الفهرس 
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Abstract
Operation Research (O.R.) is a science that deals with problem formulation, solutions and finally appropriate decision-making. O.R. is the use of mathematical models, statistics and algorithm to aid in decision-making. It is most often used to analyze complex real life problems typically with the goal of improving or optimizing performance.There are many different models of O.R. that can be used to solve the defined problem. These models can be broken into two categories, the deterministic and stochastic. Each model is created to specify a certain problem or application needed to be solved.Linear programming, sometimes called optimization modeling, is one of the many methods of O.R.
Linear Programming is the most powerful and widespread business optimization tools. Linear Programming is that branch of mathematical programming which is designed to solve optimization problems, where all the constraints as well as the objectives are expressed as linear function. LP uses a mathematical model to describe the problem of concern. The adjective linear means that all the mathematical functions in the model are required to be linear functions.
Linear program is ideally presented with mathematical models; they are expressed in terms of mathematical symbols and expressions. Mathematical model of a problem is a system of equations and related mathematical expressions that describe the essence of the problem. Thus, if there are (n) related quantifiable decisions to de made, they are represented as decision variables (say,x1, x2,….,xn) whose representative values are to be determined. The appropriate measure of performance (e.g. profit) is then expressed as a mathematical function of these decision variables (for example, p= 3x1+ 2x2+…..+5xn). This function is called the objective function. Any restrictions on the values that can be assigned to these decision variables are also expressed mathematically, typically by means of inequalities or equalities (for example x1+3x2<10). Such mathematical expressions for the restrictions often are called constraints. The constants in constraints and the objective function are called the parameters of model. The mathematical model might then say that the problem is to choose the value of decision variables to maximize the objective function.Linear programming has basic assumptions, which are certainty,proportionality, additivity, divisibility, and non-negativity.
The operating room can be seen as the engine that drives the hospital, and it represents a bottleneck in most hospitals. It accounts for approximately two thirds of hospital resource costs, including the costs of personnel and facilities.
The main aim of hospital managers is to ensure an optimal utilization of medical resources, the surgery delivery at the right time, the maximization of patient flow (hence, increase profitability) without incurring additional costs or excessive patient waiting. Inefficient and inaccurate planning and scheduling of OR time imply either delays of surgery or cancellations, which are costly to the patient and to the hospital.
This study aims to:
1. To determine the procedure mix for the department of surgery that produces optimal financial outcomes for the hospital.
2. To analyze the effect of changes in procedure mix on the hospital financial outcomes.
3. To evaluate the impact of constrained resources on the hospital financial outcomes.
The study was conducted in Al-Salama New Hospital, one of the fast-growing multi-specialty private hospitals in Alexandria affiliated to Andalusia Medical Group. It included 86 beds, 16 ICU beds, and 4 operating rooms, with a fully automated information system and electronic medical records. It had expressed willingness to provide the data necessary for developing linear programming model.
The study sample consists of all surgical procedures, performed in all the specialties within the department of surgery in the study hospital during the year 2007. For each surgical procedure; hospital number, age, sex, diagnosis, type of surgical procedure, date and time of admission, date and time of discharge, date of operation, date of ICU admission, date of ICU discharge, and total revenue are collected. And a structured questionnairewas developed by the researcher and conducted for the administrator of the hospitalto collect information about the accepted range of change in the numbers of procedures and the expected or/and planned changes in the hospital resources during 2008 including, ward beds number, operating room number, icu bed number, recovery room number.
The study reveals the following findings:
The revenue gained from the baseline module was the higher revenue among all modules although it is not applicable. The maximum revenue gained from it was 9,196,644 £.Є. instead of 7,342,993 £.Є. in the year 2007, forming an increase by 25.2%, achieved by increasing the number of procedures in only two specialties; plastic and orthopedic specialties, and omitting all procedures from other specialties, which was not applicable in this large multispecialty private hospital.
The optimum feasible solutions of other modules increase the revenue by 1.9% to 10.3% with different procedure mix and utilization of resources.
Module no. 4 was developed according to the results obtained from a questionnaire answered by the administrators of the hospital. The questionnaire results proposed; cancellation of the recovery room, increasing the operating rooms by 25%, increasing the ICU beds by 12.5% and increasing both ward beds by 9.3%. This module showed best applicable solution, with a higher increase in revenue by 10.3%, achieved by increasing the number of gynecological & obstetric, ENT, plastic, maxillofacial, orthopedic, and general surgery procedures, and decreasing the number of pediatric, cardiothoracic, neurosurgery, and urology procedures.
As regards the resources in this module, the operating room time had surplus by 27279 minutes/year, while preoperative time, ICU days, and ward days were totally consumed in this module. Each increase by one day in ICU could increase the revenue by 32539 £.Є, while each unit increase in preoperative time and ward days could increase the revenueby 8 and 437 £.Є. respectively.