Ruby owns a small café and uses a linen supplier for her tablecloths. Whenever she needs more tablecloths, she calls the supplier. She uses an average of 12 tablecloths a day with a standard deviation of 3 tablecloths. Lead time is a constant 2 days. If Ruby is willing to accept a 5% stockout risk, what is the reorder point, rounded to the nearest tablecloth? Assume demand is normally distributed.
A) 28
B) 31
C) 34
D) 42

Question

Quizplus · Accepted Answer

The reorder point (ROP) is calculated as the demand during lead time plus safety stock. The demand during lead time is the average daily demand multiplied by the lead time: $12 \text{ tablecloths/day} \times 2 \text{ days} = 24 \text{ tablecloths}$. To calculate the safety stock for a 5% stockout risk, we use the Z-score corresponding to 95% service level, which is approximately 1.645. The safety stock formula is $Z \times \sigma_{LT}$, where $\sigma_{LT}$ is the standard deviation of demand during lead time. Since demand is normally distributed, we can calculate $\sigma_{LT}$ as the daily standard deviation multiplied by the square root of the lead time: $3 \text{ tablecloths/day} \times \sqrt{2} \approx 4.24 \text{ tablecloths}$. Thus, safety stock is $1.645 \times 4.24 \approx 7 \text{ tablecloths}$. Adding this to the demand during lead time gives $24 + 7 = 31 \text{ tablecloths}$, rounded to the nearest tablecloth.

Ruby Owns a Small Café and Uses a Linen Supplier