Question

The following information is available for a product whose demand is variable. The daily demand is distributed normally, with an average demand of 5 and one standard deviation of 2. The delivery time for this product is also approximately normal, with an average of 10 days and a standard deviation of 3 days. We want a service level of 95%.

Calculate the security stock level and the order point for this product

Answer 1

Average daily demand (d) = 5 units

Standard deviation of daily demand ( $\sigma$ d) = 2 units

Average lead time(L) = 10 days

Standard deviation of lead time ( $\sigma$ L) = 3 days

Service level = 95%

At 95% service level value of Z = 1.65

Security stock = Z × √[(L x square of $\sigma$ d) +(square of d × square of $\sigma$ L) ]

= 1.65 × √[(10 x square of 2) +(square of 5 x square of 3) ]

= 1.65 x √[(10 x 4) + (25 x 9) ]

= 1.65 x √(40+225)

= 1.65 x √265

= 1.65 x 16.28

= 26.86 or rounded up to 27 units

Order point = d x L + security stock

= 5 x 10 + 27

= 50 + 27

= 77 units