qmm lecture 9

7/25/2019 QMM Lecture 9

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___________________________________________________________________________ Quantitative Methods of Management Jan Fbry

DeterministicDeterministicInventory ModelsInventory Models


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Basic EOQ ModelBasic EOQ Model

Deterministic Inventory ModelsDeterministic Inventory Models


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How much to order? How much to order? Optimum quantityOptimum quantity When to order? When to order? Optimum reorder pointOptimum reorder point

What is the total cost?What is the total cost?

What is the average inventory level?What is the average inventory level?

What is the maximum inventory level?What is the maximum inventory level?

BasicBasic EEconomicconomic OOrderrder QQuantityuantity MModelodel

EOQEOQ MModel!odel!


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EOQEOQ MModel!odel!

"ssum#tions"ssum#tions

$ingle item$ingle item

Deterministic demand static!Deterministic demand static!

Deterministic lead time constant!Deterministic lead time constant!

%ni&orm de#letion o& the inventory%ni&orm de#letion o& the inventory



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"ssum#tions"ssum#tions

'onstant order (uantity OQ!'onstant order (uantity OQ!

)urchasing cost is inde#endent o& the OQ)urchasing cost is inde#endent o& the OQ

%nit holding cost is inde#endent o& the OQ%nit holding cost is inde#endent o& the OQ

*o shortages+ no sur#luses*o shortages+ no sur#luses


EOQEOQ MModel!odel!



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,ime

Inventory

-evel

.

q

Maximum

-evel



EOQEOQ MModel!odel!

'ycle / 'ycle 0 'ycle 1

De#letion 2e#lenishment

Order

"rrives

"verage

-evelq30



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EOQEOQ MModelodel

Exam#le 4 BreweryExam#le 4 Brewery

Monthly #roduction o& 5eer 6 7 ... hlMonthly #roduction o& 5eer 6 7 ... hl

8illing into glass 5ottles 6 09: o& #roduction8illing into glass 5ottles 6 09: o& #roduction

Em#ty 5ottles stored in #lastic cases 0. #cs;!Em#ty 5ottles stored in #lastic cases 0. #cs;!

"nnual holding cost #er case 6 0. '


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EOQEOQ MModelodel


"nnual demand"nnual demand QQ6 /0. ... cases6 /0. ... cases

"nnual holding cost"nnual holding cost cc//6 0. '


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EOQEOQ MModelodel


,otal annual cost,otal annual cost

OCHCTC +=

,otal annual,otal annual HO-DI*HO-DI*costcost

,otal annual,otal annual O2DE2I*O2DE2I*costcost



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,ime

Inventory

-evel

.

q

Maximum

-evel

"verage

-evelq30

Order

(uantity


EOQEOQ MModelodel



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EOQEOQ MModelodel


Order (uantity COrder (uantity C qq Maximum inventory levelMaximum inventory level

"verage inventory level"verage inventory level

2avg

qq =

qq =max



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EOQEOQ MModelodel


,otal annual HO-DI* cost,otal annual HO-DI* cost

21avg1

qcqcHC ==

,,otal annual O2DE2I* costotal annual O2DE2I* cost

q

QcncOC 22 ==



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EOQEOQ MModelodel


,otal annual cost,otal annual cost

q

Qc

qcqTC 21

2)( +=



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,otal cost

q.


EOQEOQ MModelodel


/0. ...

/ 0/0 ...

. ...

07 ...

/. ...

077 ... OC

HC

TC



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EOQEOQ MModelodel


)olicy I)olicy I )olicy II)olicy II )olicy III)olicy III

"nnual demand"nnual demand QQ /0. .../0. ... /0. .../0. ... /0. .../0. ...

Order (uantityOrder (uantity qq /. .../. ... . .... ... /0. .../0. ...

"nnual unit holding cost"nnual unit holding cost cc// 0.0. 0.0. 0.0.

"verage inventory level"verage inventory level qq3030 9 ...9 ... 1. ...1. ... . .... ...

,otal annual holding cost,otal annual holding cost HCHC /.. .../.. ... .. ..... ... / 0.. .../ 0.. ...%nit ordering cost%nit ordering cost cc00 /0 .../0 ... /0 .../0 ... /0 .../0 ...

*um5er o& orders*um5er o& orders QQ33qq /0/0 00 //

,otal annual ordering cost,otal annual ordering cost OCOC /77 .../77 ... 07 ...07 ... /0 .../0 ...

,otal annual cost,otal annual cost TCTC 077 ...077 ... 07 ...07 ... / 0/0 .../ 0/0 ...



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EOQEOQ MModelodel


/. ...

Inventory -evel

,ime. /0

)olicy I



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EOQEOQ MModelodel


. ...

Inventory

-evel

,ime. /0

)olicy II



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EOQEOQ MModelodel


.

)olicy III

,ime

Inventory

-evel

/0. ...

/0



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EOQEOQ MModelodel


O#timum order (uantityO#timum order (uantity

1

2*2

c

Qcq =

cases122

)12)(12(2*==q



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EOQEOQ MModelodel


O#timum total annual costO#timum total annual cost

21* 2 cQcTC =

!"#2$)12)(2)(12(2* ==TC



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EOQEOQ MModelodel


/0 ....

cost

q

07. ...

OC

HC

TC



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EOQEOQ MModelodel


O#timum length o& inventory cycleO#timum length o& inventory cycle

1

2*

*

*21

Qc

c

Q

q

nt ===

days%&'yearof11* ==t


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EOQEOQ MModelodel


Inventory

-evel

,ime

days!

. 1

1;9 /.F;9

/7

/G0;9

0/F

099;9

0F0

10G;9

19

/0 ...

**max qq =

...

*avgq



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,ime

Inventory

-evel

q*

t*


EOQEOQ MModelodel


r*

d

Order

Delivery



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EOQEOQ MModelodel


q*

t*

r*

d

O#timum reorder #ointO#timum reorder #oint

dQt

dqr ==

*

**

cases122$1* ==r


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,ime

Inventory

-evel

q*

t*

r*

d

Q tit ti M th d f M t J Fb

EOQEOQ MModelodel


** mod qdQr =

dd tt**


qmm lecture 9

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