Discussion
A company orders gears in conditions identical to those considered in the economic order quantity (EOQ) model in inventory control. The annual demand is 8000 gears, the cost per order is 300 rupees, and the holding cost is 12 rupees per month per gear. The company uses an order size that is 25% more than the optimal order quantity determined by the EOQ model. The percentage change in the total cost of ordering and holding inventory from that associated with the optimal order quantity is
Answer: A
The total cost rises by 2.5%.
In the EOQ model the total of ordering and holding cost, as a fraction of its minimum, depends only on the ratio of the order size to the optimal size \(Q^{*}\):
\[ \begin{aligned} \frac{TC(Q)}{TC(Q^{*})} &= \frac{1}{2}\left(\frac{Q}{Q^{*}} + \frac{Q^{*}}{Q}\right) \\ &= \frac{1}{2}\left(1.25 + 0.8\right) = 1.025 \end{aligned} \]
so the cost is 2.5% higher. The demand and cost figures fix \(Q^{*}\) (about 183 gears with a holding cost of 144 rupees per gear per year), but the percentage change does not depend on them. The cost curve is flat near its minimum, which is why a 25% error in order size costs only 2.5%; 12.5% is half the 25% change in order size and ignores that flatness, and 0 or 5% do not follow from the formula.
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