Homework3_sol

# Homework3_sol - Stanford University Management Science and...

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Stanford University Management Science and Engineering MS&E 260 Fall 2016 Homework #3 1/3 MS&E 260: Introduction to Operations Management Homework #3 Solutions 1. Because all the models are M/M/c, we have ρ = λ /(N μ ) W = 1/(N μ ) x 𝜌 √2(𝑁+1) −1 /(1- 𝜌 ) + 1/ μ L = λ W a. 𝜌 1 = λ μ , 𝑊 1 = 1 μ−λ , 𝐿 1 = 2 λ μ−λ 𝜌 2 = λ μ , 𝑊 2 = ( 1 2 ) 1 μ − λ , 𝐿 2 = λ μ − λ The second model has half the average wait time and average number of people as the first model does. The utilization is the same. Other potential factors to consider when deciding between the two models are customer preference (will customers be discouraged if they see a long line vs. two shorter lines) and cost (cost of two regular servers vs. one “super - server”— in some situations the cost might be greater (salaried employees) and in some it might be less (computer processors)). b. 𝜌 1 = λ μ , 𝑊 1 = ρ μ(1−ρ) + 1 μ , 𝐿 1 = 2 λ μ−λ 𝜌 2 = λ μ , 𝑊 2 = ρ √6 −1 2 μ (1 − ρ) + 1 μ

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