Homework4_sol

# Homework4_sol - Stanford University Management Science and...

This preview shows pages 1–3. Sign up to view the full content.

Stanford University Management Science and Engineering MS&E 260 Fall 2016 Homework #4, Solution 1/5 MS&E 260: Introduction to Operations Management HOMEWORK #4, SOLUTION Problem 1. a. Notations for problem 1: p = retail price c = production cost s = retailer’s salvage value w = wholesale price b = buy-back price Underage cost: ? 𝑢 = 100 − 60 = 40 Overage cost: ? 0 = 60 − 5 = 55 The retailer ’s critical ratio is: ? 𝑢 ? 𝑢 + ? 0 = 40 55 + 40 = 0.42 𝑧 = 𝛷 −1 (0.42) = −0.1992 So the retailer’s optimal order quantity is: ? = µ + 𝜎𝑧 = 200 + 0.1992 ∗ 10 ≈ 198 We can evaluate the retailer ’s expected pro fit. Let 𝜋 = profit: ?[𝜋] = ??[?????] − ?? + ?(? − ?[?????]) ?[𝜋] = ?[𝜇 − 𝜎?(𝑧)] − ?? + ?(? − 𝜇 + 𝜎?(𝑧)) We have: ?[?????] (??𝑖??) = 𝜇 − 𝜎?(𝑧) = 200 − 10 ∗ 0.5064 = 194.94 ?[????????] (??𝑖??) = ? − ?[?????] = 198 − 194.94 = 3.06 ?[𝜋] = \$7,628.89 The supplier ’s profit is 198*(60 -40) = \$3,960. Total supply chain’s profit = \$11,5 88.89. b. Supply chain optimal quantity ? 𝑢 = \$100 – \$40 = \$60 . ? 0 = \$40 − \$5 = \$35 . The supply chain’s critical ration is: ? 𝑢 ? 𝑢 + ? 0 = 60 95 = 0.632 𝑧 = 𝛷 −1 (0.632) = 0.336 So the retailer’s optimal order quantity is: ? = µ + 𝜎𝑧 = 200 + 0.336 ∗ 10 ≈ 203 We can evaluate the integrated chain’s expected profit:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Stanford University Management Science and Engineering MS&E 260 Fall 2016 Homework #4, Solution 2/5 ?[?????] (??𝑖??) = 𝜇 − 𝜎?(𝑧) = 200 − 10 ∗ 0.265 ≈ 197.47 ?[????????] (??𝑖??) = ? − ?[?????] = 203 − 197 = 5.53 ?[𝜋] = \$11,654.42 .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern