Discussion
If orders are placed with the size determined by the economic order quantity, the re-order costs component is :
Answer: A
At the economic order quantity the re-order cost component is equal to the holding cost component.
With annual demand D, cost per order \(C_{o}\) and holding cost \(C_{h}\) per unit per year, ordering Q at a time costs
\[ TC(Q) = \frac{D}{Q}C_{o} + \frac{Q}{2}C_{h} \]
Setting \(TC'(Q) = 0\) gives \(\dfrac{DC_{o}}{Q^{2}} = \dfrac{C_{h}}{2}\), so \(\dfrac{D}{Q}C_{o} = \dfrac{Q}{2}C_{h}\): at \(Q^{*} = \sqrt{2DC_{o}/C_{h}}\) the two components are exactly equal.
Ordering more than the EOQ makes holding cost the larger component, and ordering less makes re-order cost the larger, which is why the other options describe non-optimal order sizes.
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