Q4-A large law firm uses an average of 40 boxes of copier paper a day. The firm
ID: 349132 • Letter: Q
Question
Q4-A large law firm uses an average of 40 boxes of copier paper a day. The firm operates 260 days a year. Storage and handlings costs for the paper are $30 a year per box, and it costs approximately $60 to order and receive a shipment of paper. a. What order size could minimize the sum of annual ordering and carrying costs? What is the annual ordering cost and annual holding cost? b. What is the average number of boxes on hand when the law firm uses EOQ model? c. If the law firm decides to use EOQ mode, what is the order cycle? How many orders will the law firm place in a year? d. Due to delivery restrictions, if the law firm has to order in multiples of 50 boxes. What is the new order quantity that you would recommend? What is the percentage increase in total annual costs from using the new order quantity compared to the original EOQ? e. If the lead-time is 2 days, what is the re-order point? f. Assume that the demand for boxes is variable. Using the following information find re-order point for variable demand and safety stock. • Mean demand during lead-time = 50 boxes • Standard deviation of lead-time demand = 10 boxes • Acceptable stock-out risk during lead-time = 1% • Lead-time demand is normally distributed and assume lead time as 2 days
Explanation / Answer
a) Demand = 40*260 = 10400
Handling Cost = 30
Ordering Cost = 60
Order Size with minimum total cost = EOQ = sqr rt ( 2 * Demand * Ordering Cost / Handling Cost ) = sqe rt (2*10400*60/30)= 204
Total Cost = Ordering Cost + Carrying Cost = (Demand*Ordering Cost/EOQ) + (EOQ*Holding Cost/2)
= 10400*60/204 + 204*30/2 = 6118.824
b) Average Number of Box in hand = EOQ/2 = 102
c) No. of Orders = Demand/EOQ = 10400/204 = 51
Firm shall make 51 orders in a year ie 52 weeks or 365 days. Thus it will make an order after every 7.16 days.
d) As order can be placed in the multiple of 50, the closest options to EOQ are 200 and 250.
Calculating Total Cost with 200 as Order Quantity = 10400*60/200+ 200*30/2 = 6120
Calculating Total Cost with 250 as Order Quantity = 10400*60/250+ 250*30/2 = 6246
As The total Cost with 200 order quantity is lesser than that of 250 order quantity. We shall order with 200 boxes in an order.
% Increase in Total Cost = Increase/Total cost in EOQ model = (6120-6118.824)/6118.824 = 0.0192%
e) If lead time is 2 days, Boxes utilized in 2 days will be the ROP. ROP= Demand in 2 Days = 40* 2 = 80
f) Demand = 50
std dev of Demand= 10
Service Level = 99%. Therefore Z = 2.33
Lead Time = 2
ROP = Demand * LT + Z * Std Dev of Demand * sqr rt (Lead time)
= 50 * 2 + 2.33 * 10 * sqr rt(2) = 133
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