3) (40 points) Since the graduation period is coming you started a new business

Question

3) (40 points) Since the graduation period is coming you started a new business of selling Commencement Brochures for the College of Engineering. Talking to the Dean you estimate your demand to be normally distributed with a mean of =300 graduates and standard deviation of = 50 (after all not everyone buys your brochure). Each brochure costs you $10 to print and you sell them for $25. Moreover, brochures not sold are worthless after the commencement ceremony. Being a student you do not try to minimize is to satisfy your captive market and provide a Service Level Type l of 90%. your cost as the usual model suggests! All you want a) (10 points) What should be your order size Q? Now given your answer from part (a) what is your Service Level Type I1? Given your answer from part (a) what is the expected number of brochures that you will be b) (15 points) c) (10 points) unable to sell (you will be short)? Now only if you have time: (10 points) d) Changing your mind you would like to achieve Service Level lype lLof 90% In this case how many brochures should you order?

Explanation / Answer

(a)

Service Level type I = CSL = 90%

Corresponding standard normal variable (Z) = 1.28 (from table or by excel)

Order size = + Z = 300 + 1.28*50 = 364

(b)

Type II service level = Fill rate(FR)

FR = 1 - .L(z)/ --------(1)

L(z) at Z=1.28 is 0.047 (from table or using excel)

So, FR = 1 - (50*0.047/300) = 99.22%

(c)

Expected Lost Sales = L(z) x = 0.047 x 50 = 2.37 (i.e. we will be unable to sell 2 brochures)

(d)

Fill Rate = 90%

Using (1), 0.90 = 1 - (50*L(z)/300)

or, L(z) = (1 - 0.90)*300/50 = 0.60

Corresponding Z from table (or using excel) = -0.35

So, Order size = + Z = 300 - 0.35*50 = 282.5 or 283

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