Question 12.11: Computing Stockout Risk for the Fixed-Interval Model Given t...
Computing Stockout Risk for the Fixed-Interval Model
Given the following information:
LT = 4 days
OI = 12 days
\overline{d} = 10 units/day
σ_d = 2 units/day
A = 43 units
Q = 171 units
Determine the risk of a stockout at
a. The end of the initial lead time.
b. The end of the second lead time.
a. For the risk of stockout for the first lead time, we use Formula 12–13. Substituting the given values, we get 43 = 10 × 4 + z(2)(2). Solving, z = +.75. From Appendix B, Table B, the service level is .7734. The risk is 1 – .7734 = .2266, which is fairly high.
b. For the risk of a stockout at the end of the second lead time, we use Formula 12–16. Substituting the given values, we get 171 = 10 × (4 + 12) + z (2)(4) − 43. Solving, z = 6.75. This value is way out in the right tail of the normal distribution, making the service level virtually 100 percent, and, thus, the risk of a stockout at this point is essentially equal to zero.