Answer to Question #291192 in Operations Research for yuvraj

Question #291192

 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? 


1
Expert's answer
2022-01-28T12:48:01-0500

Weekly demand =420=420

Daily demand =4207=60=\frac{420}{7}=60

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

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

Carrying cost, H=$0.50H= \$0.50

Ordering cost, S=$20S=\$20


a.)

The optimal order quantity, EOQ can be calculated as:


EOQ=2DSH=2×21840×200.501322EOQ=\sqrt{\frac{2DS}{H}}\\ =\sqrt{\frac{2\times 21840 \times 20}{0.50}}\\ \approx 1322

b.)

Calculating the reorder point, RR:


R=(Average daily usage rate × Lead time)+ Safety stockR=(60×4)+0R=240R= (\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:


Time=365×EOQD=365×13222184022 days\text{Time}=\frac{365 \times EOQ}{D}\\ =\frac{365 \times 1322}{21840}\\ \approx 22 \text{ days}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment