Question

A firm receives inventory in the beginning of each week. Weekly demand has a mean of 500 and standard deviation of 25. What is the service level (and corresponding probability of stockout) if the amount of initial inventory is

a. Q = 550

b. Q = 475

Answer 1

Answer to question # a :

Let z value corresponding to the relevant service level = Z1

Therefore ,

Mean weekly demand + Z1 x Standard deviation of demand = 550

Or, 500 + 25.Z1 = 550

Or, 25.Z1 = 50

Or, Z1 = 2

Corresponding probability for Z1 = 2 as derived from standard normal distribution table = 0.97725

Therefore ,

SERVICE LEVEL = 0.97725

PROBABILITY OF STOCK OUT = 1 – 0.97725 = 0.02275

Answer to question b ;

Let z value corresponding to the relevant service level = Z1

Therefore ,

Mean weekly demand + Z2 x Standard deviation of demand = 475

Or, 500 + 25.Z2 = 475

Or, 25.Z2 = - 25

Or, Z2 = - 1

Corresponding probability for Z2 = - 1 as derived from standard normal distribution table = 0.15866

SERVICE LEVEL = 0.15866

PROBABILITY OF STOCKOUT = 1 – 0.15866 = 0.84134