Question

. A manufacturer uses manages its inventory using fixed quantity system and wants to be able to fully supply its customers at least 50 out of the 52 weeks of the year. The product they sell has a daily demand of 250 units with a standard deviation of 50 units. Due to insurance requirements, this company cannot hold more than an average of 100 units as a safety stock. What is the maximum lead time in days that they need to require to their supplier?

Answer 1

Lead time needed is approximately 1 day

Step-by-step explanation:

In this question, we are asked to calculate the maximum number of lead days needed by a manufacturer to give a supplier

We proceed as follows;

They want to be able to fully supply the customer at least 50 out of the 52 weeks.

Mathematically; service probability = 50/52 = 0.96 or 96%

At 96% service level value of Z = 1.75

Standard deviation of daily demand (σd) = 50 units

Safety stock = 100 units

Suppose lead time = L

Safety stock = Z × σ d × √L

100 = 1.75 × 50 × √L

=100 = 87.5 × √L

√L = 100/87.5

√L = 1.142857142

L = 1.142857142^2

L = 1.306122448