Homework_3_Managing Uncertainty_Solutions_TTh

Homework_3_Managing Uncertainty_Solutions_TTh - 311...

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1 311 Operations Management Spring 2009 Homework # 3: Managing Uncertainty Due March 3, 2009 1. (20 pts.; 5 points per part; no partial credit) Problem 1. Page 300 in the text book. M/M/1 System λ = 4 customers/hour μ = 6 customers/hour a) 1- λ / μ = 33.33% b) W q = λ / μ ( μ - λ ) = 1/3 hours or 20 minutes c) L q = λ W q = 4/3 customers d) 1-P 0 -P 1 = 1 – (1- λ / μ ) - λ / μ (1- λ / μ ) = 4/9, or 0.44 2. (20 pts.; 5 points per part; no partial credit) Problem 21. Page 303 in the text book. M/M/S System λ = 10 vehicles/minute μ = 12 vehicles/minute a) 0.175 vehicles (or 0.201 vehicles, by general formula) b) 0.101 minutes, or 6.06 seconds (or 0.103 minutes, by general formula) 2 M/M/1 Systems λ = 5 vehicles/minute μ = 12 vehicles/minute c) 0.298 vehicles per line Î 0.298*2 = 0.596 d) 0.143 minutes, or 8.58 seconds 3. (20 pts.; 10 points per part; partial credit of ½ for each part if the student has done something reasonable) You are working at a bank and doing resource
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