Synchronous Machine Servicing
This calculator helps determine the optimal number of machines an operator should be assigned to maximize efficiency and minimize costs in synchronous servicing scenarios.
Where:
- n₁ = Optimal number of machines (lowest whole number)
- l = Operator service time per machine (loading/unloading)
- m = Machine processing time (automatic run time)
- w = Worker walking time between machines
Results
Optimal Number of Machines (n₁)
Cycle Time
Operator Utilization
Machine Utilization
Interpretation
Cost Comparison
| Number of Machines | Total Expected Cost ($/unit) | Cycle Time (min) | Cost Efficiency |
|---|
Cycle Time Visualization
The chart below shows how different numbers of machines affect the cycle time:
Practical Examples
Example 1: CNC Machining Center
Service Time (l): 2 min | Machine Time (m): 15 min | Walking Time (w): 0.5 min
n₁ ≤ (2 + 15) / (2 + 0.5) = 17 / 2.5 = 6.8 → Optimal machines: 6
Example 2: Injection Molding
Service Time (l): 1.5 min | Machine Time (m): 8 min | Walking Time (w): 0.3 min
n₁ ≤ (1.5 + 8) / (1.5 + 0.3) = 9.5 / 1.8 = 5.3 → Optimal machines: 5
Example 3: Textile Weaving
Service Time (l): 3 min | Machine Time (m): 12 min | Walking Time (w): 1 min
n₁ ≤ (3 + 12) / (3 + 1) = 15 / 4 = 3.75 → Optimal machines: 3
Understanding Synchronous Servicing
In synchronous servicing, the operator moves between machines in a fixed pattern, servicing each machine during its idle time. The goal is to balance the operator's workload with machine utilization to minimize total cost per unit produced.
The optimal number of machines (n₁) is calculated using the formula above. After determining n₁, we also calculate the total expected cost for n₁+1 machines to ensure we've found the most cost-effective assignment.
Where TEC is the Total Expected Cost per unit of production, K₁ is the operator rate, and K₂ is the machine cost rate.