Operations Analytics: Process Optimization, Queueing, and Performance Metrics
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# Operations Analytics: Process Optimization, Queueing, and Performance Metrics ## 🎯 Learning Objectives - Apply queueing theory to optimize service operations - Identify and eliminate bottlenecks in processes - Measure operational efficiency with KPIs - Design experiments to improve operations ## 📖 Core Content #...
Operations Analytics: Process Optimization, Queueing, and Performance Metrics
🎯 Learning Objectives
- Apply queueing theory to optimize service operations
- Identify and eliminate bottlenecks in processes
- Measure operational efficiency with KPIs
- Design experiments to improve operations
📖 Core Content
1.1 Operations KPIs
| KPI | Definition | Target |
|---|---|---|
| Throughput | Units processed per time period | Maximize |
| Cycle Time | Time from start to completion | Minimize |
| Utilization | Active time / Total time | 70-85% (too high = queue buildup) |
| WIP (Work in Progress) | Items in the system | Minimize |
| Takt Time | Available time / Customer demand | Match demand rate |
1.2 Queueing Theory (M/M/1 Model)
For a single-server queue:
- Average queue length:
- Average wait time:
- Utilization: where = arrival rate, = service rate, = utilization.
Worked Example
A call center receives 8 calls/hour. Each agent handles 10 calls/hour. (80% utilization). calls waiting on average. hours = 24 minutes average wait.
Adding a second agent: , (combined). , , hours = 2 minutes.
1.3 Why This Matters
Operations analytics is the basis for process improvement in any business: manufacturing, call centers, hospitals, restaurants, and logistics. The math is simple but the impact is enormous — a 10% reduction in cycle time can mean millions in savings.
2. 📝 Practice Questions
Q1: A hospital ER has 5 doctors, each seeing 3 patients/hour. Patients arrive at 12/hour. What's the average wait time?λ = 12 patients/hour μ = 5 × 3 = 15 patients/hour (total capacity) ρ = 12/15 = 0.8 (80% utilization)For an M/M/5 queue (multiple servers), the wait time calculation is more complex (Erlang C formula). But approximately:Using M/M/1 with the same ρ=0.8: W_q = 0.4 hours = 24 minutes. With 5 servers, the wait will be significantly less because customers can be served in parallel.Estimated wait with 5 servers and ρ=0.8: ~5-10 minutes (using Erlang C tables).The key insight: ρ < 1 means the system is stable. At ρ = 0.8, wait times are manageable. If arrivals increase to 14/hour (ρ = 0.93), wait times explode. Join Discord PreviousPricing AnalyticsNextDashboard Design