Tenside Hospital is experiencing a surge in emergency room (ER) visits during the weekend evenings, particularly...

 

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Tenside Hospital is experiencing a surge in emergency room (ER) visits during the weekend evenings, particularly between 8:00 PM and 1:00 AM. During this period, the hospital traditionally allocates five examination rooms for emergency cases. However, the healthcare landscape is changing as a competing hospital has recently announced its plans to discontinue emergency services within the next six months. In response to this announcement, Tenside Hospital expects a significant increase in patient arrivals during the 8:00 PM to 1:00 AM window. It is anticipated that the number of emergency cases will rise by one-third in the future. Analyzing the data from the previous year, which included records of arrival and service times, the hospital has identified little seasonal variation in ER usage. Additionally, ER personnel have indicated that their protocols and procedures have remained relatively consistent since the ER was reorganized two years ago. Based on the past year's data, over a period of twenty Saturday nights (equivalent to one hundred hours), the hospital recorded 900 emergency patients coming to the ER. These patient arrivals follow a pattern that approximates a Poisson distribution. Through a comprehensive time-study, the hospital determined that the average service time is 30 minutes per emergency patient. Service times follow exponential distribution. Note that operating each emergency room costs $1000/hour, while the waiting cost for each customer is $750/hour. Find the number of examination rooms required for emergency patients to minimize total cost in the future (remember that the arrival rates will increase in the future). Tenside Hospital is experiencing a surge in emergency room (ER) visits during the weekend evenings, particularly between 8:00 PM and 1:00 AM. During this period, the hospital traditionally allocates five examination rooms for emergency cases. However, the healthcare landscape is changing as a competing hospital has recently announced its plans to discontinue emergency services within the next six months. In response to this announcement, Tenside Hospital expects a significant increase in patient arrivals during the 8:00 PM to 1:00 AM window. It is anticipated that the number of emergency cases will rise by one-third in the future. Analyzing the data from the previous year, which included records of arrival and service times, the hospital has identified little seasonal variation in ER usage. Additionally, ER personnel have indicated that their protocols and procedures have remained relatively consistent since the ER was reorganized two years ago. Based on the past year's data, over a period of twenty Saturday nights (equivalent to one hundred hours), the hospital recorded 900 emergency patients coming to the ER. These patient arrivals follow a pattern that approximates a Poisson distribution. Through a comprehensive time-study, the hospital determined that the average service time is 30 minutes per emergency patient. Service times follow exponential distribution. Note that operating each emergency room costs $1000/hour, while the waiting cost for each customer is $750/hour. Find the number of examination rooms required for emergency patients to minimize total cost in the future (remember that the arrival rates will increase in the future).

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SOLUTION To minimize the total cost we need to determine the number of examination rooms that will m... View the full answer