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Business Operations Management EBK PRODUCTION AND OPERATIONS ANALYSIS

(a) To find out what is the expected total time in the system, if there is only a single doctor working at any point in time. 1.238 hour. In the question, it is given that patients arrive to a small hospital emergency room according to a Poisson process with an average of 1.5 per hour. Suppose that the average service time is 26 minutes. Thus, we have that, λ = 1.5 per hour μ = 60 26 = 2.31 per hour Thus, the utilization rate will be: p = λ μ = 1.5 2.31 = 0.65 Now, the expected number of patients in the system is calculated as: l = p 1 − p = 0.65 1 − 0.65 = 1.857 Thus, the expected total time in the system is calculated as: w = l λ = 1.857 1.5 = 1.238 (b) To find out what is the expected time each customer has to wait, if there is only a single doctor working at any point in time. 0.8047 hour. In the question, it is given that patients arrive to a small hospital emergency room according to a Poisson process with an average of 1.5 per hour. Suppose that the average service time is 26 minutes. Thus, we have that, λ = 1.5 per hour μ = 60 26 = 2.31 per hour Thus, the utilization rate will be: p = λ μ = 1.5 2.31 = 0.65 Now, the expected number of patients in the system is calculated as: l = p 1 − p = 0.65 1 − 0.65 = 1.857 And, the expected number of customer has to wait is calculated as: l q = l p = 1.857 × 0.65 = 1.2071 Thus, the expected time each customer has to wait is calculated as: w q = l q λ = 1.2071 1.5 = 0.8047 (c) To find out what is the expected number of patients waiting for service, if there is only a single doctor working at any point in time. 1.2071 patients per hour. In the question, it is given that patients arrive to a small hospital emergency room according to a Poisson process with an average of 1.5 per hour. Suppose that the average service time is 26 minutes. Thus, we have that, λ = 1.5 per hour μ = 60 26 = 2.31 per hour Thus, the utilization rate will be: p = λ μ = 1.5 2.31 = 0.65 Now, the expected number of patients in the system is calculated as: l = p 1 − p = 0.65 1 − 0.65 = 1.857 And, the expected number of patients waiting for serviceis calculated as: l q = l p = 1.857 × 0.65 = 1.2071 (d) To explain qualitatively how that would change your results to part (a), (b) and (c) and what additional information would one need to know to analyze a system like this. In the question, it is given that patients arrive to a small hospital emergency room according to a Poisson process with an average of 1.5 per hour. Suppose that the average service time is 26 minutes. Thus, we have that, λ = 1.5 per hour μ = 60 26 = 2.31 per hour Thus, the utilization rate will be: p = λ μ = 1.5 2.31 = 0.65 Now, if the emergency room has a triage nurse who gives priority to more serious conditions, then the expected total time in the system will change as the time to priority patients will increase, the expected time each customer has to wait will also increase according to time spent in priority cases and the expected number of patients wai6ting for service will change according to the patients coming in the priority case. The additional information one would need to know to analyze a system like this is the time spent on the customer or time given for service in priority cases by the nurse.

(a) To find out what is the expected total time in the system, if there is only a single doctor working at any point in time. 1.238 hour. In the question, it is given that patients arrive to a small hospital emergency room according to a Poisson process with an average of 1.5 per hour. Suppose that the average service time is 26 minutes. Thus, we have that, λ = 1.5 per hour μ = 60 26 = 2.31 per hour Thus, the utilization rate will be: p = λ μ = 1.5 2.31 = 0.65 Now, the expected number of patients in the system is calculated as: l = p 1 − p = 0.65 1 − 0.65 = 1.857 Thus, the expected total time in the system is calculated as: w = l λ = 1.857 1.5 = 1.238 (b) To find out what is the expected time each customer has to wait, if there is only a single doctor working at any point in time. 0.8047 hour. In the question, it is given that patients arrive to a small hospital emergency room according to a Poisson process with an average of 1.5 per hour. Suppose that the average service time is 26 minutes. Thus, we have that, λ = 1.5 per hour μ = 60 26 = 2.31 per hour Thus, the utilization rate will be: p = λ μ = 1.5 2.31 = 0.65 Now, the expected number of patients in the system is calculated as: l = p 1 − p = 0.65 1 − 0.65 = 1.857 And, the expected number of customer has to wait is calculated as: l q = l p = 1.857 × 0.65 = 1.2071 Thus, the expected time each customer has to wait is calculated as: w q = l q λ = 1.2071 1.5 = 0.8047 (c) To find out what is the expected number of patients waiting for service, if there is only a single doctor working at any point in time. 1.2071 patients per hour. In the question, it is given that patients arrive to a small hospital emergency room according to a Poisson process with an average of 1.5 per hour. Suppose that the average service time is 26 minutes. Thus, we have that, λ = 1.5 per hour μ = 60 26 = 2.31 per hour Thus, the utilization rate will be: p = λ μ = 1.5 2.31 = 0.65 Now, the expected number of patients in the system is calculated as: l = p 1 − p = 0.65 1 − 0.65 = 1.857 And, the expected number of patients waiting for serviceis calculated as: l q = l p = 1.857 × 0.65 = 1.2071 (d) To explain qualitatively how that would change your results to part (a), (b) and (c) and what additional information would one need to know to analyze a system like this. In the question, it is given that patients arrive to a small hospital emergency room according to a Poisson process with an average of 1.5 per hour. Suppose that the average service time is 26 minutes. Thus, we have that, λ = 1.5 per hour μ = 60 26 = 2.31 per hour Thus, the utilization rate will be: p = λ μ = 1.5 2.31 = 0.65 Now, if the emergency room has a triage nurse who gives priority to more serious conditions, then the expected total time in the system will change as the time to priority patients will increase, the expected time each customer has to wait will also increase according to time spent in priority cases and the expected number of patients wai6ting for service will change according to the patients coming in the priority case. The additional information one would need to know to analyze a system like this is the time spent on the customer or time given for service in priority cases by the nurse.

EBK PRODUCTION AND OPERATIONS ANALYSIS

EBK PRODUCTION AND OPERATIONS ANALYSIS

7th Edition

ISBN: 8220102480681

Author: Olsen

Publisher: WAVELAND

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EBK PRODUCTION AND OPERATIONS ANALYSIS

Ch. 7.1 - Prob. 1P Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.2 - Prob. 8P Ch. 7.2 - Prob. 9P Ch. 7.2 - Prob. 10P

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