Answer to Question #291192 in Operations Research for yuvraj

Question

 The Super Discount store (open 24 hours a day, every day) sells 8-packs of paper towels, at the rate of approximately 420 packs per week. Because the towels are so bulky, the annual cost to carry them in inventory is estimated at $.50. The cost to place an order for more is $20 and it takes four days for an order to arrive.

a. Find the optimal order quantity.

b. What is the reorder point?

c. How often should an order be placed? 

Answer 1

Weekly demand $=420$

Daily demand $=\frac{420}{7}=60$

Number of days for an order to arrive or lead time $=4$

Annual demand, $D=420 \times 52=21840$

Carrying cost, $H= \$0.50$

Ordering cost, $S=\$20$

a.)

The optimal order quantity, EOQ can be calculated as:

$$EOQ=\sqrt{\frac{2DS}{H}}\\ =\sqrt{\frac{2\times 21840 \times 20}{0.50}}\\ \approx 1322$$

b.)

Calculating the reorder point, $R$:

$$R= (\text{Average daily usage rate } \times \text{ Lead time})+\text{ Safety stock}\\ R=(60 \times 4)+0\\ R=240$$

c.)

Frequency in which order should be placed:

$$\text{Time}=\frac{365 \times EOQ}{D}\\ =\frac{365 \times 1322}{21840}\\ \approx 22 \text{ days}$$