Nikola Dudar Program Manager Microsoft Corporation Session Code: DTL 311.
311 Session 5 1 Littles law
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Transcript of 311 Session 5 1 Littles law
Little’s Law
BUAD311 Operations ManagementSession 5
1
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)
3
Objectives: Little’s Law
Relationship among– Flow (Throughput) Time– Flow (Throughput) Rate– WIP
Little’s Law– A general rule that links various performance
measures
4
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
5
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)
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
Group B:FT = WIP/FR = 200 / 1000 = 0.2 mo. = 6 days
11
Example: Admission Flow (cont’d)
Accept
Reject
1000
500
500
200
50Stage 1
Stage 2
Group A:– Stage 2: FT = WIP/FR=50/(1000*50%) = 0.1 mo. = 3 days– Receive answer in 6+3 = 9 days on average
12
Example: Admission Flow (cont’d)
Accept
Reject
1000
500
500
200
50Stage 1
Stage 2
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
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.
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
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
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.