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 seling 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 your cost as the usual model suggests! All you want is to satisfy your captive market and provide a Service Level Type 1 of 90%. a) (10 points) What should be your order size Q? b) (15 points) Now given your answer from part (a) what is your Service Level Type I1? c) (10 points) Given your answer from part (a) what is the expected number of brochures that you will be 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 Type 11 of 90%. In this case how many brochures should you order?

Explanation / Answer

(a)

Type-I service level refers to the Cycle Service Level = 90%

The corresponding value of Z from the standard normal table for Z~Normal(0,1) is 1.28

So, the order quantity (Q) = + Z = 300 + 1.28*50 = 364

(b)

Normal loss function, L(Z) corresponding to Z=1.28 is L(Z) = 0.047

Expected shortage = L(Z) x = 0.047 x 50 = 2.35

Type-II service level = Fill Rate = 1 - (Expected shortage / ) = 1 - (2.35 / 300) = 99.22%

(c)

Already found, Expected shortage = L(Z) x = 0.047 x 50 = 2.35 brochures

(d)

Fill Rate = 90%

Target L(Z) = *(1 - Fill Rate) / = 300*(1 - 0.90) / 50 = 0.60

Corresponding Z = -0.35

Q = + Z = 300 - 0.35*50 = 283

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.