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Unformatted text preview: Practice Questions: Managing Uncertainty 1. To support national health week, the heart association plans to install a free blood pressure testing booth in a shopping mall for a week. Previous experience indicates that, on the average, 10 persons per hour request a test. Assume the inter-arrival times are exponentially distributed. The blood measurements can be made in a constant time of 4.8 minutes. a. What is the utilization of the blood pressure machine? 8 . 6 8 . 4 = = ρ b. What is the average number in system (those waiting and those getting their blood pressure checked)? customers C C N s a s l 6 . 1 5 . * 2 . 8 . 2 1 2 . 8 . 2 1 2 4 2 2 ) 1 ( 2 = = + = + − = + ρ ρ customers N N l s 4 . 2 8 . 6 . 1 = + = + = ρ c. What is the average time in the system (waiting + service time)? From Little’s rule we know 4 . 14 24 . * 60 24 . 10 4 . 2 = = = = hours t s d. What is the average waiting time? min 6 . 9 16 . * 60 16 . 10 6 . 1 = = = = hours t s e. What is the average number in line? 1.6 customers 2. At the California border inspection station, vehicles arrive at the rate of 10 per minute. The inter-arrival times are exponentially distributed. For simplicity assume that the there is only one lane and one inspector, who can inspect at the rate of 12 per minute in an exponentially distributed fashion. a. What is the average number of cars waiting? 6 5 12 10 = = ρ customers C C N s a s l 17 . 4 6 25 2 1 1 ) 6 / 1 ( ) 6 / 5 ( 2 1 4 2 2 ) 1 ( 2 = = + = + − = + ρ ρ b. What is the average number in the system – either waiting or being inspected? customers N N l s 5 83 . 17 . 4 = + = + = ρ c. What is the average time in the system –waiting + inspection? min 5 . 10 5 = = = λ s s N t d. What is the average time waiting? min 417 . 10 17 . 4 = = = λ l l N t 3. Since the deregulation of the airline industry, fierce competition has forced Global Airlines to reexamine their operations for efficiency and economy. As part of their campaign to improve customer service they have focused on passenger check-in operations at the terminal. Global operates a common check-in system wherein passengers for all Global’s flights line up in a single “snake line”. The arrival rate is estimated to be 52 passengers per hour. The check-in process takes an average of three minutes. Agents are paid \$20 an hour. The customer relation department estimates that every minute a customer spends waiting in line to be checked in it costs Global \$1 due to missed flights, customers’ dissatisfaction, and loss of future business....
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