​Ruby-Star Incorporated is considering two different vendors for one of its​ top-selling products which has an average weekly demand of 30
 
units and is valued at ​$90
 
per unit. Inbound shipments from vendor 1 will average 380
 
units with an average lead time​ (including ordering delays and transit​ time) of 5
 
weeks. Inbound shipments from vendor 2 will average 460
 
units with an average lead time of 3
 
weeks
. 
​Ruby-Star operates 52 weeks per​ year; it carries a 5
​-week 
supply of inventory as safety stock and no anticipation inventory.
Part 2
a. The average aggregate inventory value of the product if​ Ruby-Star used vendor 1 exclusively is ​$enter your response here
. 
​(Enter your response as a whole number.​)

To calculate the **average aggregate inventory value**, we need to account for the following components of inventory:

1. **Cycle stock**: The average inventory on hand during the replenishment cycle, calculated as:
   \[
   \text{Cycle Stock} = \frac{\text{Order Quantity}}{2}
   \]

2. **Pipeline inventory**: The inventory in transit, calculated as:
   \[
   \text{Pipeline Inventory} = \text{Demand per Week} \times \text{Lead Time}
   \]

3. **Safety stock**: This is a fixed value equal to:
   \[
   \text{Safety Stock} = \text{Demand per Week} \times \text{Safety Weeks}
   \]

Finally, the **average aggregate inventory value** is:
\[
\text{Aggregate Inventory Value} = (\text{Cycle Stock} + \text{Pipeline Inventory} + \text{Safety Stock}) \times \text{Value per Unit}
\]

---

### Step 1: Determine the inputs for Vendor 1
- Weekly demand ($D$) = 30 units
- Order quantity ($Q$) = 380 units
- Lead time ($L$) = 5 weeks
- Value per unit ($V$) = $90
- Safety stock weeks = 5 weeks

---

### Step 2: Calculate the components of inventory
1. **Cycle Stock**:
   \[
   \text{Cycle Stock} = \frac{Q}{2} = \frac{380}{2} = 190 \, \text{units}
   \]

2. **Pipeline Inventory**:
   \[
   \text{Pipeline Inventory} = D \times L = 30 \times 5 = 150 \, \text{units}
   \]

3. **Safety Stock**:
   \[
   \text{Safety Stock} = D \times \text{Safety Weeks} = 30 \times 5 = 150 \, \text{units}
   \]

---

### Step 3: Calculate the total average inventory
\[
\text{Total Inventory} = \text{Cycle Stock} + \text{Pipeline Inventory} + \text{Safety Stock} = 190 + 150 + 150 = 490 \, \text{units}
\]

---

### Step 4: Calculate the average aggregate inventory value
\[
\text{Aggregate Inventory Value} = \text{Total Inventory} \times V = 490 \times 90 = 44,100
\]

---

### Final Answer:
The **average aggregate inventory value** if Ruby-Star uses vendor 1 exclusively is **$44,100**.

---

Would you like assistance with calculations for Vendor 2 or other related parts? Here are some follow-up questions to consider:

1. How does the calculation change for Vendor 2?
2. What are the total costs of inventory for each vendor when including holding costs?
3. How does safety stock affect the inventory values for each vendor?
4. What are the operational implications of choosing a vendor with a shorter lead time?
5. How would changes in demand (e.g., an increase to 40 units per week) affect these calculations?

**Tip:** Shorter lead times typically reduce the need for pipeline inventory, lowering aggregate inventory values.

Ruby-Star Incorporated is considering two different vendors for one of its top-selling products which has an average weekly demand of 30 units and is valued at $90 per unit. Inbound shipments from vendor 1 will average 380 units with an average lead time (including ordering delays and transit time) of 5 weeks. Inbound shipments from vendor 2 will average 460 units with an average lead time of 3 weeks. Ruby-Star operates 52 weeks per year; it carries a 5-week supply of inventory as safety stock and no anticipation inventory. Part 2a. The average aggregate inventory value of the product if Ruby-Star used vendor 1 exclusively is $____.

Learn how to calculate the average aggregate inventory value for Ruby-Star Incorporated when selecting between two vendors. This problem explores key inventory management concepts, including cycle stock, pipeline inventory, and safety stock, with real-world data such as weekly demand of 30 units and a $90 unit value. Ideal for students and professionals in Grades 11-12 and college-level supply chain courses.

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