In the EOQ model with planned shortages,if annual demand is 100,holding cost is $400,ordering cost is $20,and back-order cost is $200,the quantity back-ordered per replenishment cycle,rounded to the next whole number,is:
A)3
B)4
C)5
D)7
E)20

Question

Quizplus · Accepted Answer

The Economic Order Quantity (EOQ) model with planned shortages involves calculating the optimal order quantity that minimizes total inventory costs, including holding, ordering, and shortage costs. The quantity back-ordered per replenishment cycle can be found using the formula: $Q_b = \sqrt{\frac{2DS}{H}}$, where $D$ is the annual demand, $S$ is the ordering cost, and $H$ is the holding cost. Substituting the given values: $Q_b = \sqrt{\frac{2 \times 100 \times 20}{400}} = \sqrt{10} \approx 3.16$. Rounding to the next whole number gives 4.

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