week 13 eoq
TRANSCRIPT
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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
.2.6 Inventory Model
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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
2.6 Inventory Model (EOQ)
stration 3: Graphical Illustration ofEOQ
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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)
2.6 Inventory Model (EOQ)
stration 3: Graphical Illustration ofEOQ
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More units must be stored if more are ordered
Purchase Order
Description Qty.Microwave 1
Purchase Order
Description Qty.Microwave 1000
Order
quantity
hy Holding Cost Increase
Order
quantity
2.6 Inventory Model (EOQ)
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Cost is spread over more units
hy Order Cost Decrease
2.6 Inventory Model (EOQ)
PurchaseOrder
Description Qty.
Microwave 1
Purchase Order
Description Qty.
Microwave 1
PurchaseOrder
Description Qty.Microwave 1
Purchase Order
Description Qty.Microwave 1
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
2.6 Inventory Model (EOQ)
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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
2.6 Inventory Model (EOQ)
ustration 4: Economic Order Quantity
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2.6 Inventory Model (EOQ)
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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2.6 Inventory Model (EOQ)
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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2.6 Inventory Model (EOQ)
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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2.6 Inventory Model (EOQ)
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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2.6 Inventory Model (EOQ)
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
.2.6 Inventory Model
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
.2.6 Inventory Model
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
.2.6 Inventory Model
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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2.6 Inventory Model (EOQ)
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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2.6 Inventory Model (EOQ)
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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2.6 Inventory Model (EOQ)
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
=
2.6 Inventory Model (EOQ)
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