Operations Research
Systems engineering and operations research provide the mathematical and analytical foundations for understanding how constrained service systems behave under pressure and how to redesign them using measurable tools.
Core principle: A system’s throughput is governed by its binding constraint, not by its average capacity. Most healthcare improvement efforts fail because they optimize non-binding resources.
Why This Matters Now
- Rural hospitals operating at negative margins cannot absorb inefficiency — every wasted hour of provider time or bed-day has direct financial consequences
- Workforce shortages make capacity optimization existential, not aspirational
- Grant-funded transformation programs require measurable operational improvement, not narrative progress reports
- Prior authorization and administrative burden consume clinical capacity that OR methods can quantify and reclaim
- AI decision-support tools are being deployed into workflows whose baseline performance characteristics are unmeasured
Modules
| Module | Focus | Pages |
|---|---|---|
| 1. Foundations | What OR is, systems as models, deterministic vs stochastic | 3 |
| 2. Queueing Theory | Wait-time dynamics, Little’s Law, utilization-delay curve | 4 |
| 3. Optimization | Constrained optimization, shadow prices, allocation | 3 |
| 4. Networks | Network flow, referral networks, critical path | 3 |
| 5. Scheduling | Appointment models, staff rostering, no-shows | 4 |
| 6. Simulation | DES, Monte Carlo, scenario stress testing | 4 |
| 7. Applications | ED flow, surgical scheduling, bed management, behavioral health, prior auth | 5 |
| 8. Product Synthesis | OR metrics for operators, capacity planning, embedding OR in product | 4 |
Integration Points
| This Module | Connects To | Nature of Connection |
|---|---|---|
| Queueing Theory | Human Factors: Fatigue | High utilization drives both long waits and clinician overload via the same nonlinear curve |
| Queueing Theory | Workforce: Capacity | Staffing levels set service rates; vacancy directly shifts the utilization-delay curve |
| Optimization | Public Finance: Financial Controls | Budget allocation under grant constraints is a constrained optimization problem |
| Networks | Human Factors: Error & Failure | Network handoffs are where human error concentrates; topology determines propagation |
| Scheduling | Human Factors: Fatigue | Shift design determines fatigue exposure; scheduling and fatigue science must be co-optimized |
| Simulation | All disciplines | Simulation is the integration method for combining OR, human factors, workforce, and financial models |