I. Introduction to Operations Research


NATURE OF OPERATIONS RESEARCH

Operations Research maybe described as a scientific approach to decision making that involves the operations of organizational systems. As the nature applies, operations research involves "research on operations". This tells us something about both the approach and the area of the application of the field.

Operations Research (OR) seeks the determination of the best (optimum) course of action of a decision problem under the restriction of limited resources. The term operations research quite often is associated almost exclusively with the use of mathematical techniques to model and analyze decision problems.

Today, the term operations research means a scientific approach to decision making, which seeks to determine how best to design and operate a system, usually under conditions requiring the allocation of scarce resources.

In summary, operations research is concern with optimal decision making is, and modeling of, deterministic and probabilistic system that originate from real life.

3 MAJOR ASPECTS IN PROBLEM DEFINITION OF OPERATIONS RESEARCH

  1. a description of the goal or objective of the study
  2. an identification of decision alternatives of the system
  3. a recognition of the limitations, restrictions, and requirements of the system
BASIC COMPONENTS IN CONSTRUCTING MATHEMATICAL MODELS

  1. The objective of the system
  2. The limitations imposed on the system
MATHEMATICAL MODEL OF AN OR PROBLEM

Mathematical models are idealized representations, they are expressed in terms of mathematical symbols and expressions. The mathematical model of a business problem is the system of equation and related mathematical expressions that describe the essence of the problem. Thus, if there are n related quantifiable decisions to be made, they are represented as DECISION VARIABLES (say X1, X2,....Xn) whose respective value are to be determined. The appropriate measure of performance (e.g. e=3X1+2X2+...+5Xn). This function is called the OBJECTIVE FUNCTION. Any assign to these variables are also expressed mathematically, typically by means of inequalities or equations (e.g. X1+3X1X2+2X2 <= 10). Such mathematical expressions for the restrictions are called CONSTRAINTS. The constants (coefficients or right-handed sides) in the constraints and the objective function are called the PARAMETERS of the model. The mathematical model might then say that the problem is to choose the values of the decision variables so as to maximize the objective function, subject to the specified constraints. Such a model,and minor variation of it , typify the models used in operations research.

CONSTRUCTION OF THE MATHEMATICAL MODEL

The construction of a mathematical model can be initiated by answering the following questions:

  1. What does the model seek to determine? In other words, what are the variables (unknown) of the problem?
  2. What restrictions must be imposed on the variables to satisfy the limitations of the model system? In other words, what are the constraints of the problem?
  3. What is the objective or goal that needs to be achieved to determine the optimum solution from among all feasible values of the variables?
Send your comments and/or suggestions to yeng21@hotmail.com