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Quantity Discount ModelsQuantity Discount Models

To increase sales, companies offer quantitydiscounts to customers

Quantity discount is simply reduced cost foritem when purchased in larger quantities

Quantity discounts, which are price incentivesto purchase large quantities, create pressure tomaintain a large inventory

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ExampleExample

A supplier forSt. Roy Hospital has introduced quantitydiscounts to encourage larger order quantities of aspecial catheter. The price schedule is

Order Quantity Price per Unit

0 299 $60.00300 499 $58.80500 or more $57.00

Annual demand (D) = 936 unitsOrdering cost (S) = $45

Holding cost (H) = 25% of unit price

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Finding EOQFinding EOQwith Quantity Discountswith Quantity Discounts

Step 1. Beginning with the lowestprice,calculate the EOQ for each price level until afeasible EOQ is found.

It is feasible if it lies in the range corresponding to its price. Step 2. If the first feasible EOQ found is for the

lowest price level, this quantity is the best lotsize. Otherwise, calculate the total cost for the first feasible EOQ and

for the larger price break quantity at each lower price level. Thequantity with the lowest total cost is optimal.

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Step 1: Start with lowest price level:

EOQEOQ 57.0057.00 ==22DSDS

HH

2(936)(45)2(936)(45)

0.25(0.25(57.0057.00))== = 77 units= 77 units

Not feasible

EOQEOQ 58.8058.80 ==22DSDS

HH

2(936)(45)2(936)(45)

0.25(0.25(58.8058.80))== = 76 units= 76 units

Not feasible

EOQEOQ 60.0060.00 ==22DSDS

HH

2(936)(45)2(936)(45)

0.25(0.25(60.0060.00))== = 75 units= 75 units

Feasible

This quantity is feasible because it lies in the range corresponding to its price.

Order Quantity Price per Unit

0 299 $60.00300 499 $58.80

500 or more $57.00

Annual demand (Annual demand (DD) = 936 units) = 936 unitsOrdering cost (Ordering cost (SS) = $45) = $45

Holding cost (Holding cost (HH) = 25% of unit price) = 25% of unit price

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Step 2: The first feasible EOQ of 75 does not correspond to thelowest price level. Hence, we must compare its total cost withthe price break quantities (300 and 500 units) at the lower price

levels ($58.80 and $57.00):

CC= (= (HH) + () + (SS) +) + PPDDQQ

22

DD

QQ

CC7575 = [(= [(0.25)($60.000.25)($60.00)] + ($45) + $60.00()] + ($45) + $60.00(936936))757522

936936

7575 CC7575 = $57,284= $57,284

CC300300 = [(0.25)($58.80)] + ($45) + $58.80(936)= [(0.25)($58.80)] + ($45) + $58.80(936)300300

22

936936

300300= $57,382= $57,382

CC500500 = [(0.25)($57.00)] + ($45) + $57.00(936)= [(0.25)($57.00)] + ($45) + $57.00(936)50050022

936936500500

= $56,999= $56,999

The best purchase quantity is 500 units, which qualifies for the deepest

discount.

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Quantity Discount Example 2Quantity Discount Example 2

DiscountNumber Discount Quantity Discount (%)

DiscountPrice (P)

1 0to 999 no discount $5.00

2 1,000to 1,999 4 $4.80

3 2,000and over 5 $4.75

Table 12.2Table 12.2

A typical quantity discount scheduleA typical quantity discount schedule

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Ordering costs = $49 per order

Annual demand is 5000 cars

Inventory carrying charge is I is 20% or .2(I holding cost as percentage of Unit Price)

Example 2Example 2

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STEP 1STEP 1

Calculate Q* for every discountCalculate Q* for every discount

QQ11**= = 700= = 700 cars ordercars order2(5,000)(49)2(5,000)(49)(.2)(5.00)(.2)(5.00)

QQ22**= = 714= = 714 cars ordercars order2(5,000)(49)2(5,000)(49)

(.2)(4.80)(.2)(4.80)

QQ33**= = 718= = 718 cars ordercars order2(5,000)(49)2(5,000)(49)

(.2)(4.75)(.2)(4.75)

1,0001,000 adjustedadjusted

2,0002,000 adjustedadjusted

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STEP2STEP2

DiscountNumber

UnitPrice

OrderQuantity

AnnualProduct

Cost

AnnualOrdering

Cost

AnnualHolding

Cost Total

1 $5.00 700 $25,000 $350 $350 $25,700

2 $4.80 1,000 $24,000 $245 $480 $24,725

3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50

Table 12.3Table 12.3

Choose the price and quantity that givesChoose the price and quantity that givesthe lowest total costthe lowest total cost

BuyBuy1,0001,000 units atunits at$4.80$4.80per unitper unit