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EOQ for Production not Order (EPQ)

We do not buy the product.

We produce it.Total demand / year isD

Demand / day or consumption rate is u

Production rate isp/ day

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Example

A toy manufacturer uses 48000 parts for one of its products.Consumption rate is uniform throughout the year.

Woring days are !40 / year.

The firm can produce at a rate of 800 parts / day

Carrying cost is "# / part / year

$etup cost for production run is "4% / setup

What is the optimal production si&e'

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Example

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Instantaneous and Incremental Replenishment

(nstantaneous )eplenishment

(ncremental )eplenishment

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EPQ: Incremental Replenishment

(Production and Consumption)

u

p

p-u

u* + number of ,oring days - D Total demand per year

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EPQ: One period and One year

ne Period

p-uu

ne ear

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EPQ: Ordering Cost and Carrying Cost

I max I max I max I max

+

(f ( can stateImaxin terms of Q1 then ( am done.

( can easily find 2conomic 3uantity.

SQ

DH

I

!ma=TC

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EPQ : Production & Consumption rate & time

5o, much do ,e produce each time' 3

5o, long does it tae to produce 3' d#What is our production rate per day' p

#pdQ =

-+ !# dduQ +=

#ma -+ dupI =

!ma4 udI =

p-u u

I max

d1 d2

5o, long does it tae to consume 3' d# 6d!

What is our consumption rate per day ' u

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EPQ : Optimal Q

-+!

upHSDpEPQ

=

up

p

H

SDEPQ

=!

up

p

H

SDEOQ

=!

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Example

A toy manufacturer uses 48000parts for one of its products.

Consumption rate is uniform throughout the year.

Woring days are 240 / year.

The firm can produce at a rate of 800 parts / day

Carrying cost is $1 / part / year$etup cost for production run is $45 / setup

What is the optimal production si&e'

up

p

H

SDEPQ

=!

!00800

800

#

-48000-+4%+!

=EPQ

!400=EPQ

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!hat is Run "ime# !hat is Cycle "ime

#pdQ=

#800!400 d=

7# =d

-+ !# dduQ +=

-+!00!400 !# dd +=#!-+ !# =+ dd

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!hat is the Optimal "otal Cost

!

MaxIHQ

DSTC +=

#ma -+ dupI =

!MaxIH

QDSTC +=

#800ma =I

7-!00800+ma =

I

!

#800#!400

480004% +=TC

#8000000 =+=

TC

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ROP

(f setup time taes ! days1 at ,hich le9el of in9entory ,eshould start setup'

!+!00- 400

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A company has a yearly demand of 120,000 boxes of its

product. he product can be produced at a rate of 2000boxes per day. he shop operates 240 days per year.

Assume that demand is uniform throu!hout the year.

"etup cost is $8000 for a run, and holdin! cost is $10 per

box per year.

a# hat is the demand rate per day

b# hat is the %conomic &roduction 'uantity (%&'#

c# hat is the run time

d# hat is the maximum in)entory

e# hat is the total cost of the system

Practice

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a# hat is the demand rate per day

*emand per year is 120,000 there are 240 days per year

*emand per day + 120000/240 + 500

u + */240 + 500

b# hat is the %conomic &roduction 'uantity (%&'#

$ssignment %'

up

p

H

SD

EPQ =!

#%00!000

!000

#0

-#!0000-+8000+!

=EPQ *+,,,

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c# hat is the run time

e produce 1000 units

-ur production rate is 2000 per day

t taes 1000/2000 + 8 days

d1+ %&'/p+ 8 days

d# hat is the maximum in)entory

e produce for 8 days. %ach day e produce 2000 units ande consume 500 units of it. herefore e add to our

in)entory at rate of 1500 per day for 8 days. hat is

Imax+ 8(1500# + 12000

Imax+pd1 8(1500# + 12000

$ssignment %'

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e# hat is the total cost of the system

$ssignment %'

!MaxIH

Q

DSTC +=

!

#!000#0

#:000

#!00008000 +=TC

#!0000:0000:0000 =+=TC

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&roblem The Dine Corporation is both a producer and a user of brass

couplings. The firm operates !!0 days a year and uses the couplingsat a steady rate of %0 per day. u = 50. Couplings can be produced at

rate of !00 per day.p=200.Annual storage cost is "# per coupling1

H=11 and machine setup cost is "7% per run1S=35. $ince there are

!!0 days per year and u is e;ual to %01 yearly demand is %0+!!0-1D= 11000.

a- Determine the economic run si&e.

b- Approimately ho, many runs per year ,ill there be'

c- Compute the maimum in9entory le9el.

d- Determine the cycle time1 run time and pure consumption time.

e- Compute the total cost.

$ssignment *-c