### Document

```BA 301
Operations Management
Spring 2003
Inventory Management
Chapter 12
Quantity Discounts
Determining the
Order Size
for Part A-63 (40-Gig Hard Drive)
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We have 3 suppliers for the 40-Gig hard
drive: Intel, Micron, and Minnesota Data
Products.
All three suppliers have quoted a price of \$70
per hard drive.
All three quote a 5-day delivery time.
We want to determine the amount to order
each time we place an order.
We also want to determine when to place an
order, aka the “reorder point”.
Types of Inventory
 Raw
material
Work-in-progress (WIP)
 Maintenance/repair/operating supply
 Finished goods

Order Quantity for the 40 Gig Hard
Drive
We forecast a demand for 2003 of the
40-Gig hard drives (Part A-63) during
the coming year. (D = 2000)
 Our ordering cost each time we place
and order is \$200. (S = 200)
 Our inventory holding cost/year is 25%
of the item cost. (H = 0.25 P)
 All of the assumptions for the EOQ
model hold.
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Calculating the Order Quantity
using EOQ
EOQ = square root (2D*S/H)
EOQ = sq rt (2*2000*200/0.25*70)
EOQ = 214 (rounded)
 To minimize the annual inventory costs
for the A-63 (40-Gig hard drive), we
would buy in order quantities of 214.

Calculating the
Total Annual Inventory Cost
TAIC = Annual Holding Cost +
Annual Ordering Cost
 TAIC = (Q/2)H + (D/Q)S
 TAIC = (214/2)*17.50 + (2000/214)*200
 TAIC = 1872.50 + 1869.16 = \$3741.66
 Notice that the AHC and AOC are
almost the same.

At the Optimal Order Quantity,
Annual Holding Costs=Annual Order Costs
Annual Cost
Order (Setup) Cost Curve
Optimal
Order Quantity (Q*)
Order Quantity
Determining the Reorder Point
We want to “reorder” raw material items
so that we don’t run out of the item
 Our “lead time” with the suppliers of
part A-63 (40-Gig hard drive) is 5 days.
 At what inventory level do we need to
reorder so that we won’t run out while
the order is in process?
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EOQ Model
“Reorder Point”
Inventory Level
Average
Inventory
(Q*/2)
Optimal
Order
Quantity
(Q*)
Reorder
Point
(ROP)
Time
Determining the Reorder Point
To calculate the Reorder Point, we
have to calculate the demand during
lead time (DDLT), i.e. the amount we
will use during the five days that the
shipment will take to receive after we
have placed the order.
 DDLT = Demand per Day * Lead Time
 D = 2000, WDPY = 250,
 Demand per Day = 8
 DDLT = 8 * 5 = 40 = Reorder Point
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Calculating Order Size
with Quantity Discounts
Minnesota Data Products has sent us
the following price information for part
A-63, the 40 Gig Hard Drive
 Order Quantity
Price each
1 – 299
\$70.00
300 – 999
67.50
1000 & over
66.50
 How does this change our Order Size?
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Since we have Quantity Discounts, the EOQ
becomes the starting point for determining
order size
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First, calculate the EOQ for each “Price”.
Next, we determine which EOQ is feasible.
Order Oty. Price
H
EOQ
1 – 299 \$70.00 \$17.50
300 – 999
67.50 16.875
1000 & +
66.50
16.62
Feasible?
Finding the order quantity that minimizes
TAC
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Order Oty. Price
H
1 – 299 \$70.00 \$17.50
300 – 999
67.50 16.875
1000 & +
66.50
16.625
EOQ
214
218
219
Feasible?
Yes
No
No
Now, calculate the Total Annual Costs for the “feasible”
EOQ:
TAC = AHC + AOC + Product Cost
= (214/2)17.5 + (2000/214)200 + 2000(70)
= \$1,872.50 + \$1,869.16 + \$140,000
= \$143,741.66
Finding the order quantity that minimizes
TAC

Determine if there are any lower price options than the
“feasible” EOQ. If so, calculate the TAC for the lower
price option, using the minimum order size necessary
to obtain that price.
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Price = \$67.50
Price = \$66.50
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Chose the order quantity that minimizes TAC!
Order Qty = 300
Order Qty = 1000
TAC = ?
TAC = ?
Finding the order quantity that minimizes TAC
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Price = \$67.50 Order Qty = 300
TAC = (300/2)16.875 + (2000/300)200 + (2000)67.50
= 2,531.25 + 1,333.33 +135,000
= \$138,864.58

Price = \$66.50 Order Qty = 1000
TAC = (1000/2)16.625 + (2000/1000)200 + (2000)66.50
= 8,312.5 + 400 + 132,000
= \$141,712.50
What order size would you choose?
Other Options?
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```