Zainab 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 with respect to this pump's sales:
$\begin{array} { l l }
\text { Demand } = 5 \text { units per week } & \text { Store operates } 50 \text { weeks } / \text { year } \
\text { Order cost } = \$ 40 / \text { order } & \text { Lead time } = 3 \text { weeks } \
\text { Item cost } = \$ 80 / \text { pump } & \
\text { Inventory-holding cost } = 15 \% \text { per year } &
\end{array}$
-If Zainab decides to use a fixed-period system (FPS), the fixed-order interval based on store economics is:

Question

Zainab 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 with respect to this pump's sales:
$\begin{array} { l l } 
\text { Demand } = 5 \text { units per week } & \text { Store operates } 50 \text { weeks } / \text { year } \
\text { Order cost } = \$ 40 / \text { order } & \text { Lead time } = 3 \text { weeks } \
\text { Item cost } = \$ 80 / \text { pump } & \
\text { Inventory-holding cost } = 15 \% \text { per year } &
\end{array}$
-If Zainab decides to use a fixed-period system (FPS), the fixed-order interval based on store economics is:

Quizplus · Accepted Answer

In a fixed-period system (FPS), the order interval is determined by balancing ordering costs and holding costs to minimize total inventory costs. Given the data, we can calculate the inventory holding cost per unit per year as $15\% \times \$80 = \$12$. Since the store operates 50 weeks a year and demand is 5 units per week, the annual demand is $5 \times 50 = 250$ units. The order cost is given as \$40. To find the optimal order quantity (EOQ) which minimizes total costs in an FPS, we use the EOQ formula: $\sqrt{\frac{2DS}{H}}$, where $D$ is the demand, $S$ is the ordering cost, and $H$ is the holding cost per unit per year. Substituting the given values, we get $\sqrt{\frac{2 \times 250 \times 40}{12}}$, which simplifies to a quantity that suggests an order interval that balances between ordering too frequently and holding too much inventory, typically resulting in an interval of more than 5 weeks but less than or equal to 10 weeks, considering the operational and economic constraints of the store. This interval allows for efficient inventory management without excessive holding costs or frequent reordering costs.

Zainab Opens an Aquarium Store in a Lively Shopping Mall