capacity little s law students

8/3/2019 Capacity Little s Law Students

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CAPACITY PLANNING ANDLITTLE'S LAW

Capacity

Why is capacity important tomanagement? All companies have a capacity but what is it?

Can it be measured?

Does it have a unit of measure?

What is the capacity of Coca Cola bottlingplant? University?

Met Police?

Bank branch?


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Real capacity issues

200 people

applications

0

500

1000

1500

2000

2500

3000

date

applications

2002-2005

days to offer

0

10

20

30

40

50

60

days

days to offer

2002-2005

loan to value

0

10

20

30

40

50

60

70

80

date

loan to value

2002-2005

Working out capacity

apps/tto/ltv

0

20

40

60

80

100

120

140

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

Series1

Series2

Series3

Days to offer

applications (/20)

loan to value

days


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What is capacity?

Capacity is the potential abilityof a system to produce outputof a given quality, according toattributes promised to

customers, over a given timeperiod. Ng, Maull, Godsiff

Capacity limits

Companies operate at below maximum Reason; Insufficient demand or policy, seasonality

Some parts work at capacity ceiling


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Capacity decisions affect

Cost: under utilised assets means higher unit costs

Revenue: if cant meet demand have lost revenue(football stadium)

Working capital: might build up finished goods but..

Quality: hiring temporary staff meets demand but.

Speed: have surplus capacity to avoid queues

Dependability: closeness of demand level to capacity

Flexibility: volume flex enhanced by excess capacity

QUEUING THEORY


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Basic Issues

Queuing theory applies primarily to the

transformation of customers.

Also applies to information processing operations butthe implications are not so immediate. Why?

If customers have to wait too long in a queue

they baulk.

Baulking/reneging, customers leaving a queue,

examples include retail checkouts, call centres etc. If the queue is too long then revenue is lost,

what is the penalty for a call centre?

Calculating Capacity

Assumptions

Applies to stable system No consideration of arrival and service rates

Lots of people turn up together eg dinner queue at a school, Limited opening hours

Batch production, crucially no slack time


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Throughput time is time available egopening hours

Cycle time is time available per job,

Work content is time needed per job

Example

At the London Palladium the interval of aperformance of Thomas the Tank Enginelasts for 20 minutes and in that time 86women need to use the toilet. On average,

a woman spends three minutes in thecubicle. There are 10 toilets available.Does the London Palladium have sufficienttoilets?


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Calculation

We want to calculate the number ofservers (toilets) required

So need to know cycle time,

Throughput time = 20 mins

Work in progress is 86 woman

Cycle time is 0.233 minutes per woman. Number of toilets is 3/0.233 = 12.9 toilets

Do we have enough?

What can we do to help?

What are the alternatives?


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LITTLES LAW

Poisson distribution

Random processes have bursts ofaction

() is the average, (k) is the number ofevents


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Example

Assume we have on average 2 people

arriving per hour () what is the chance we

will get 6 (k).

Plugging into formula

The formula can be re-arranged for use withthe Microsoft scientific calculator as,

/( x !) = p

x

The numerical value of e is approximately2.71

/( x !) = p


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What does this mean?

About once every 80 hrs (fortnight) we willget six customers turning up.

What are the chances of having onecustomer in an hour?

Chances of 1 customer anhour?

1 2 3 4

25% 25%25%25%1. 25%

2. 27%

3. Over 50%

4. None of the above


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Other uses of Queuing theory

Queues form when a customer arrives anda server is busy

A denotes the distribution of arrival times

B denotes the distribution on the servicerate

m denotes the number of servers at eachstation

b denotes the maximum number of itemsallowed in the system

A/B/m/b represents a queueing system

The most common distribution torepresent A B is an exponential orMarkovian (M) distribution

The most common type of queues areM/M/1 or G/G/1 (where G represents ageneral or normal distribution)


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Littles law

6 minutes per injection

10 people per hour4 people per hour arrive

Nurse is busy 24 minutes per hour40% of her time.

What is the average queue?

Arrival rate Service rate

Simple Derivation

60% of people arriving have no queue

40% people arriving have to queueHow long do 40% queue?If arrive when no-one else is alreadywaiting then

It could be between 0..6 minsaverage waiting time is treatment time.

SO.40% of 4 people (per hr) wait on average 3 mins0.4*4*3 = 4.8 minutes per hrSome will have to wait 6 mins (ie someone is already in waiting room and)

+ average of 3 mins. (someone in treatment room)


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Capacity and wait time

)(/ l

t

Calculate the remaining wait times, for arrival rateof 30, 40, 45, 50, 55, 56, 57, 58, (customer per hour)

Draw graph (approximately)

10/60 (60-10) = 0.003 20/60 (60-20) = 0.008

Relationship between

Capacity Utilization and Waiting Time

Exhibit S11.8


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See for yourself

as the arrival rateincreases relative to theservice rate theproportion findingsomeone alreadywaiting increases andwe observe anexponential rise.

http://archive.ite.journal.informs.org/Vol7No1/DobsonShumsky/

Importance of CV

Need to know co-efficient of variationfor

Arrival

Task Cv= standard deviation/mean

CV of greater than 1 is a long tail.
http://archive.ite.journal.informs.org/Vol7No1/DobsonShumsky/http://archive.ite.journal.informs.org/Vol7No1/DobsonShumsky/


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Klassen & Menor Process Triangle

0.0 0.2 0.4 0.6 0.8 1.0

Capacity Utilization

Inventory

(orleadtime)

High Inventory(or long lead time)

Low

High

Kasra Ferdows, Jose M.D. Machuca, Michael Lewis

Summary

Queues are important in service systemsparticularly customer processingoperations

Stable systems have simple equations

Poisson distribution for random arrivalrates

Once arrival rates become close to 80%choking occurs.

capacity little s law students

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