Operations Management: Processes and Supply Chains, 12th Edition

Solved Problem 3

Nelson’s Hardware Store stocks a 19.2-volt cordless drill that is a popular seller. Annual demand is 5,000 units, the ordering cost is $15, and the inventory holding cost is $4/unit/year.

1. What is the economic order quantity?

2. What is the total annual cost for this inventory item?

Solution

1. The order quantity is

   $$\begin{array}{lll}\text{ EOQ}\hfill & =\hfill & \sqrt{\frac{2DS}{H}}=\sqrt{\frac{2\left(5,000\right)\left(\text{\$}15\right)}{\text{\$}4}}=\sqrt{37,500}\hfill \\ \hfill & =\hfill & 193.65,\text{ or }194\text{ drills}\hfill \end{array}$$

2. The total annual cost is

   $$C=\frac{Q}{2}\left(H\right)+\frac{D}{Q}\left(S\right)=\frac{194}{2}\left(\text{\$}4\right)+\frac{5,000}{194}\left(\text{\$}15\right)=\text{\$}774.60$$