Operations

Problem 1

A company operates 365 days a year and its annual demand for a product is 18,250 units. The company estimates that the standard deviation for daily demand is 15 units. The cost to place an order is $31.20 and the time from ordering to receipt is 36 days. The annual inventory carrying cost is $0.10 per unit. Determine the optimal ordering quantity per order and find the reorder point necessary to provide a 98 percent service probability.

D=18250, S=31.20, H=.10

Qopt = (2*18250*31.20/.1)^(1/2) = 3374.6 -> 3375 units

R=avg lead time + safety stock = dL + safety stock (z * σL)

dL = 18250/365*36 = 1800

z = 2.10

σL = σd * L^.5 = 15*36^.5 = 90 units

R = 1800+2.1*90 = 1989 units

Problem 2

University Drug Pharmaceuticals orders its antibiotics every two weeks (14 days) when a salesperson visits from one of the pharmaceutical companies. Tetracycline is one of its most prescribed antibiotics, with average daily demand of 2,000 capsules. The standard deviation of daily demand was derived from examining prescriptions filled over the past three months and was found to be 800 capsules. It takes five days for the order to arrive. University Drug would like to satisfy 99 percent of the prescriptions. The salesperson just arrived and there are currently 25,000 capsules in stock. How many capsules should be ordered for the current visit of the salesperson?

T = 14 days, d = 2000 cap/day, σ = 800 capsules, L = 5 days, Service level = .99, I = 25000 units

q = d(T+L) + safety stock – I

safety stock = z* σ(T+L) = 2.35 * 800 * (14+5)^.5 = 8194.73

q = 2000 * (14 + 5) + 8194.73 - 25000 = 21194.73 -> 21195 capsules

Problem 3

J.C. Penny in Cumberland Mall sells fashion dresses for $50 each. The cost for the store to order from an outside supplier is $20 per dress. All dresses not sold during the summer season are sold for 30% of the original retail price in an end-of-season clearance sale. Demand for the suits has historically been normally...