•• 12.15 the course of a year. These brackets are purchased from a supplier 90 miles away. The following information is known about the brackets: Joe Henry's machine shop uses 2,500 brackets during Annual demand: 2,500 Holding cost per bracket per year: $1.50 Order cost per order: $18.75 Lead time: 2 days Working days per year: 250 a) Given the above information, what would be the economic order quantity (EOQ)? b) Given the EOQ, what would be the average inventory? What would be the annual inventory holding cost?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Can you assist me with Question 12.15 . Please right out the steps it's easier to understand verses on the excel spreadsheet. If you do it in excel can you make it easy to follow along to. Thank you kindly.
**Section 12.15**

Joe Henry’s machine shop utilizes 2,500 brackets annually. These brackets are sourced from a supplier located 90 miles away. Below is the detailed information regarding the brackets:

| **Parameter**                       | **Value**     |
|-------------------------------------|---------------|
| Annual demand                       | 2,500 units   |
| Holding cost per bracket per year   | $1.50         |
| Order cost per order                | $18.75        |
| Lead time                           | 2 days        |
| Working days per year               | 250 days      |

**Questions:**

a) Based on the information provided, calculate the Economic Order Quantity (EOQ).

b) Once the EOQ is determined, what would be the average inventory? Additionally, compute the annual inventory holding cost.

**Explanation for Educational Content:**

- **Annual Demand**: The total quantity of brackets needed in a year (2,500 units).
- **Holding Cost**: The cost to hold a single bracket in inventory for a year ($1.50).
- **Order Cost**: The cost to place a single order for brackets ($18.75).
- **Lead Time**: The time taken from placing an order until receipt of the brackets (2 days).
- **Working Days**: The number of working days per year (250 days), which affects inventory planning and lead time calculation.

### [EOQ Formula and Explanation]

The EOQ can be calculated using the formula:

\[ EOQ = \sqrt{\frac{{2 \times \text{Annual Demand} \times \text{Order Cost}}}{{\text{Holding Cost per unit}}}} \]

This formula helps in determining the optimal order quantity that minimizes the total inventory costs, balancing both ordering and holding costs.

### [Average Inventory and Holding Cost Calculation]

The average inventory is half of the EOQ, which represents typical inventory levels throughout the ordering cycle.

\[ \text{Average Inventory} = \frac{\text{EOQ}}{2} \]

The annual inventory holding cost can be determined by multiplying the average inventory by the holding cost per unit.

\[ \text{Annual Holding Cost} = \text{Average Inventory} \times \text{Holding Cost per unit} \]

These computations are vital for optimizing inventory management and ensuring cost-efficiency in operations.
Transcribed Image Text:**Section 12.15** Joe Henry’s machine shop utilizes 2,500 brackets annually. These brackets are sourced from a supplier located 90 miles away. Below is the detailed information regarding the brackets: | **Parameter** | **Value** | |-------------------------------------|---------------| | Annual demand | 2,500 units | | Holding cost per bracket per year | $1.50 | | Order cost per order | $18.75 | | Lead time | 2 days | | Working days per year | 250 days | **Questions:** a) Based on the information provided, calculate the Economic Order Quantity (EOQ). b) Once the EOQ is determined, what would be the average inventory? Additionally, compute the annual inventory holding cost. **Explanation for Educational Content:** - **Annual Demand**: The total quantity of brackets needed in a year (2,500 units). - **Holding Cost**: The cost to hold a single bracket in inventory for a year ($1.50). - **Order Cost**: The cost to place a single order for brackets ($18.75). - **Lead Time**: The time taken from placing an order until receipt of the brackets (2 days). - **Working Days**: The number of working days per year (250 days), which affects inventory planning and lead time calculation. ### [EOQ Formula and Explanation] The EOQ can be calculated using the formula: \[ EOQ = \sqrt{\frac{{2 \times \text{Annual Demand} \times \text{Order Cost}}}{{\text{Holding Cost per unit}}}} \] This formula helps in determining the optimal order quantity that minimizes the total inventory costs, balancing both ordering and holding costs. ### [Average Inventory and Holding Cost Calculation] The average inventory is half of the EOQ, which represents typical inventory levels throughout the ordering cycle. \[ \text{Average Inventory} = \frac{\text{EOQ}}{2} \] The annual inventory holding cost can be determined by multiplying the average inventory by the holding cost per unit. \[ \text{Annual Holding Cost} = \text{Average Inventory} \times \text{Holding Cost per unit} \] These computations are vital for optimizing inventory management and ensuring cost-efficiency in operations.
**Chapter 12: Inventory Management**

Page 521

c) Given the EOQ, how many orders would be made each year? What would be the annual order cost?  

d) Given the EOQ, what is the total annual cost of managing the inventory?  

e) What is the time between orders?  

f) What is the reorder point (ROP)?  

Note: "EOQ" stands for Economic Order Quantity, a model used in inventory management to determine the optimal order quantity that minimizes total inventory costs. "ROP" or Reorder Point is the inventory level at which a new order should be placed to replenish stock before it runs out.
Transcribed Image Text:**Chapter 12: Inventory Management** Page 521 c) Given the EOQ, how many orders would be made each year? What would be the annual order cost? d) Given the EOQ, what is the total annual cost of managing the inventory? e) What is the time between orders? f) What is the reorder point (ROP)? Note: "EOQ" stands for Economic Order Quantity, a model used in inventory management to determine the optimal order quantity that minimizes total inventory costs. "ROP" or Reorder Point is the inventory level at which a new order should be placed to replenish stock before it runs out.
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