5. (20 points) The annual demand, ordering cost, and the annual inventory carryi

Question

5. (20 points) The annual demand, ordering cost, and the annual inventory carrying cost rate for a certain item are 600 units S20/order and 30% of item price, respectively. Pr by the following quantity discount schedule. ice is established l to 49 0 to 249 50 and up Quantity Price 5.00 per unit S4.50 per unit $4.10 per unit (a) Assume the discount applied to all the units in the order, what should the order quantity be in order to minimize the average annual cost? Also, show the minimal avcrage annual cost. (b) Assume the discount is applied only to the number of units above the breakpoint(i.e. incremental discounts), what should the order quantity be in order to minimize the average annual cost? Also, show the minimal average annual cost.

Explanation / Answer

a)

Demand (D) = 600

Ordering cost (S) = 20

Holding % = 30

Holding cost (H) = Price*30%

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

Total cost = D/EOQ*S + EOQ/2*H + Price*D

1) Assume Price = 5

EOQ = sqrt(2*600*20/(30%*5)) = 126

It is out of range

2) Price = 4.5

EOQ = sqrt(2*600*20/(30%*4.5)) = 133

Total cost = 600/133*20 + 133/2*(4.5*30%) + 4.5*600 = 2880

3) Price = 4.1, EOQ = 250

Total cost = 600/250*20 + 250/2*(4.1*30%) + 4.1*600 = 2662

Hence, Optimal point is 250 units as the cost is lowest

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