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426 CHAPTER 10 INVENTORY MODELS

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Q ¼ ¼ 700
1
DISCOUNT ð0:20Þð5:00Þ
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Q ¼ ¼ 711
2 ð0:20Þð4:85Þ
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Q ¼ ¼ 718
3 ð0:20Þð4:75Þ
Because the only differences in the EOQ formulas come from slight differences in
the holding cost, the economic order quantities resulting from this step will be
approximately the same. However, these order quantities will usually not all be of
the size necessary to qualify for the discount price assumed. In the preceding case,
both Q 2 and Q 3 are insufficient order quantities to obtain their discounted costs of
*
*
E4.85 and E4.75, respectively. For those order quantities for which the assumed
price cannot be obtained, the following procedure must be used.
Step 2. For the Q* that is too small to qualify for the assumed discount price,
adjust the order quantity upward to the nearest order quantity that will
allow the product to be purchased at the assumed price.

In our example, this adjustment causes us to set:

Q ¼ 1000
2
and

Q ¼ 2500
3
Problem 14 at the end of If a calculated Q* for a given discount price is large enough to qualify for a bigger
the chapter asks you to discount, that value of Q* cannot lead to an optimal solution. Although the reason
show that this property is
true. may not be obvious, it does turn out to be a property of the EOQ quantity discount
model.
In the previous inventory models considered, the annual purchase cost of the item
was not included because it was constant and never affected by the inventory order
policy decision. However, in the quantity discount model, the annual purchase cost
depends on the order quantity and the associated unit cost. So, annual purchase cost
(annual demand D unit cost C) is included in the equation for total cost as shown
here.
In the EOQ model with
quantity discounts, the Q D
annual purchase cost TC ¼ 2 C h þ Q C o þ DC (10:28)
must be included
because purchase cost
depends on the order
quantity. So, it is a Using this total cost equation, we can determine the optimal order quantity for
relevant cost. the EOQ discount model in step 3.
Step 3. For each order quantity resulting from steps 1 and 2, calculate the total
annual cost using the unit price from the appropriate discount category
and equation (10.28). The order quantity yielding the minimum total
annual cost is the optimal order quantity.
The step 3 calculations for the example problem are summarized in Table 10.4. As
you can see, a decision to order 1000 units at the 3 per cent discount rate yields the
minimum cost solution. Even though the 2500-unit order quantity would result in a
Problem 13 will give you 5 per cent discount, its excessive holding cost makes it the second-best solution.
practise in applying the
EOQ model to situations Figure 10.7 shows the total cost curve for each of the three discount categories.
with quantity discounts. Note that Q* ¼ 1000 provides the minimum cost order quantity.

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