week 13 eoq

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Part 4:QUANTITATIVE TECHNIQUES

SOFTWARE GENERATED INFORMATION

Part 4.2:

Outcome 4:Use software-generated information to make

decisions at operational, tactical and strategic levelsin an organization.

Assessment Criteria:

4.3 Prepare a spreadsheetto enable materialrequirements planning and calculate economic

order quantities.

INVENTORY CONTROL

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.2.6 Inventory Model

1. Fixed order-quantitymodels Economic order quantity

Production order quantity Quantity discount

2. Probabilistic models

3. Fixed order-period models

EOQ1. Fixed order-quantity

models Economic order quantity

Production order quantity Quantity discount

2. Probabilistic models

3. Fixed order-period models

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a. Known and constant stockholding cost

b. Known and constant ordering cost

c. Known and constantdemandd. Known and constant lead time

e. Instantaneous replenishment of material

f. Constant price per unit /no discounts

g. Nostockouts

EOQ Assumptions


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1. Costs ofholdingstock-

associatedwith holdingor carrying

inventory overtime

2. Costs ofobtaining

stock-associated

with costs ofplacing orderand receiving

goods

3. Stock-out

Costs -associated

with

4. Cost ofStock itself

cost ofbuying in

price/ direct

StockCost

.2.3 Inventory Cost

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Stock costs 1.Costs of holding/ carrying stock

a) Interest on capital invested in thestock

b) Warehousing/ Storagecharges

(rent, lighting, heating, refrigeration,air conditioning, etc.)

c) Stores staffing, equipment maintenance andrunning costs

d) Insurance,

security

e) Pilferage, vermindamage

f) Deteriorationandobsolescence

.2.3 Inventory Cost

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Stock costs 2.Costs of obtaining stock

a) Clerical & administration costassociated with purchasing,

accounting, andGoods Received Dept.

b)

Transportationcostsc) Cost associated with internalordering

.2.3 Inventory Cost

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2.6 Inventory Model (EOQ)

A company use 50,000 bulbs per annum which areRM7 each to purchase. The ordering costs areRM50 per order and carrying costs are 5% ofpurchase price per annum, i.e. it cost RM0.35 p.ato carry a widget in stock (RM7 x 5%)Various cost calculation:

i. Total cost per annum = Co p.a + Cc p.awhere Co p.a = No. of order x Cost

per order No. of orders = Annual

Demand/Order Quantity Cc p.a = Average stock level

stration 3: Graphical Illustration ofEOQ

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Total cost per annum = Co p.a + Ccp.ai. No. of orders = Annual Demand/OrderQuantity

= 50,000 / 5,000 = 10 timesii. Co p.a = 10 x RM50 = RM500

iii. Average stock= 5,000 / 2 = 2,500 units

iv. Cc p.a = 2,500 x RM0.35 =RM875

** From various assumption of quantity order, we

may plot the various cost in a graph as follows



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Order quantity

Annual Cost

Holdin

gCost

Curve

TotalC

ostCurv

e

Order (Setup) Cost Curve

Minimum totalcost

Howm

uch

to orde

r?OptimalOrderQuantity(EOQ)



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More units must be stored if more are ordered

Purchase Order

Description Qty.Microwave 1

Purchase Order


Order

quantity

hy Holding Cost Increase

Order

quantity


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Cost is spread over more units

hy Order Cost Decrease


PurchaseOrder

Description Qty.

Microwave 1

Purchase Order

Description Qty.

Microwave 1

PurchaseOrder


Purchase Order


1 Order (Postage RM

0.33)

1000 Orders (Postage

RM330)

Order

quantity

PurchaseOrder

Description Qty.

Microwave 1000

Example: You need 1000 microwave ovens

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sic Model Economic Order Quanti

c

o

C

DC2EOQ

=

EOQ formula: Ordering cost per order

Demand per cycle

Carrying cost per item

(per cycle)Notes:Always take care that demand and carrying

costs are expressed for the same time period.A year is the usual period used.In some problems the carrying cost is

expressed as a percentage of the value

whereas in others it is expressed directly as a


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Based on Illustration 3

Demand = 50,000 bulbs, Price per item = RM7

Ordering cost = RM50 per order, Carrying cost= 5% x RM7 = RM0.35

c

o

C

DCEOQ

=

2

35.0

000,50502 =

64.3779=

units3780


ustration 4: Economic Order Quantity

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ost Equation for Basic Model

co C2

qC

q

DC +=

Where

C= total ordering cost +

totalcarrying cost

Co = Annual ordering costCc = Annual carrying cost

q = quantity orderAsq get larger:Annual ordering cost become smallerAnnual holding cost become larger

& Total annual inventory cost isminimised when the order quantity, qtakes the value ofEOQ

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co C2

qC

q

DC += ( ) ( )35.0

2

378050

3780

000,50+=

50.66138.661 +=

88.1322RM=

Based on Illustration 3

Demand = 50,000 bulbs, Price per item = RM7

Ordering cost = RM50 per order, Carrying cost= 5% x RM7 = RM0.35

stration 5: Cost Equation for Basic Model

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Suppose that the present quantity order by thiscompany is;

a. 5000 bulbs or,b. 2000 bulbs

If other cost are unchanged, calculate thepresent total

annual cost incurred by each present quantity

order?

tration 5: Cost Equation for Basic Model (con

( ) ( )35.02

500050

5000

000,50

5000+=

=

qC

875500 +=

00.1375RM=

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tration 5: Cost Equation for Basic Model (con

( ) ( )35.02

200050

2000

000,502000 +==qC

3501250 +=

1600RM= Whatsy

our

conclusion

?

