Solve in arena : Urban Clinic Problem: $(20$ points$)$

An urban health clinic is seeking to optimize its patient service process to reduce waiting times and

improve patient experience. The clinic has three main service points:

Check$-$In Desk

Examination Rooms

Pharmacy Counter

Your objective is to create a discrete$-$event simulation model for this health clinic's service process.

Details:

Arrivals: Patients arrive at the clinic at an average rate of $6$ patients per hour with an exponentially

distributed interarrival time of $10$ minutes. The last patient is scheduled to arrive at $5$:$30$ PM$.$

Check$-$In: Check$-$in time per patient is uniformly distributed between $5$ to $10$ minutes. After check$-$in$,$

patients are directed to wait for an examination room.

Examination Rooms: Examination time depends on the patient's condition: General Checkup: Take a

Triangular $(20,25,30)$ minutes and Specialized Consultation: Take a Normally distributed $40$ minutes

with a standard deviation of $10$ minutes. $60\%$ of patients come for a General checkup, while $40\%$

need Specialized Consultation.

Pharmacy Counter: After the examination, $75\%$ of patients are directed to the Pharmacy Counter to

collect prescribed medications, while the remaining $25\%$ can leave directly. Medication preparation

and payment process take a uniformly distributed $10$ to $20$ minutes per patient.

Other Information: The clinic operates from $8$:$00$ AM to $6$:$00$ PM$,$ Monday to Friday.

There is $1$ check$-$in desk, $3$ examination rooms, and $2$ pharmacy counters.

Tasks:

Design a discrete$-$event simulation model that represents the clinic's patient service process. Run

the simulation for $100$ replications and output all statistics in minutes.

Analysis:

a$.$ Whiat is the average number of patients served in one day?

b$.$ What is the average Clinic Duration $($the time that all patients have left the system$)?$

c$.$ What is the average time a patient spends in the clinic from check$-$in to departure?

d$.$ What is the bottleneck in the service process?

Optimize the system:

The clinic's goal is to ensure that $90\%$ of patients spend no more than $1$ hour in total at the clinic.

Adding resources where needed, what changes would you need to make to achieve this goal?