Transcript
Page 1: 311 Session 5 1 Littles law

Little’s Law

BUAD311 Operations ManagementSession 5

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Announcements

The first homework is due before the end of the class on Sep/17The first quiz is on Sep/19 and it covers process analysisRead “The Goal” (2-page paper is due on Sep/24)

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Objectives: Little’s Law

Relationship among– Flow (Throughput) Time– Flow (Throughput) Rate– WIP

Little’s Law– A general rule that links various performance

measures

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Little’s Law

WIP = 6

Time

Flow rate

Now

1 min later

2 min later

You

Flow time

2

3

Flow Time = WIP / Flow Ratetime speeddistance

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Little’s Law

Transformation ProcessTransformation Process(components)(components)

InputsInputs(customers(customers

and/orand/ormaterials)materials)

OutputsOutputs(goods(goods

andandservices)services)

Flow Time = WIP / Flow Rate

Little’s Law holds for any stable systems.

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Little’s Law

Example: Bank Teller– (Average) WIP: 6 customers– (Average) Flow rate: 12 customers per hour– (Average) Flow time: 6/12 = 0.5– A customer spends (on average) 0.5 hours in the bank

Does this mean each customer spends 0.5 hour in the bank?

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Implications of Little’s Law

Which one is (usually) difficult to measure ?– Flow Rate– WIP– Flow time

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Implications of Little’s Law: Example

Average number of customers in a restaurant: 50Average number of customers arriving (and leaving) per hour: 30What is the flow time?– 50/30 = 1.66 hrs– A customer spends (on average) 1hr and 40 mins.

How can we increase the revenue? Revenue is proportional to Flow Rate = WIP / Flow Time

Increase WIP:Add more chairs

Reduce FT:Faster service

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Example: Admission FlowMarshall undergraduate program receives about 1000 applications per month.The evaluation starts with a preliminary classification with basic information (Stage 1) :– Group A: Applicants with desired recommendations, extracurricular activities,

etc. (50% of the applicants) Applicants in this group will advance to a secondary review.

– Group B: Other applicants. (50% of the applicants) Applicants in this group will be rejected.

On average there are:– 200 applications in the preliminary stage (Stage 1) – 50 applications in the advanced review stage (Stage 2)

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How long:– do Group B applications spend in the process?– do Group A applications spend in the process?– is the average process time?

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Example: Admission Flow (cont’d)

Accept

Reject

1000

500

500

200

50Stage 1

Stage 2

FT = WIP/FR

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Group B:FT = WIP/FR = 200 / 1000 = 0.2 mo. = 6 days

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Example: Admission Flow (cont’d)

Accept

Reject

1000

500

500

200

50Stage 1

Stage 2

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Group A:– Stage 2: FT = WIP/FR=50/(1000*50%) = 0.1 mo. = 3 days– Receive answer in 6+3 = 9 days on average

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Example: Admission Flow (cont’d)

Accept

Reject

1000

500

500

200

50Stage 1

Stage 2

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What is the average processing time?• 6*0.5+9*0.5 = 7.5 days

Is there a simple way to calculate the average waiting time? 13

Example: Admission Flow (cont’d)

Accept

Reject

1000

500

500

200

50Stage 1

Stage 2

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Simple way:– System WIP=200 (stage 1) + 50 (Stage 2)= 250 applications– System FR=1000 applications per month– System FT=250/1000=0.25 month=7.5 days 14

Example: Admission Flow (cont’d)

Accept

Reject

1000

500

500

200

50Stage 1

Stage 2

Little’s Law still holds.Little’s Law still holds.

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Example: Clinic

Imagine a clinic in which a patient can be treated in exactly 15 minutes. Two patients arrive 15 minutes past the hour (every hour), and one patient arrives 45 minutes past the hour: FR of 3 per hour

Patient 1&2

15 30 45 60

1 3

75

3

2

Waiting

Service

2

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Example: Clinic

What is the average waiting time? By Little’s law:

Average WIP = (0 + 1 + 0 + 0) / 4= 0.25 patientsAverage waiting time = 0.25 patients/(3 patients/ hr) = (0.25/3)*60 mins/hr = 5 min

Directly from the Chart:Average waiting time = (0 + 15 + 0)/3 = 5 min

Patient 1&2

15 30 45 60

1 3

75

3

2

Waiting

Service

2

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Example: Clinic

What is the average total time spent (waiting + service)? Directly from the Chart:Average total time = (15 + 30 + 15)/3 = 20 minBy Little’s law:Average WIP = (0 + 2 + 1 + 1) / 4= 1Average total time = 1 patient/(3 patients per hr) = (1/3)*60 mins/ hr= 20 min

Patient 1&2

15 30 45 60

1 3

75

3

2

Waiting

Service

2

Little’s Law holds for variable/random arrivals

Little’s Law holds for variable/random arrivals

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Example: Clinic

Do we have enough capacity?– Patient arrival rate=3 patients per hour– Clinic Capacity=60 min/(15 mins per patient)= 4 patients

per hour

What is the utilization rate? – 3/4=0.75 or 75%

Why do patients wait?– Arrivals are bunched up--not evenly spread out over the

hour

Randomness/Variability forces resource idleness & longer waiting time.

Randomness/Variability forces resource idleness & longer waiting time.


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