Question

Problem 1

Consider a clinic similar to the Student Health Services at OSU. You are asked to perform a capacity analysis for the clinic. The current resources of the clinic are as follows (assume that the information is steady throughout the day):

Number of Service Providers	Processing Time (min/patient)
Reception	3	5
Primary care provider	10	20
Nurse	3	30
Radiologist	2	40
Diabetes care	1	30
Nutrition care	1	25

In addition, the following information is presented to you on the operations of the clinic.

• All patients need to register with the receptionist before they can see a nurse/doctor. The average time to register at the reception desk is 5 minutes.

• On average, 30% of the incoming patients are considered to have only minor problems that can be handled by nurses. The remaining 70% are given appointments to see a primary care provider.

• The average consultation time with a nurse is 30 minutes. After diagnosis by a nurse, 30% of the patients are asked to see a primary care provider for further diagnosis.

• An appointment with a primary care provider lasts 20 minutes, on average. After check up by a primary care provider, 20% of the patients are referred to a radiologist, 10% are referred to the diabetes care center, 20% are referred to the nutrition care center and the remaining 50% either don’t need further referral or are referred to an outside hospital.

• The average consultation time with the radiologist is 40 minutes.

• It takes 30 minutes, on average, for diagnosis at the diabetes care center.

• An appointment at the nutrition care center usually takes 25 minutes.

The manager of the clinic is interested in the following questions:

a. What is the capacity of each resource in the clinic (reception, primary care provider, nurse, radiologist, diabetes care, and nutrition care) in number of patient-arrivals per hour?

b. What is the system capacity of the clinic in number of patient-arrivals per hour? Identify the bottleneck(s). What is the slack of each resource in total number of patient -arrivals per hour?

c. If the clinic hires two additional units for the bottleneck resource, what would be the new system capacity and bottleneck(s)?

d. Suppose that the proposal in part (c) is implemented and all employees work 10 hours per day, how many patients can the clinic serve each day?

Answer 1

a. What is the capacity of each resource in the clinic (reception, primary care provider, nurse, radiologist, diabetes care, and nutrition care) in number of patient-arrivals per hour?

To calculate patientt arrival per hour use the formula =(60/( Procesing time in min/patient)) *Number of service providers

Resources	Number of Service Providers	Processing Time in patient arrival/hour
Reception	3	5 = 60/5*3 = 36
Primary care provider	10	20 = 60/20*10 = 30
Nurse	3	30 = 60/30*3 = 6
Radiologist	2	40 = 60/40 *2 = 3
Diabetes care	1	30 = 2
Nutrition care	1	25 = 60/25 = 2.4

b.

The bottleneck in the entire system is the Nutrition Care who can only see 2.4 patient per hour, hence to calculate the system capacity :

• Nutrition Care can see 2.4 patient/hour
• Nutrition Care sees 20 % of the patients referred to the primary care provider: 20 % of x = 2.4 patients per hour i.e capacity of nutrition care
• Therefore x = 12 patients are referred to the primary care provider 12 patients/hour
• Also, we know that the primary care provider sees 70 % of the patients and 30% of the patients observed by nurses are referred to the primary care provider = 0.3*30 = 9 %
• Therefore a primary care provider sees a total of 79% of the patients.

Hence the total system capacity is roughly : 12/0.79 = 15.18 patients/hour

The slack are :

• Reception = 36 - 15.18 = 20.82 patients/hour
• Primary Care Provider = 70% of 20.82 and 30% of nurse patients = 10) = 0.7*15.18 + 10 = 20.626 patients/hour
• Nurse = ( 30% of 15.18) = 4.554 patients/hour
• Radiologist = 20% of 12 = 2.4 patients per hour
• Diabetes Care = 10% of 12 patients = 1.2 patients/hour .
• Nutrition Care = 0 patients/hour ( since it is the bottleneck)

c.

The bottleneck i.e nutrition care could see now = 7.2 patients/hour and the new bottleneck would be Diabetes Care = 2 patients/hour

Therefore the 10% of X = 2

therefore X = 20 patients are primary care patients

Now the primary care provider could see 20 patients per hour

Primary care provider sees 79 % of the patients

New system capacity = 20/0.79 = 25.316 patients /hour

d.

The clinic can serve = 25.316*10 = 253 patients on a daily basis ( approximately )