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Quiz 3_Solution

Quiz 3_Solution - 2 Instead of hiring one more cashier and...

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311 Operations Management Fall 2007 Name________________________ Section_______________________ Quiz #3 – Waiting Lines 1. A bank currently has one cashier available. The arrival rate of customers to the bank is 12 customers per hour and the average service time is 3 minutes. Both inter- arrival time and service time follow exponential distributions. a. What is the utilization rate (30 points)? λ = 12 customers/hour, μ = 20 customers/hour, S = 1 (15 pts.) ρ = λ/(Sμ) = 0.6 (15 pts.) b. What is the average waiting time in line (30 points)? C a = C s = 1 (15 pts.) N l = ρ 2 /(1 – ρ)*(1+1)/2 = 0.9 customers t l = N l /λ = 0.075 hours = 4.5 minutes
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Unformatted text preview: 2. Instead of hiring one more cashier and lowering the utilization rate, the bank decides to train the cashier. After the training, the cashier can serve customers at a constant time of three minutes each. Assume that the bank faces the same demand pattern as in problem 1. a. What is the utilization rate (20 points)? λ = 12 customers/hour, μ = 20 customers/hour, S = 1 (10 pts.) ρ = λ/(Sμ) = 0.6 (10 pts.) b. What is the average waiting time in line (20 points)? C a = 1, C s = 0 (10 pts.) N l = ρ 2 /(1 – ρ)*(1+0)/2 = 0.45 customers t l = N l /λ = 0.0375 hours = 2.25 minutes (10 pts.)...
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