Kelly opens an aquarium store in a lively shopping mall and finds business to be booming, but she often stocks out of key items customers want. She decides to experiment with inventory control methods such as using a fixed order quantity (FQS) and/or fixed order period (FPS) systems. The Fluval 303 pump, a high margin and profitable pump, is one of her best sellers, but it stocks out frequently. She collects the following data about the pump's sales.
$\begin{array} { l l }
\text { Demand } = 10 \text { units per week } & \text { Store operates } 45 \text { weeks } / \text { year } \
\text { Order cost } = \$ 30 / \text { order } & \text { Lead time } = 3 \text { weeks } \
\text { Item cost } = \$ 80 / \text { pump } & \text { Standard deviation of weekly demand } = 4 \text { units } \
\text { Inventory-holding cost } = 15 \% \text { per year } & \text { Desired service level } = 90 \text { percent }
\end{array}$
-The reorder point with safety stock rounded to the next highest whole number is:

Question

Kelly opens an aquarium store in a lively shopping mall and finds business to be booming, but she often stocks out of key items customers want. She decides to experiment with inventory control methods such as using a fixed order quantity (FQS) and/or fixed order period (FPS) systems. The Fluval 303 pump, a high margin and profitable pump, is one of her best sellers, but it stocks out frequently. She collects the following data about the pump's sales.
$\begin{array} { l l } 
\text { Demand } = 10 \text { units per week } & \text { Store operates } 45 \text { weeks } / \text { year } \
\text { Order cost } = \$ 30 / \text { order } & \text { Lead time } = 3 \text { weeks } \
\text { Item cost } = \$ 80 / \text { pump } & \text { Standard deviation of weekly demand } = 4 \text { units } \
\text { Inventory-holding cost } = 15 \% \text { per year } & \text { Desired service level } = 90 \text { percent }
\end{array}$
-The reorder point with safety stock rounded to the next highest whole number is:

Quizplus · Accepted Answer

The reorder point (ROP) is calculated as the demand during lead time plus safety stock. Demand during lead time is 10 units/week * 3 weeks = 30 units. Safety stock is calculated using the formula: $Z \times \sigma \times \sqrt{L}$, where $Z$ is the Z-score for the desired service level (1.28 for 90%), $\sigma$ is the standard deviation of demand, and $L$ is the lead time. Safety stock = 1.28 * 4 * √3 ≈ 9 units. Therefore, ROP = 30 + 9 = 39 units, which rounds to 40 units.

Kelly Opens an Aquarium Store in a Lively Shopping Mall