Homework_5_Managing Uncertainty_Solution

# Homework_5_Managing Uncertainty_Solution - 311 Operations...

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1 311 Operations Management Fall 2007 Homework # 5: Managing Uncertainty (Waiting Lines) Due 10/18/2007 1. (30 points; 10pts. for (a),(b),(c) each) Problem 7. Page 313 in the text book. a) = 10 person/hour, C a = 1 S = 1, = 12 person/hour, C s = 0 = 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 + S = 2.92 people c) W q = L q / = 0.208 hour 2. (30 points) Problem 21. Page 316 in the text book. Assume both inter-arrival time and the service time follow exponential distributions. = 2 car/hour, C a = 1 (5pts.) If we have one repairer, = 2 car/hour, = 1, W q = , cost is /hour (5pts.) If we have two repairer, = 3 car/hour, = 2/3, L q = (2/3) 2 /(1/3) = 4/3 car L s = L q + S = 2 car cost is 40*2+20*2=\$120/hour (5pts.) If we have three repairer, = 4 car/hour, = 2/4 = 0.5, L q = (0.5) 2 /(0.5) = 0.5 car L s = L q + S = 1 car cost is 40*1+20*3=\$100/hour (5pts.) We should hire 3 repairers. (10pts.) 3. (20 pts.) The Northern Emergency Computer Support has a call center with 10 customer service representatives. Historical statistics shows that customer calling times are exponentially distributed, and are 20 minutes on average.

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