Question

At a local hardware store, daily demand for winter tires is normally distributed with a mean of 50 tires and standard deviation of 20 tires. The source of supply is reliable and maintains a constant lead time of four days. The cost of placing the order is $20 and annual total holding costs are $1.00 per tire. Assume that the store operates 320 days a year and service level of 95%. Calculate the total holding cost (including the holding cost of maintaining the safety stock). (Round to the nearest whole number)

Answer 1

Daily demand d = 50

Standard deviation = 20

Lead time L = 4 days

Cost of placing order S= 20

Holding cost H = 1

Annual demand D = 320*50 = 16,000

Service level = 95%

Z = 1.64

Order quantity Q

Q= 800

Safety Stock SS

SS = 65.6 or 67

Average inventory = (Q/2) + Safety stock = (800/2)+ 67 = 467

Total holding cost = Average inventory * Holding cost = 467*1 = 467

Total holding cost = 467