. Consider a convenience store that is open 24/7 and stocks paper towel rolls. E
ID: 389425 • Letter: #
Question
. Consider a convenience store that is open 24/7 and stocks paper towel rolls. Each roll of paper towels sells for $2.25. The paper towel vendor sells the convenience store rolls based on the quantity purchased. The purchase price for the store is $1.25 if the order quantity is less than 500 rolls, $1.15 if the order quantity if at least 500 rolls but less than 1000 rolls, and $1.05 is the order quantity if 1000 rolls or greater. The average demand for paper towel rolls is 12.5 rolls per day, and stays at this rate throughout the year. The ordering cost is $15 per order and the annual holding cost rate is estimated to be 35%. a. If the company used a fixed order quantity model, calculate the optimal economic order quantity (EOQ). Show all work. b. About how often will orders be placed (in days)? Show all work.
Explanation / Answer
Demand (D) = Daily demand*365 = 12.5*365 = 4562.5
Ordering cost (S) = 15
Holding cost (H) = 35%*Price
Three cases are:
1) Price 1.25 if Q<500
2) Price 1.15 if 500 <= Q < 1000
3) Price 1.05 if 1000 <= Q
EOQ = sqrt(2*D*S/H)
Assuming Price as 1.25
EOQ = sqrt(2*4562.2*15/(35%*1.25)) = 559
As the EOQ is greater than 500, so the case is discarded
Assuming Price as 1.15
EOQ = sqrt(2*4562.2*15/(35%*1.15)) = 583
Total cost = D/EOQ*S + EOQ/2*H + Price*D = 4562.5/583*15 + 583/2*(35%*1.15) + 1.15*4562.5 = 5482
Assuming Price as 1.05 and EOQ of 1000
Total cost = D/EOQ*S + EOQ/2*H + Price*D = 4562.5/1000*15 + 1000/2*(35%*1.05) + 1.05*4562.5 = 5043
a) EOQ = 1000
b) How often orders will be placed = 365/(D/EOQ) = 365/(4562.5/1000) = 80 days
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