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hw_3_solution

# hw_3_solution - Homework#3 Solutions Managing Uncertainty...

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1 Homework #3 Solutions Managing Uncertainty BUAD311- Operations Management Fall 2008 Hiroshi Ochiumi 1. (30 points, 6 points each) Chapter 8A Question 7 (page 301 in the textbook). a. M/D/1 system λ = 10 persons/hour, C a = 1 S = 1, μ = 12 persons/hour, C s = 0 ρ = 5/6 = 83% 08 . 2 12 25 2 1 6 / 1 ) 6 / 5 ( 2 1 2 2 2 ) 1 ( 2 s a S q C C L persons (You can also use model2 formula from the textbook.) b. L s = L q + = 2.92 persons c. W q = L q / λ = 0.208 hour d. W s = W q + 1/ μ = 0.292 hour e. λ = 12 person/hour, L q becomes infinity 2. (20 points, 5 points each) Chapter 8A Question 16 (page 303 in the textbook). a. M/M/1 system λ = 6 persons/hour, μ = 10 persons/hour, L s = λ / ( μ λ ) = 1.5 persons W s = L s / λ = 0.25 hour = 15 minutes b. ρ = λ / μ = 6/10 = 60% c. P 0 = 1 λ / μ = 40%, P 1 = (1 λ / μ ) ( λ / μ ) = 24%, P 2 = (1 λ / μ ) ( λ / μ ) 2 = 14.4%, P (N>2) = 1 ( P 0 + P 1 + P 2 ) = 21.6% d. M/M/2 system Macro gives us L q = 0.0593 W q = L q / λ = 0.0099 hour W s = W q + 1/ μ = 0.1099 hour

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2 Or λ = 6 person/hour, C a = 1 S = 2, μ = 10 persons/hour, C s = 1 ρ = 6/(2*10) = 30% 0748 . 0 7 . 0 3 . 0 2 1 6 2 2 ) 1 ( 2 s a S q C C L persons W q = L q / λ = 0.0125 hour W s = W q + 1/ μ = 0.1125 hour 3.
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