1. IE450 Models Relating Cycle-time, Throughput, WIP and Batch Sizes
Planning manufacturing capacity
Dr. R. A. Wysk

2. Learning Objectives
To be able to name the most important factors that contribute to the increase in the cycle time of a production system.
To be able to explain the Little’s Law and its application to the operations of a production system.
To be able to explain the fundamental relationship between resource utilization, cycle time and process and arrival variability in a production system.

3. Any Production System
Resources
Output
Input
WIP

4. Any Production System Output Input WIP
Input = Output [– defects] (1st Law of Factory Physics)
WIP - Work-In-Process
Idle time - % of time a resource is not working

5. Any Production System Output Input
Throughput – the average output per unit time (a rate)
Lead time – the time needed to process a part through a facility
Cycle time, flow time or sojourn time – the average time from release of a job to completion

6. Relating Throughput and WIP
One unit in WIP
Lead time ?
Idle time ?
Throughput?
Assuming each process takes 1 minute.

7. More WIP (everything else the same) ...
Lead time ?
Idle time ?
Throughput?

8. More WIP - “keep all machines busy” ...
Lead time ?
Idle time ?
Throughput?

9. More WIP - diminishing returns ...
Lead time ?
Idle time ?
Throughput?

10. Active Exercise: Diminishing return?
At some point more WIP does not achieve anything except for longer lead times
Take 3 minutes to complete the following task.
Draw graphs relating WIP to throughput.

11. Relating WIP and Throughput
100%
Throughput
What is the limiting throughput?
WIP

12. A very useful relationship
Little’s Law:
WIP = (Throughput) x (Lead Time)
Little’s Law is a fundamental law of system dynamics
Gives good results for a variety of scenarios
Throughput (Units/time).
Example: A facility can produce 200 units per week, and the average lead time is 2 weeks. According to Little’s law the average WIP = 200 x 2 = 400 units.

13. Scenario 1: No Variability (Ideal World)
1st part arrives
2nd part arrives
3rd part arrives
1st part processing
2nd part processing
3rd part processing 10 20 30 8 18 28
1st part departs
2nd part departs
3rd part departs

14. Scenario 2: Processing Variability
Same average !!!
1st part arrives
2nd part arrives
3rd part arrives
Same utilization but . . .
More queue time
More lead time
Parts waiting in queue
1st part processing
2nd part processing 3 10 30 12 21 24 20
1st part departs
2nd part departs
3rd part departs

15. Scenario 3: Arrival Variability
Same average !!!
Again, same utilization but . . .
More queue time
More lead time
1st part arrives
2nd part arrives
3rd part arrives
13.5 hours
6.5 hours
Part 3 waiting in queue
1st part processing
2nd part processing
3rd part processing
21.5 8
29.5 10
13.5 20
1st part departs
2nd part departs
3rd part departs

16. Scenario 4: Increased utilization
Larger Batch Sizes
1st part arrives
2nd part arrives
3rd part arrives
Increased utilization but …
more queue time
longer lead times
Parts waiting in queue
1st part processing
2nd part processing 3 10 13 23 27 20 30
1st part departs
What would happen if the processing time variability is eliminated?
2nd part departs
3rd part departs

17. Example Summary
Utilization alone is not sufficient to estimate the lead-time performance
One must also consider the products arrival and processing variability.
A mathematical model is needed to study the system.

18. Questions??