IE450Models Relating Cycle-time, Throughput, WIP and Batch

Sizes

Planning manufacturing capacity

Dr. R. A. Wysk

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.

Any Production System

Input Output

WIP

Resources

Any Production System

Input Output

WIP

Input = Output [– defects] (1st Law of Factory Physics)

WIP - Work-In-Process

Idle time - % of time a resource is not working

Any Production System

Input Output

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

Relating Throughput and WIP

One unit in WIP

Lead time ?

Idle time ?

Throughput?Assuming each process takes 1 minute.

Lead time ?

Idle time ?

Throughput?

More WIP (everything else the same) ...

More WIP - “keep all machines busy” ...

Lead time ?

Idle time ?

Throughput?

More WIP - diminishing returns ...

Lead time ?

Idle time ?

Throughput?

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.

Relating WIP and ThroughputT

hrou

ghpu

t

WIP

100%

What is the limiting throughput?

A very useful relationship

• 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.

Little’s Law:WIP = (Throughput) x (Lead Time)

Scenario 1: No Variability (Ideal World)Data and Calculations

Planning Horizon 30 hoursProcessing time 8 hour/unitInter-arrival time 10 hoursUtilization 80%Average queue time 0 hoursAverage lead time 8 hours

0 10 20 30

1st part processing

2nd part processing

3rd part processing

1st part arrives

2nd part arrives

3rd part arrives

1st part departs

3rd part departs

2nd part departs

8 18 28

Scenario 2: Processing VariabilitySCENARIO 1 2Planning Horizon 30 hours sameProcessing time 8 hour/unit 12, 9, 3Inter-arrival time 10 hours sameUtilization 80% sameAverage queue time 0 hours 1 hourAverage lead time 8 hours 9 hours

0 10 30

1st part processing2nd part

processing3

1st part arrives

2nd part arrives

1st part departs

3rd part departs

2nd part departs

12 21 2420

3rd part arrives

Parts waiting in queue

Same average !!!Same average !!!

Same utilization but . . .• More queue time

• More lead time

Scenario 3: Arrival VariabilitySCENARIO 1 2 3Planning Horizon 30 hours same as 1 same as 1Processing time 8 hour/unit 12, 9, 3 same as 1Inter-arrival time 10 hours same 13.5, 6.5Utilization 80% same as 1 same as 1Average queue time 0 hours 1 hours 0.5 hoursAverage lead time 8 hours 9 hours 8.5 hours

0 10

1st part processing

2nd part processing

3rd part processing

1st part arrives

2nd part arrives

1st part departs

3rd part departs

2nd part departs

8 21.5 29.520

3rd part arrives

Part 3 waiting in queue

Same average !!!Same average !!!

Again, same utilization but . . .

• More queue time

• More lead time

13.5

13.5 hours 6.5 hours

Scenario 4: Increased utilizationSCENARIO 1 2 3 4Planning Horizon 30 hours same as 1 same as 1 same as 1Processing time 8 hour/unit 12, 9, 3 same as 1 (2) + 1 hourInter-arrival time 10 hours same as 1 13.5, 6.5 same as 1Utilization 80% same as 1 same as 1 90%Average queue time 0 hours 1 hours 0.5 hours 2 hoursAverage lead time 8 hours 9 hours 8.5 hours 11 hours

0 10

1st part processing 2nd part processing 3

1st part arrives

2nd part arrives

1st part departs

3rd part departs

2nd part departs

13 23 2720

3rd part arrives

Parts waiting in queue

30

Increased utilization but …

• more queue time

• longer lead times

What would happen What would happen if the processing if the processing time variability is time variability is eliminated?eliminated?

Larger Batch Sizes

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.

SCENARIO 1 2 3 4Planning Horizon 30 hours same as 1 same as 1 same as 1Processing time 8 hour/unit 12, 9, 3 same as 1 (2) + 1 hourInter-arrival time 10 hours same as 1 13.5, 6.5 same as 1Utilization 80% same as 1 same as 1 90%Average queue time 0 hours 1 hours 0.5 hours 2 hoursAverage lead time 8 hours 9 hours 8.5 hours 11 hours

Questions??