CC Rainger is a business to business distributor of MRO (maintain, repair and operate) products. They have more than 300 retail stores that they serve from a central warehouse. The company uses a 98% service level calculated on the proportion that can be satisfied directly from stock (demand fill rate). The cost for placing an order is $100 and the annual holding cost is 20%. They work 365 days/year.

Item property	 Data value
Lead time from supplier	 14 days
Lead time to Retailer	3 days
Internal price	$25
Daily demand	75 units
σ, Standard deviation during lead time	103 units
Inventory carrying cost	20%

a. How much is the Economic Order Quantity (EOQ)
b. What Safety Stock level does the company need to reach the desired service level?
c. What Re-Order Point (ROP) level does the company need to reach the desired service level?

To solve the problem, we need to apply the following formulas:

### Part A: Economic Order Quantity (EOQ)

The Economic Order Quantity (EOQ) is given by the formula:

\[
EOQ = \sqrt{\frac{2DS}{H}}
\]

Where:
- $D$ is the annual demand.
- $S$ is the cost per order.
- $H$ is the annual holding cost per unit.

Given:
- Daily demand = 75 units
- Number of working days = 365 days
- Annual demand, $D = 75 \times 365$ units
- Order cost, $S = \$100$
- Holding cost percentage = 20% of the internal price
- Internal price per unit = \$25

First, calculate the annual holding cost per unit $H$:

\[
H = 0.20 \times 25 = \$5 \text{ per unit per year}
\]

Then, calculate the annual demand $D$:

\[
D = 75 \times 365 = 27,375 \text{ units per year}
\]

Now, we can calculate the EOQ:

\[
EOQ = \sqrt{\frac{2 \times 27375 \times 100}{5}} = \sqrt{\frac{5475000}{5}} = \sqrt{1095000} \approx 1046.42 \text{ units}
\]

### Part B: Safety Stock Level

To calculate the Safety Stock (SS), we use the formula:

\[
SS = Z \times \sigma_L
\]

Where:
- $Z$ is the Z-score corresponding to the desired service level (98% service level, $Z \approx 2.05$)
- $\sigma_L$ is the standard deviation of demand during the lead time.

Given:
- $\sigma$ during lead time = 103 units
- Lead time from supplier = 14 days

The Safety Stock is:

\[
SS = 2.05 \times 103 \approx 211.15 \text{ units}
\]

### Part C: Reorder Point (ROP)

The Reorder Point (ROP) is given by the formula:

\[
ROP = d \times L + SS
\]

Where:
- $d$ is the daily demand.
- $L$ is the lead time in days (sum of lead time from supplier and to retailer).

Given:
- $L$ (Total lead time) = 14 + 3 = 17 days
- Daily demand, $d = 75$ units
- Safety Stock, $SS = 211.15$ units

The ROP is:

\[
ROP = 75 \times 17 + 211.15 = 1275 + 211.15 = 1486.15 \text{ units}
\]

### Summary of Results:
a. **EOQ** = 1046.42 units  
b. **Safety Stock** = 211.15 units  
c. **Reorder Point (ROP)** = 1486.15 units

Do you want more details on any of these steps or have any other questions?

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**Related Questions:**
1. How would the EOQ change if the order cost increases?
2. What would be the impact on safety stock if the service level is increased to 99%?
3. How does a higher standard deviation in demand affect the reorder point?
4. Can you explain the relationship between holding cost and EOQ?
5. How would changes in lead time affect the reorder point?
6. What happens to EOQ if the daily demand doubles?
7. How can the company reduce its safety stock while maintaining the same service level?
8. What alternative methods can be used to calculate reorder points besides the given formula?

**Tip:** Regularly reviewing and adjusting your safety stock levels can help in maintaining optimal inventory levels and avoiding stockouts.

Learn how to calculate Economic Order Quantity (EOQ), Safety Stock, and Reorder Point for CC Rainger, a business distributing MRO products across 300 retail stores. Solve using formulas and detailed calculations for inventory management optimization.

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