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Solution_ Homework3_Managing Uncertainty

Solution_ Homework3_Managing Uncertainty - 311 Operations...

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311 Operations Management Fall 2008 Solution: Homework # 3 – Managing Uncertainty 1. (30 points, 6 points each) Chapter 8A Question 7 (page 301 in the textbook). a. M/D/1 system λ = 10 person/hour, C a = 1 S = 1, μ = 12 person/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 ρ ρ people b. L s = L q + = 2.92 people 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 person/hour, μ = 10 person/hour, L s = λ / ( μ λ ) = 1.5 people W s = L s / λ = 0.25 hour = 15 minutes If the students use a different equation (the general approximation this is fine) 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 Or 1
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λ = 6 person/hour, C a = 1 S = 2, μ = 10 person/hour, C s = 1 ρ = 6/(2*10) = 30% 0748 . 0 7 . 0 3 . 0
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