Question

Whole Foods Market sells Kaiser brand sausages. The market demand for Kaiser Sausages is uncertain but the mean is estimated to be 108000 packages/year with a standard deviation of 6800 packages/year. For each supply order processed the fixed cost includes a handling cost of $165/order plus a shipping cost of $400/order from the Kaiser warehouse to the Whole Foods Market. The holding cost for the sausage is $1.35/package/year. The supply lead time is fixed at 2 weeks. The supply chain manager discovers that the supply time is not constant but normally distributed with a standard deviation of 0.75 weeks. What is the new reorder level in 2 decimal places?

90% target service level Assume 52 weeks in year.

Answer 1

Average demand, d = 108000 per year
Stdev of annual demand, σ = 6800
Average lead time, L = 2 weeks = (2/52) years= 0.0385 years
Stdev of lead time, σ_L = 0.75 weeks = (0.75/52) years = 0.0144 years

Average lead time demand, d_LT = d.L = 108000*0.0385 = 4153.846

The standard deviation of lead time demand, σ_LT = [σ².L + (d.σ_L)²]^1/2 = (6800^2*0.0385 + (108000*0.0144)^2)^0.5 = 2050.577

So,

ROP = d_LT + z*σ_LT = 4153.846 + 1.28*2050.577 = 6778.59

[The accuracy of the answer will depend on the accuracy of the z-value i.e. the table used to find z.]