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The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are D = 10,000 units, S= $75/order and I = 20% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost?

The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are D = 10,000 units, S= $75/order and I = 20% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are D = 10,000 units, S= $75/order and I = 20% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost? 

 

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**Understanding Inventory Management with Quantity Discounts** In this scenario, we explore an inventory management problem with the annual demand (\(D\)), ordering cost (\(S\)), and inventory carrying cost rate (\(I\)) for a particular item. The goal is to determine the optimal order quantity that minimizes total annual cost. Let's delve into the specifics: ### Problem Details: - **Annual Demand (\(D\)):** 10,000 units - **Ordering Cost (\(S\)):** $75 per order - **Inventory Carrying Cost Rate (\(I\)):** 20% of item price ### Quantity Discount Schedule: This discount schedule offers reduced prices for larger order quantities, as detailed below: | **Quantity** | **Price** | |--------------------|----------------| | 1 to 999 | $2.50/unit | | 1,000 to 4,999 | $2.30/unit | | 5,000 and up | $1.85/unit | ### Objective: To identify the order quantity that minimizes the total annual cost, which includes both ordering and holding costs considering the quantity discount. By evaluating different order quantities under these price brackets, the total cost can be computed to find the optimal strategy.
Transcribed Image Text:**Understanding Inventory Management with Quantity Discounts** In this scenario, we explore an inventory management problem with the annual demand (\(D\)), ordering cost (\(S\)), and inventory carrying cost rate (\(I\)) for a particular item. The goal is to determine the optimal order quantity that minimizes total annual cost. Let's delve into the specifics: ### Problem Details: - **Annual Demand (\(D\)):** 10,000 units - **Ordering Cost (\(S\)):** $75 per order - **Inventory Carrying Cost Rate (\(I\)):** 20% of item price ### Quantity Discount Schedule: This discount schedule offers reduced prices for larger order quantities, as detailed below: | **Quantity** | **Price** | |--------------------|----------------| | 1 to 999 | $2.50/unit | | 1,000 to 4,999 | $2.30/unit | | 5,000 and up | $1.85/unit | ### Objective: To identify the order quantity that minimizes the total annual cost, which includes both ordering and holding costs considering the quantity discount. By evaluating different order quantities under these price brackets, the total cost can be computed to find the optimal strategy.
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