Question

2. A specialty coffee house sells Colombian coffee at a steady rate of 285 pounds per year. The beans are purchased from a local supplier for $3.00 per pound. An estimated $38 are spent in paperwork and labor each time an order is placed for the coffee beans, and holding costs are based on a 20 percent annual interest rate. The lead time for an order to arrive from the supplier is exactly 1 month after it is placed. a. Determine the optimal order quantity for the beans. b. On the average how many orders are placed annually? What is the time between placement of orders? c. What are the average annual costs of (1) holding, (2) setup and (3) purchase? d. What is the reorder point? e. The manager of the coffee house insists that the order cost of K=$38 is wrong. He claims that it is actually lower, and that orders should be placed more frequently; he suggests three equal orders each year. For what range of values of K is your EOQ (based on K=$38) preferable (in terms of a lower total order and carrying cost) to the manager's suggested ordering scheme?

Answer 1

a. Based on the data in the question,

D = 285 pounds per year

S = $38

H = 0.2 * 3 = $0.6

Optimal order quantity, Q^*= sqrt(2DS/H) = sqrt(2 * 285* 38/0.6) = 190 pounds

b. Total number of orders placed = 285/190 = 1.5 = 2 orders.

Replenishment time = T^* = 190/285 = 0.67 year = 31.28 weeks

c. Average annual holding cost = Average inventory * holding cost per unit = (285/2)*0.6 = 85.5$

Setup cost = Number of Orders * Order cost for 1 order = 2 * 38 = $76

Purchase cost = 285 * 3 = $855

d. Reorder point = Safety stock needed for 1 month i.e., 4 weeks

Safety stock for 4 weeks = (190/31.28)*4 = 24.29 pounds.

e.For 3 equal orders, quantity for one order = 285/3 = 95 pounds per order = Q^*_new

95 = sqrt(2*285*S/0.6)

S = $9.5 per order