Appendix $11$A

Economic Order Quantity

Objective

Derive the economic order quantity $($EOQ$)$ formula.

Analysis:

Given an annual demand $D,$ order cost $S,$ unit cost $C,$ and annual holding cost $h,$ our goal is to estimate the lot size $Q$ that minimizes the total annual cost. For a lot size of $Q,$ the total annual cost is given by

Total annual cost, $TC=(\frac{D}{Q})S+(\frac{Q}{2})hC+CD$

To minimize the total cost, we take the first derivative with respect to the lot size $Q$ and set it to zero. Taking the first derivative with respect to $Q,$ we have

$d(TC)dQ=DSQ2+hC2$

Setting the first derivative to be zero, the EOQ is given by

$Q2=2$DShCorQ:$x=2DShC$