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
Foundations
What operations research is and isn't. How to think of healthcare delivery as a system of flows and constraints, and the fundamental distinction between deterministic models (where inputs are known) and stochastic models (where variability is the defining feature).
Module 2Queueing Theory
The mathematics of waiting. How arrival rates, service rates, and utilization interact to produce wait times that grow nonlinearly as systems approach capacity. Little's Law, the utilization-delay curve, and why "80% full" is not a comfortable operating point.
Module 3Optimization
How to allocate scarce resources when everything is constrained. Linear and integer programming, the meaning of shadow prices — what one more unit of a constrained resource is worth — and how to frame allocation decisions as formal optimization problems.
Module 4Networks
How patients, referrals, and information flow through connected structures. Network flow models, referral network analysis, critical path methods, and why the topology of connections matters as much as the capacity of individual nodes.
Module 5Scheduling
The operational mechanics of time allocation. Appointment scheduling models, staff rostering under constraints, no-show dynamics, and the gap between the schedule as planned and the schedule as executed.
Module 6Simulation
When analytical models reach their limits, simulation takes over. Discrete-event simulation for process modeling, Monte Carlo methods for uncertainty quantification, and scenario stress testing for systems too complex for closed-form solutions.
Module 7Applications
Where OR meets operational reality. Emergency department flow analysis, surgical scheduling optimization, inpatient bed management, behavioral health access modeling, and prior authorization burden quantification.
Module 8Product Synthesis
Translating OR into operational tools. Metrics that operators can act on, capacity planning frameworks, and the design principles for embedding operations research into decision-support products.
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 |