptimality?
We formalize this as a coupled SEIR-MILP stochastic program and prove that the general problem is NP-hard (Theorem 1). We then develop the Sequential Decomposition with Learning-Based Oracles (SD-LO) algorithm, which iterates between (i) maximum-likelihood estimation of epidemiological parameters, (ii) training of a Temporal Fusion Transformer with an epidemiologically structured loss, and (iii) Benders decomposition of a distributionally robust MILP whose right-hand side is informed by the ML oracle. We prove that if the ML predictor is Lipschitz continuous with bounded error , the optimality gap of the coupled system is where T is the planning horizon (Theorem 2), and that SD-LO converges to a local optimum of the coupled problem (Theorem 3).
We validate the framework on a computational study designed around Nepal’s 77-district health system, using DHIS2 epidemiological records (2015–2024), NASA POWER climate rasters, OpenStreetMap road networks, and Logistics Management Information System (LMIS) pharmaceutical flow data. On held-out 2023–2024 test data, SD-LO achieves a 12.7% MAPE on dengue forecasting (vs. 24.1% for ARIMA and 15.3% for pure ML without epidemiological structure), reduces pharmaceutical stock-out rates from 12.3% to 4.1%, and yields a 31% cost reduction over heuristic allocation. An ablation study demonstrates that removing the epidemiological layer increases DALYs lost by +180, removing the OR layer by +520, and removing the ML layer by +340. The full MILP with 12,000 variables solves in 4.3 seconds using Gurobi 10.0; the SD-LO outer loop converges in 18 iterations (average 2.1 minutes per iteration).