Question

In: Operations Management

A supplier offers you the following discount table for the purchase of your main product, whose...

A supplier offers you the following discount table for the purchase of your main product, whose annual demand you have estimated at 5,000 units. The cost of issuing a purchase order is $ 49, and it has also been estimated that the annual cost of storing a unit in inventory is 20% of the cost of purchasing the product. What is the order quantity that minimizes the total cost of inventory?

Q ( Cantidad)	Discount %	Costo Unitario
0 - 999	0 %	5
1 000 - 1 999	2 %
2 000 o más	3 %

Expert Solution

Answer: 1000 units

Explanation:

Annual Demand (D) = 5000

Price per unit (P) =(1 - Discount %/100)*5

Annual Holding Cost per unit = 20% of P

Cost per order (S) = $49

EOQ = SQRT(2*S*D/H)

If EOQ > the upper limit of the range then there is no feasible solution

If EOQ < lower limit of the range then lower limit is the Feasible EOQ

Annual Ordering Cost = (D/Q)*S

Annual Holding Cost = (Q/2)*H

Annual Purchasing Cost = D*P

Total Cost = Annual Ordering Cost + Annual Holding Cost + Annual Purchasing Cost

Total cost for Q=1000 is the lowest

so, Optimal Order Quantity = 1000 units

keosha answered 2 years ago

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