Total annual cost for quantity order based oncalculated EOQ is the lowest compared toother two order quantities which are larger andsmaller than the EOQ. These calculated costproved that the EOQ minimise the balance of

costs between inventory holding cost and re-

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llustration 6 (Graphical): EOQ

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Inventory Model

DO IT YOURSELF!!!

1. A company uses 100,000 units of EGper year which cost RM3 each. Carryingcosts are 1% per month and ordering costsare RM250 per order.

Currently, the company purchase this EGin batches of 7500 units each.

Suggest the best quantity order for thiscompany and explains the total cost savedby using EOQ.

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Inventory Model

DO IT YOURSELF!!!

A building materials supplier obtains its baggedcement from a single supplier. Demand is reasonablyconstant throughout the year and last year thecompany sold 2000 tones of this product. It estimatesthe cost of placing an order at around RM25 each time

an order is placed, and calculates that the annual costof holding inventory is 20% of purchase cost. Thecompany purchases the cement at RM60 per tone.How much should the company order at a time?

After calculating the EOQ the operations

manager feels that placing an order using EOQ

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Inventory Model

SOLUTION

312

0001002502

=

%

,

1111785.=

units11785

c

o

C

DC2EOQ

=

coEOQ C2qC

qDC += ( ) ( )360

211785250

11785000100 ., +=

302121342121 .. +=

644242RM .=

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co7500 C2

qC

q

DC += ( ) ( )360

2

7500250

7500

000100.

,+=

1350333333 += .

334683RM .=

Inventory Model

SOLUTION (cont.)

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EOQ with Discount


Unrealistic assumption with the basicEOQ assumption is that the price per

item remains constant Consider the costs associated with the

normal EOQ and compare these costs

with the costs at each succeedingdiscount point

Find the best quantity to order

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EOQ with Discount


Financial consequences of discountThree financial effect;

Saving comes from lower price per item The larger order quantity means that fewer orders

need to be placed so that total ordering costs arereduced.

Increased costs arise from the extra stockholdingcosts caused by the average stock level beinghigher due to the larger order quantity.

Bene

fit

Effect

Adve

rse

Effect

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alculating EOQ with Discount


1. Find EOQ using basic price

2. Compare the savings from the lower

price and ordering costs and the extrastock-holding at each discount point,with the costs associated with the basic

EOQ.- find various costs and savingcomparisons based on EOQ

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lustration 6: Equation with Discount A company uses a special bracket in the

manufacturer of its product which it orders fromoutside suppliers. The appropriate data are

Demand 2,000 per annum Order cost RM20 per order Carrying cost 15% of item price Basic item price RM10 per bracketThe company is offered the following discounts on

the basic price: For order quantities 400 700less 2%

800 1,599 less 4% 1,600 and over less 5%

What is the most economical quantity to order?

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No.

OrderQuantity

1. Discount

2. Average No. ofOrder perannum

3. Average No. ofOrder Saver

per annum

4. Ordering CostSaving perannum

5. Price Saving

lustration 6: Equation with DiscountEOQ 400 800 1600

Minimum quantity

entitled for each

discount rate

- 2% 4% 5%

78230

2000

.=

= 230

5400

2000= 52800

2000

.= 2511600

2000

.=

times73

578

.

.

=

times26

5278

.

..

=

times457

25178

.

..

=

Comparison

Quantity, EOQ

74RM

20RM73

=

.

124RM

20RM26

=

.

149RM

20RM457

=

.

400RM

D210RM

=

%

800RM

D410RM

=

%

1000RM

D510RM

=

%

474RM 924RM 1149RM

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No.

OrderQuantity

EOQ 400 800 1600

7. StockholdingCost perannum

8. AdditionalCostsIncurred by

IncreasedOrder

9. Net Gain/Loss

lustration 6: Equation with Discount

50172RM15

102

230

.%

=

294RM15

8092

400

=

%

.

576RM15

6092

800

=

%

.

1140RM15

5092

1600

=

%

.

50121RM

50172294

.

.

=

50403RM

50172576

.

.

=

50967RM

501721140

.

.

=

50352RM . 50520RM . 50181RM .

10 X 2% = RM0.2

Price after disc

= 10 0.20

= RM9.80

at is the most economical quantity to order?

Why?

1600 buckets

Company will saved RM710 due to discount offered (5%)

frequency of orders to made

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1015

2000202

=

%

94230.=

brackets230

c

o

C

DC2EOQ

=


lustration 6: Equation with Discount

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EOQ

DO IT YOURSELF!!! KABANA Bhd buy 100,000kg perannum of barites, a raw materials. Thecompany purchases this commodity inbatches of 2,000kg and pays RM10 per kg.The cost of ordering is estimated at Rm70

and the cost of holding each kg in stock isestimated at 10% of the purchase costs. Calculate the economic order quantity How much money would be saved by

ordering the EOQ rather than the present

week 13 eoq

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