In the EOQ model with planned shortages,if annual demand is 500,holding cost is $200,ordering cost is $15,and back-order cost is $400,EOQ (rounded to the next whole number)is:
A)8
B)9
C)11
D)13
E)113

Question

Quizplus · Accepted Answer

Using the EOQ formula:
EOQ = sqrt((2DS)/(H+B))
where D = annual demand, S = ordering cost, H = holding cost, and B = backorder cost
Plugging in the given values:
EOQ = sqrt((2*500*15)/(200+400))
EOQ = sqrt(7500/600)
EOQ = sqrt(12.5)
EOQ ≈ 4.43
Since we can only order in whole numbers, we round up to EOQ = 5.
However, since there are planned shortages, we can allow for backorders. This means we can set the reorder point to be below the actual demand. 
The optimal order quantity then becomes the minimum point of the total cost curve, which occurs when the holding cost equals the backorder cost. 
Using the formula for this point:
Q* = sqrt((2DS)/(H+B))
*sqrt(B/H)*D
*sqrt(400/200)*500
= 11.18
Rounding up to the next whole number, EOQ = 11. Thus, choice C is the best answer.

In the EOQ Model with Planned Shortages,if Annual Demand Is