Question

Use Excel & show work - The Dynaco Manufacturing Company produces a particular product in an assembly line operation. One of the machines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked on every 7.5 minutes, on average. The machine operator can process an average of 10 parts per hour. Determine the average number of parts waiting to be worked on, the percentage of time the operator is working and the percentage of time the machine is idle.

Answer 1

The manufacturing system represents single server queuing model.

Excel Model for the problem is as follows:

Dynaco Manufacturing Company - Single Server Queuing Model
Inter-arrival time		7.5	minutes per unit
Arrival rate	λ	8	units per hour
Serivce rate	µ	10	units per hour
Utilization of server	ρ	0.8
Average number of requests that will be waiting for service	Lq	3.20	Units
average waiting time in hour before service begins	Wq	0.40	Hours per unit
average waiting time in minutes before service begins	Wq	24.00	Minutes
Percentage of time the operator is busy		80.00%
Percentage of time the operator or machine is idle		20.00%

Excel Formula:

Dynaco Manufacturing Company - Single Server Queuing Model
Inter-arrival time		7.5	minutes per unit
Arrival rate	λ	=60/C2	units per hour
Serivce rate	µ	10	units per hour
Utilization of server	ρ	=+λ/µ
Average number of requests that will be waiting for service	Lq	=λ^2/(µ*(µ-λ))	Units
average waiting time in hour before service begins	Wq	=+C6/λ	Hours per unit
average waiting time in minutes before service begins	Wq	=+C7*60	Minutes
Percentage of time the operator is busy		=+ρ
Percentage of time the operator or machine is idle		=1-ρ

Snapshot:

1 Dynaco Manufacturing Company - Single Server Queuing Model 2 Inter-arrival time 3 Arrival rate 4 Serivce rate 5 Utilization of server 7.5 minutes per unit 8 units per hour 10units per hour 0.8 6 will be waiting for service 7 before service begins 8 before service begins 9 is busy Average number of requests that average waiting time in hour average waiting time in minutes Percentage of time the operator Percentage of time the operator Lq 3.20 Units Wq 0.40 Hours per unit Wq 24.00 Minutes 80.00% 10 or machine is idle 20.00% Dynaco Manufacturing Company - Single Server Queuing Model 2 Inter-arrival time 3 Arrival rate 4 Serivce rate 5 Utilization of server 7.5 60/C2 10 minutes per unit units per hour units per hour 6 be waiting for service 7 service begins 8 before service begins 9 busy Average number of requests that will average waiting time in hour before average waiting time in minutes Percentage of time the operator is Percentage of time the operator or Lq A2/(u*(μ-λ)) |Units Wq Hours per unit Wq +C7 60 Minutes 10 machine is idle

the average number of parts waiting to be worked on: 24 minutes

the percentage of time the operator is working: 80%

and the percentage of time the machine is idle.: 20%