Question

1. Normal distribution, Re-order Point (6 Marks)

During the summer, the demand for electric fans at Courts is quite strong. The company tracks

inventory using a computer system so that it knows how many fans are in the inventory at any

time. The policy is to order a new shipment of 500 fans when the inventory levels falls to the

re-order point which is 100. However this policy has resulted in frequent shortages, resulting

in lost sales because both lead-time and demand is highly variable. The manager would like to

reduce the incidence of shortages; so that only 2.5% of orders will arrive after the inventory

drops to zero (resulting in a shortage / stockout). From previous periods, the company has

determined that the demand during lead-time is normally distributed with a mean of 200 and

a standard deviation of 30. Determine the re-order point.

Answer 1

The demand during the lead time with mean 200 and the standard deviation is 30.

It is saying that the reorder point should be like that 2.5% of orders will arrive after inventory drops to zero, i.e the seller call serve(sell) 97.5% of customers.

Let reorder point is x.

so, x= Mean+ z_(1-alpha)*Std_dev ,

Here , Mean= 200, alpha =0.025, Std_dev=30

x= 200+z_(1-0.025) * 30 = 200+1.96*30= 258.8 =259 (approximately)

The reoder point is 259.