As an inventory manager,you must decide on the order quantity for an item.Its annual demand is 350 units.Ordering cost is $20 each time an order is placed,and the holding cost is 30 percent of the per-unit price.Your supplier provided the following price schedule. What is the annual cost discrepancy between the optimal order policy and the second best order policy?
A)Less than $5
B)Between $5 and $10
C)Between $10 and $20
D)More than $20

Question

As an inventory manager,you must decide on the order quantity for an item.Its annual demand is 350 units.Ordering cost is $20 each time an order is placed,and the holding cost is 30 percent of the per-unit price.Your supplier provided the following price schedule.  What is the annual cost discrepancy between the optimal order policy and the second best order policy?
A)Less than $5 
B)Between $5 and $10 
C)Between $10 and $20 
D)More than $20

Quizplus · Accepted Answer

First, we need to calculate the per-unit holding cost:

Per-unit holding cost = 30% * $22.50 = $6.75

Using the formula for economic order quantity (EOQ), we can calculate the optimal order quantity:

EOQ = sqrt((2 * annual demand * ordering cost) / holding cost)
EOQ = sqrt((2 * 350 * $20) / $6.75) ≈ 53 units

Now, we can calculate the total annual cost for the EOQ:

Total ordering cost = (annual demand / EOQ) * ordering cost
Total ordering cost = (350 / 53) * $20 ≈ $131.13

Total holding cost = (EOQ / 2) * per-unit holding cost
Total holding cost = (53 / 2) * $6.75 ≈ $113.06

Total annual cost = Total ordering cost + Total holding cost
Total annual cost = $131.13 + $113.06 ≈ $244.19

To find the second best order policy, we need to calculate the total annual cost for each order quantity in the price schedule. From the schedule, we can see that the order quantity of 60 units has the lowest total annual cost after the EOQ:

Total ordering cost = (annual demand / 60) * $20 = (350 / 60) * $20 ≈ $116.67
Total holding cost = (60 / 2) * $6.75 = $202.50
Total annual cost = $116.67 + $202.50 = $319.17

Therefore, the annual cost discrepancy between the optimal order policy and the second best order policy is:

$319.17 - $244.19 ≈ $75.98

Since $75.98 is between $5 and $10, the answer is B.

The best choice is to order the EOQ of 53 units because it minimizes the total annual cost.

As an Inventory Manager,you Must Decide on the Order Quantity