Question

Vance Armstrong is making his monthly order (every 30 days) for a supply of racing tires for the Sunshine Bicycle Shop. The order will take two days to arrive. Vance sells tires at an average rate of five per day (six days per week) with a standard deviation of demand of one per day. He desires to have stock of racing tires at a 98 percent service probability to satisfy his customers. He currently has 35 racing tires in inventory. How many should be ordered? From standard normal distribution table, z = 2.05

Answer 1

Z value for 98 percent service probability = 2.05

Given are following data :

Order interval = T = 30 days

Lead time of delivery = L = 2 days

Therefore , Protection interval = P = T + L = 30 + 2 = 32 days

It is also given that standard deviation of daily demand = 1 unit

Therefore , standard deviation of demand during protection period

= 1 x Square root ( Protection period )

= 1 x square root ( 32 )

= 5.65

Therefore ,

safety stock = z value x standard deviation of demand during protection period= 2.05x 5.65 =11.58 ( 12 rounded to nearest whole number )

Theoretical Reorder point

= Average daily demand x Protection period + safety stock

= 5 x 32 + 12

= 160 + 12

= 172

Current inventory of racing tire = 35

Therefore , quantity to be ordered by Vance Armstrong = 172 – 35 = 137

137 RACING TIRES SHOULD BE ORDERED