A research project exploring how machine learning, uncertainty quantification, and mathematical optimization can be integrated into a unified decision-making framework for workforce planning under uncertainty.
Organizations frequently make staffing and resource allocation decisions without knowing future demand with certainty.
Traditional forecasting methods answer:
What is likely to happen?
Optimization methods answer:
What should we do?
This project combines both approaches into a predictive optimization framework capable of forecasting demand, quantifying uncertainty, generating future scenarios, and producing optimal staffing decisions.
The project is motivated by real-world applications in:
- Healthcare Operations
- Workforce Planning
- Supply Chain Management
- Call Center Scheduling
- Emergency Response Systems
- Resource Allocation
Develop an end-to-end decision support system that:
- Forecasts future demand using machine learning.
- Quantifies forecast uncertainty.
- Generates multiple future demand scenarios.
- Optimizes staffing decisions under uncertainty.
- Evaluates operational tradeoffs between cost, service quality, and workforce stability.
Historical Demand Data
↓
Demand Forecasting
↓
Uncertainty Quantification
↓
Scenario Generation
↓
Optimization Engine
↓
Recommended Staffing Decision
A synthetic hospital demand dataset was created containing:
- Weekly seasonality
- Annual seasonality
- Random demand fluctuations
A Random Forest Regressor was trained using:
- Day of Week
- Month
- Lag-1 Demand
- Lag-7 Demand
Forecast uncertainty was estimated using an ensemble of Random Forest models with varying random seeds.
This produced:
- Mean Demand Forecast
- Forecast Standard Deviation
- Confidence Intervals
allowing future demand to be represented as a probability distribution rather than a single point estimate.
Multiple demand scenarios were generated to capture uncertainty in future demand.
Instead of optimizing for:
Demand = 71
the system optimized across multiple possible futures:
62, 66, 69, 71, 73, 76, 80, 84, 88, 92
The following optimization models were implemented:
- Single-Day Staffing Optimization
- Scenario-Based Staffing Optimization
- Multi-Day Workforce Planning
- Workforce Stability-Constrained Scheduling
- Penalty Sensitivity Analysis
All optimization models were formulated using Linear Programming.
| Metric | Result |
|---|---|
| Mean Absolute Error (MAE) | 7.24 Patients |
The forecasting model achieved strong predictive performance relative to average daily demand.
| Metric | Result |
|---|---|
| Optimal Nurses | 18 |
| Patient Capacity | 90 |
| Expected Shortage | 0.20 Patients |
| Total Expected Cost | $5,600 |
The optimizer successfully balanced staffing costs against shortage risk.
| Shortage Penalty | Optimal Nurses |
|---|---|
| 100 | 14 |
| 300 | 17 |
| 500 | 18 |
| 1500+ | 19 |
Key Finding:
Higher shortage penalties lead to larger staffing levels and reduced expected shortages.
A workforce stability constraint limited staffing changes to two nurses per day.
| Metric | Without Stability | With Stability |
|---|---|---|
| Weekly Cost | $37,200 | $40,200 |
| Service Level | 100% | 100% |
| Average Staff Change | 2.00 | 1.50 |
| Maximum Staff Change | 6 | 2 |
Workforce stability constraints:
- Increased operating costs by 8.06%
- Reduced staffing volatility by 25%
- Reduced maximum staffing swings from 6 nurses to 2 nurses
- Maintained a 100% service level
The stability-constrained policy proactively ramps staffing levels ahead of demand spikes, producing smoother workforce schedules while maintaining service quality.
This project demonstrates several important principles:
Accurate predictions alone do not create value.
Organizations must convert forecasts into operational decisions.
Decision-makers should optimize against multiple possible futures rather than a single forecast.
Operationally stable schedules often require additional staffing investment.
The optimization model quantifies this tradeoff.
Mathematical optimization provides a systematic framework for balancing:
- Cost
- Service Quality
- Resource Utilization
- Operational Stability
- Python
- Pandas
- NumPy
- Scikit-Learn
- PuLP
- Matplotlib
ai-optimization-lab
│
├── data/
│
├── src/
│ ├── forecasting/
│ ├── uncertainty/
│ └── optimization/
│
├── research/
│ ├── project_summary.md
│ ├── stability_comparison.png
│ └── analysis scripts
│
├── tests/
│
├── README.md
└── requirements.txt
Potential extensions include:
- Real hospital demand datasets
- Quantile Regression Forests
- Monte Carlo Simulation
- Robust Optimization
- Stochastic Programming
- Multi-resource allocation
- Reinforcement Learning for dynamic workforce planning
- Supply chain and inventory optimization applications
Mehul Gupta
Master of Business Analytics University of Illinois Chicago
- Operations Research
- Optimization Under Uncertainty
- Machine Learning
- Decision Analytics
- Workforce Planning
- Industrial Engineering