# Economic Order Quantity: Order quantity

1. XYZ company would like to pursue the optimal quantity based on the situation that a supplier of a particular raw material is offering at five different prices, depending on the size of the order.

0 < Q < = 300 pounds => $20 per pound

300 < Q < = 600 pounds => 3% discount from the original price

600 < Q < = 1000 pounds => 5% discount from the original price

1000 < Q < = 5000 pounds => 10% discount from the original price

> 5000 pounds => 15% discount from the original price

The cost of placing an order is $40. Annual demand is 3,000 pounds. Holding cost is 25 percent of the material price.

a. What replenishment size should be used? Show all possible total costs.

b. If the supplier improves the discount rate of the 600 < Q <= 1000 pounds from 5% discount to 9% discount, would the replenishment size change?

c. Continuing from part b, at what price will ordering at lot size 5000 or more be more attractive than ordering at lot size <= 5000?

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#### Solution Summary

This posting contains solution to following problem on Inventory models: quantity discount model.

Economic Order Quantity (EOQ), Ordering Costs, and Average Cycle Stock

Monthly demand for an inventory item currently averages 160 units. The annual carrying cost is $10 per unit. Ordering cost is $60 per order. This information applies to all of the questions on this page.

Find the EOQ. Please show the formula (with values) you used.

2.Suppose instead of using the EOQ, we decide to use Q = 200 for the item in the question above.

What is the average cycle stock inventory under this policy? Show your work and clearly label your answer.

3.

Suppose instead of using the EOQ, we decide to use Q = 200 for the item in the question above.

What is the average number of orders per year under this policy? Show your work and clearly label your answer.

4.

Suppose instead of using the EOQ, we decide to use Q = 200 for the item in the question above.

What is the average annual ordering cost under this policy? Show your work and clearly label your answer.

5.

Suppose instead of using the EOQ, we decide to use Q = 200 for the item in the question above.

What is the average annual carrying cost under this policy? Show your work and clearly label your answer.