A company begins a review of ordering policies for its continuous review system by checking the policies for a sample of SKUs. The following data are given to you.
Demand (D) = 64 units per week (assume 52 weeks per year)
Ordering cost (S) = $ 50 per order
Holding cost = $13 unit/year
Lead time (L) = 2 weeks
Standard Deviation of weekly demand = 12 units
Cycle-service level = 88%
a.	What is the EOQ for this item? 160
b.	What is the desired SS (safety stock)? 
c.	What is the reorder point?


Let's break down the calculations for each part:

### Given Data:
- Annual Demand $ D = 64 $ units/week × 52 weeks = $ 3328 $ units/year
- Ordering Cost $ S = 50 $ dollars per order
- Holding Cost $ H = 13 $ dollars per unit per year
- Lead Time $ L = 2 $ weeks
- Standard Deviation of Weekly Demand $ \sigma_d = 12 $ units
- Cycle-Service Level $ \text{CSL} = 88\% $

The Economic Order Quantity (EOQ) has been calculated as 160 units.

### b. Calculating Safety Stock (SS)

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

\[
SS = z \times \sigma_L
\]

where:
- $ z $ is the z-score for the desired cycle-service level,
- $ \sigma_L $ is the standard deviation of demand during lead time, calculated as:

\[
\sigma_L = \sigma_d \times \sqrt{L}
\]

1. **Find $ \sigma_L $:**
   \[
   \sigma_L = 12 \times \sqrt{2} = 12 \times 1.414 = 16.97 \approx 17
   \]

2. **Determine $ z $ for an 88% cycle-service level:**
   For a cycle-service level of 88%, we find the corresponding z-score from the z-table, which is approximately 1.175.

3. **Calculate $ SS $:**
   \[
   SS = 1.175 \times 17 \approx 20
   \]

Therefore, the **desired safety stock (SS) is 20 units**.

### c. Calculating the Reorder Point (ROP)

The reorder point (ROP) considers both the average demand during lead time and the safety stock:

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

where:
- $ d $ is the weekly demand, and
- $ L $ is the lead time in weeks.

1. **Calculate $ d \times L $:**
   \[
   d \times L = 64 \times 2 = 128
   \]

2. **Calculate $ ROP $:**
   \[
   ROP = 128 + 20 = 148
   \]

Therefore, the **reorder point (ROP) is 148 units**.

---

### Summary of Answers:
- **b. Safety Stock (SS):** 20 units
- **c. Reorder Point (ROP):** 148 units

Would you like further details on any part of the calculations?

### Related Questions
1. How would an increase in lead time impact the safety stock?
2. If the cycle-service level were raised to 95%, what would the new safety stock be?
3. How does demand variability affect the reorder point?
4. What is the impact on EOQ if the holding cost per unit changes?
5. How can the cycle-service level be balanced with cost considerations?

#### Tip:
For a continuous review system, frequently check both demand patterns and lead time variability, as changes in these factors can directly impact reorder points and safety stock.

A company begins a review of ordering policies for its continuous review system by checking the policies for a sample of SKUs. The following data are given to you.
Demand (D) = 64 units per week (assume 52 weeks per year)
Ordering cost (S) = $50 per order
Holding cost = $13 unit/year
Lead time (L) = 2 weeks
Standard Deviation of weekly demand = 12 units
Cycle-service level = 88%
a. What is the EOQ for this item? 160
b. What is the desired SS (safety stock)?
c. What is the reorder point?

Learn how to calculate Economic Order Quantity (EOQ), Safety Stock, and Reorder Point for a continuous review system with demand of 64 units per week, ordering cost of $50, and a cycle-service level of 88%. This problem covers key inventory management concepts, formulas, and statistical methods for accurate reorder planning.

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