This project presents an Integer Linear Programming (ILP) and Discrete Event Simulation model to optimize nurse workforce scheduling in a healthcare call centre. The goal is to minimize total staffing cost while meeting varying hourly patient demand and complying with operational constraints. The model is implemented in Excel Solver and simulated in SIMUL8 to evaluate queue performance and nurse utilization.
-
Objective: Minimize total cost = £80 × full-time nurses + £64 × part-time nurses
-
Decision Variables:
F: Full-time nurses (9am–5pm, with 1-hour lunch break)P1–P5: Part-time nurses starting between 9am and 1pm for 4-hour shifts
-
Constraints:
- Cover patient demand (5 patients/hour/nurse)
- Minimum 4 and max 20 full-time nurses
- Max 20 part-time nurses
-
Optimal Solution:
- 10 full-time nurses
- 14 part-time nurses (1 at 9am, 9 at 11am, 2 at 12pm, 2 at 1pm)
- Total cost: £1,696/day
-
Arrival Rate: Based on hourly patient demand (exponential distribution)
-
Service Time: Normally distributed (mean: 12 mins, std dev: 4 mins)
-
Performance Metrics:
- Nurse utilization: 80.70%
- Avg queue time: 2.01 mins
- Max queue time: 9.16 mins
- Avg queue size: 2.23 patients
- ILP successfully identifies cost-effective staffing while covering all time periods
- Simulation reveals moderate wait times and high nurse efficiency
- System can be fine-tuned to further reduce peak-time delays
- Future improvements could target more balanced break scheduling to improve service continuity during lunch hours
nurse-scheduling-callcentre/
1. ilp-model/ # Excel Solver files for optimization
2. sim-model/ # SIMUL8 files and simulation screenshots
3. report/ # Full project write-up and charts
4. README.md # Project overview (this file)