3/21: The Quantity Discount Model• Roll call, return homework, collect homework

• Review EOQ model

• Quantity Discount Model

• Small group exercise

• Homework

Review EOQ Model

• TC = Ann. Hold. Cost + Ann. Order Cost

• Ideal OrderQuantity(EOQ)

• Cycle Time

hC2

QAHC oC

Q

DAOC

h

o

C

CD2*Q

D

*Qyear/daysworkingT

EOQ Model: Curves• The EOQ will be the quantity that minimizes the

overall annual cost.

Holding cost curveMinimum

annual cost

Ann

ual C

ost

Order Quantity

Setup cost curve

Combined curve:holding + setup.

Optimal order quantity

Quantity Discount Model• Often, there are price breaks for ordering greater

quantities of a product.

• The formulas used to determine the EOQ remain, but…

Q1 Q2 Q3

C1

C2

C3

Quantity Discount Model• Often, there are price breaks for ordering greater

quantities of a product.

• EX: Q1 < 1000 units C1 = $4.03 1000 <= Q2 < 2000 C2 =

$4.00 2000 <= Q3 C3 = $3.97

Q1 Q2 Q3

C1

C2

C3

Quantity Discount Model• Calculate the Q* for each price.

• If the Q* is out of the range of the price level, use the nearest point possible.

• Calculate the total cost of the system (not just inventory system) to see which is lowest.– Must include the cost of product to compare!

Unit Costs vs. Total Cost of System

$19,800.00

$19,900.00

$20,000.00

$20,100.00

$20,200.00

$20,300.00

$20,400.00

$20,500.00

$20,600.00

0 500 1000 1500 2000 2500 3000

Order Quantity

To

tal C

os

t o

f In

ve

nto

ry S

ys

tem

C1

C2

C3

Example• You order a product that has a price break

offered:– Order less than 1000 $4.03 / unit– Order 1000 to less than 2000 $4.00 / unit– Order 2000 or more $3.97 / unit

• Your annual holding cost rate is 10%

• Your cost per order is $5.00

• Your annual requirement is 5,000 units.

see spreadsheet

Group Exercise• You order a high-demand software package that

has a price break offered:– Order less than 5 $169.00 / unit– Order 5 to less than 50 5% discount / unit– Order 50 to less than 100 8% discount / unit– Order 100 or more 10% discount / unit

• Your annual holding cost rate is 30%

• Your cost per order is $ 5.00

• Your annual requirement is 2,500 units.

Homework (due 4/4)• Ch. 11 #20, 21, 22 (show your work)

• You can use Excel to do this, or do it by hand. TURN IT IN ON PAPER REGARDLESS on 4/4.

• No class next week – Holy Thursday. Happy Easter!