HessQ Bulletin 9 - Optimization for Hospitals and Health Systems

This bulletin presents a systems-level framework for optimizing hospital and health-system operations by treating clinical services, infrastructure, and administrative processes as tightly coupled operational systems. Rather than modeling departments as isolated workflows, hospitals are represented as interconnected units in which patient flow, energy usage, staffing capacity, and governance processes interact dynamically.

The proposed approach introduces a quantum-inspired, physics-motivated optimization architecture that integrates operational dynamics, queueing theory, and compressed state representations to support scalable decision-making across emergency departments, operating rooms, and intensive care units. Interdepartmental congestion and coordination effects are captured through a coupled flow--dissipation model of the form
\begin{equation}
\ddot{x}_i
=
- K\left(2x_i - x_{i-1} - x_{i+1}\right)
- \sum_{j} L_{ij}\,\dot{x}_j,
\end{equation}
where \(x_i(t)\) denotes a normalized congestion state for department \(i\), \(K\) represents capacity coupling, and \(L_{ij}\) encodes dissipative interactions between operational units.

Analytical queueing formulations are used to quantify waiting times, utilization, and capacity risk under variable demand, while the use of structured, low-complexity state representations enables rapid system-wide updates and forecasting. This unified framework supports simultaneous analysis of patient throughput, energy efficiency, staffing balance, audit integrity, and ESG-related performance indicators within a single decision-support layer.

The bulletin is intended for healthcare operators, public-sector decision-makers, and applied researchers seeking scalable, system-aware optimization strategies for modern hospital and health-system management.