INEN 455 Fall 2017 Homework 6 Released on 10/302017 Due by 11/03/2017 10am n har
ID: 359061 • Letter: I
Question
INEN 455 Fall 2017 Homework 6 Released on 10/302017 Due by 11/03/2017 10am n hard sepy) 10. A specialty coffeehouse sells Colombian coffee at a fairly stcady rate of 280 pounds annually. The beans are purchased from a local supplier for $2.40 per pound. The cof- estimates that it costs $45 in paperwork and labor to place an order for the feehouse coffee, and holding costs are based on a 20 percent annual intcrest rate. a. Determine the optimal order quantity for Colombian coffee. b. What is the time between placement of orders? c. What is the average annual cost of holding and setup due to this item? d. If replenishment lead time is three weeks, determine the reorder level based on the on-hand inventory 12. A large automobile repair shop installs about 1,250 mufflers per year, 18 percent of which are for imported cars. All the imported-car mufflers are purchased from a single local supplier at a cost of $18.50 each. The shop uses a holding cost based on a 25 percent annual interest rate. The sctup cost for placing an order is esti- mated to be $28. a. Determine the optimal number of imported-car mufflers the shop should pur- chase each time an order is placed, and the time between placement of orders. b. If the replenishment lead time is six weeks, what is the reorder point based on the level of on-hand inventory? c·The current reorder policy is to buy imported-car mumers only once a year. What are the additional holding and setup costs incurred by this policy? Note: Question 10.(20 points) Question 12 (15 points). This homework could be a group assignment with group discussion as noceded. But each group should have no more than 3 group members. Please sign your name when you suhanit your homework Hint: Read through Chapter 4.4 and 4.5 (esp. examples in 4.5Explanation / Answer
10.
Annual Demand, D = 280 pounds.
Unit ordering cost, Co = $ 45 per year.
Unit purchase Cost, Cp = $ 2.40 per pound.
Unit holding cost, Ch = 20% of unit purchase cost = 0.2 x 2.40 = $ 0.48
a.
Optimal Order Quantity = Economic Order Quantity (EOQ) = Q = [(2 D. CO/Ch) = (2 x 280 x 45) / (0.48) ] = 229.13 229 pounds.
b.
Time between placement of orders = Q / D = 229 / 280 = 0.82 of a year = 0.82 x 365 days = 299.3 days 299 days.
c.
Total Annual Cost of Holding and Setup, TC = Holding Cost + Ordering Cost = Ch.(Q/2) + CO . (D/Q) = [0.48 x (229 / 2)] + [45 x (280 / 229)] = 54.96 + 55.02 = $ 109.98
d.
Lead Time, LT = 3 weeks = 3 x 7 days = 21 days.
Reorder Level, ROL = Average Daily Demand x Lead Time (Assuming zero safety stock) = (280 / 365) x 21 = 16.11 16 pounds.
12.
Annual Demand for imported-car mufflers, D = 0.18 x 1250 = 225 units.
Unit ordering cost, Co = $ 28.
Unit purchase Cost, Cp = $ 18.50
Unit holding cost, Ch = 25% of unit purchase cost = 0.25 x 18.50 = $ 4.625
a.
Optimal number of imported-car mufflers to be purchased by the shop = Economic Order Quantity (EOQ) = Q = [(2 D. CO/Ch) = (2 x 225 x 28) / (4.625) ] = 52.20 52 units.
Time between placement of orders = Q / D = 52 / 225 = 0.23 of a year = 0.23 x 365 days = 83.95 days 84 days.
b.
Lead Time, LT = 6 weeks = 6 x 7 days = 42 days.
Reorder Point, ROP = Average Daily Demand x Lead Time = (225 / 365) x 42 = 25.89 26 units.
c.
Total Annual Cost of Holding and Setup, TC = Holding Cost + Ordering Cost = Ch.(Q/2) + CO . (D/Q) = [4.625 x (52 / 2)] + [28 x (225 / 52)] = 120.25 + 121.15 = $ 241.40
Number of orders for imported-car muffler in a year = D /Q = 1.
So Q = D = 225 units.
Total Annual Cost of Holding and Setup, TCNew = Holding Cost + Ordering Cost = Ch.(Q/2) + CO . (D/Q) = [4.625 x (225 / 2)] + [28 x (225 / 225)] = 520.3125 + 28 = $ 548.3125 $ 548.31
Additional Annual Cost of Holding and Setup due to the new policy
= TCNew – TC = 548.31 – 241.40 = $ 306.91