Operations Research

AIR UNIVERSITY, ISLAMABAD

Operations Research Final Project

A study of Armed Forces Institute of Cardiology, Rawalpindi

Submitted To:

Mr. Muhammad Umar

Submitted By:

Zubash Jawed

Sadaf Noor

Mehwish Rizwan

Nandana Zubair

Qurat-ul-Ain Arshad

Saba Areeg

Dated: 7th May, 2013

TABLE OF CONTENTS

INTRODUCTION...................................................................................................3

DETAILED PROBLEM DESCRIPTION.................................................................4

PROBLEM STATEMENT......................................................................................4

METHODOLOGY...................................................................................................5

Step One......................................................................................................5

Step Two.....................................................................................................6

Step Three..................................................................................................8

CONCLUSION AND RECOMMENDATIONS.........................................................8

INTRODUCTION

As part of our Operations Research course requirement, we were asked to choose any organization, identify a problem within that organization and then by applying any Operations Research Models to maximize or minimize the firm's profits or Cost.

We chose Armed Forces Institute of Cardiology (AFIC), and used Two- Variable LP model and Graphical LP solution to maximize their Profits. Although the Two-Variable LP model is very simple, we chose it because it was what was providing us with a solution that we could easily interpret.

The first part of the report is a detailed problem description and the problem statement, the second part of the report is the model that we have applied and a step-by-step brief of all calculations. In the third and final part of the report we have concluded the entire report by interpreting the results and then made recommendations keeping the findings in mind.

DETAILED PROBLEM DESCRIPTION

Currently on average, 200 civilian patients visit Armed Forces Institute of Cardiology's (AFIC) Out-patient Department. At present there is only one consultant who attends to these patients. The consultant works 12 hours a day on week days throughout the month (22 days on average). His/ her monthly salary is Rs. 120,000. Each patient pays Rs. 900 per visit. Since the consultant works 12 hours a day (inclusive of time he /she spends on ward rounds in the evening), he only manages to attend to 48 patients on average a day. The revenue generated from these 48 patients is their daily earning i.e. 48*900= Rs. 43200. One day salary of the consultant is calculated to be 120,000/22= Rs. 5454/ day. So profit per day is Rs. 37,746. The earnings that are lost are from the remaining 152 patients that remain unattended because of only one consultant. If 3 more consultants are hired, the revenue from the remaining 152 patients will also be added in profits hence maximizing the Profit of AFIC. The cost of hiring these consultants will be balance by the profits the department will make on daily basis. Earnings from 152 patients daily = 152*900= Rs. 136,800. Salary per day of 3 consultants is 5454*3= Rs. 16,362/ day. So we still end up with a profit of Rs.120, 438/day.

For our ease we are taking daily earnings from patients along with consultants' daily salary. We are not taking into account any commission consultants charge on daily basis.

PROBLEM STATEMENT

AFIC is looking forward to maximizing profits from its OPD. Number of patients is not more than 200, and the department can only hire 3 more consultants.

In Scenario 1; there is 1 consultant and he can attend to 48 patients on average per day. The profit from scenario 1 is Rs. 37,746.

In scenario 2, 3 more consultants are hired, so that the remaining 152 patients are also being catered. The profit in this scenario is Rs. 120,436.

Following is the Data derived from Problem description and statement.

Table 1: Data

Scenario 1 Scenario 2 Limits

Consultants 1 3 4

Patients 48 152 200

...