What is Operations Research and Why is it Important?

2024-09-23Last Updated: 2024-09-23

Operations research is concerned with the optimal decision making in and modeling of deterministic and probabilistic systems that originate from real life. It is a collection of mathematical techniques and tools, which, in conjunction with a systems approach, are applied to solve practical decision problems of an economic or engineering nature.

Operations research seeks the determination of the best course of action in a decision problem under the restriction of limited resources.

The phases of an operation research can be broadly broken down into the following steps:

Problem Identification
Development of the Mathematical Model
Solution of the Model
Model Validation / Sensitivity Analysis
Implementation of the Results

Implementation of the model results is the most important stage. The following issues has to be carefully and properly dealt with in order for this critical stage to be successful.

Model data management
Input and Output modeles
Model Documentation
User Education and Awareness
Model Maintenance

Operations research uses mathematical techniques to model and analyze decision problems. However, purely mathematical solutions are not always effective. Human motives, needs and behaviour must be given due consideration.

Components of a Decision Problem

1. Objective

The end result we desire to achieve by selecting a specific course of action (policy, alternative) for the system under study.

Typical objectives are profit, revenue, cost, quality of service, safety, market share.

In many cases there are multiple and sometimes conflicting objectives. In Operations Research studies it is very important to be able to define and work with measurable objectives.

2. Variables

Factors under the control of the decision maker (selections/alternatives available to the decision maker).

Determination of the correct variables is usually a crucial first aspect in many decision problems.

There is usually a mathematically definable (simple or complex) relationship between the decision variables and the objective.

3. Parameters

Factors not under the control of the decision maker. They may be deterministic or random, static (constant in time) or dynamic (changing in time).

Mathematical Modeling

A model is a representation of an actual object or situation. As such, models show the direct or indirect relationships and the interrelationships (action and reaction) in terms of cause and effect.

A model is an abstraction of reality. It must be less complex than reality itself; however, it must be representative of those aspects of reality that are being investigated, if it is to be of any use.

In Mathematical Models the relationships and the interrelationships associated with the object or situation under study (and which are usually between objectives, constraints and variables) are presented in terms of mathematical functions involving the parameters and the variables.

A mathematical model should be:

As simple and understandable as possible
Reasonable
Adaptive
Easily to maintain and control
Complete on important issues.

Complexity in mathematical models is usually associated with:

The number of variables involved
The number of functions involved
The functional forms involved

Simplification is achieved through the identification of dominating variables, parameters, constraints and other relationships.

Advantages of Modeling

Provides a frame of reference in communications and discussions
Indicates flows, gaps, inconsistancies in the actual system
Facilitates inexpensive and fast experimentation
Provides information about the system on sensitivity issues, bottlenecks; critical parameters
It is quite a valuable tool for training and learning
Fast straightforward solutions free managers for other duties; leads to cost and time savings.

Disadvantages of Modeling

Oversimplification may lead to inaccuracies
It may fail to account for all exceptions
May lead to an unhealthy attachment by the developer
May be difficult to document, maintain and update
May be expensive to use

Simulation Models

Simulation models imitate the behaviour of the real system being investigated over a period of time. Time flow is achieved by specifying a number of events whose occurance signifies that important information pertaining to the behaviour of the real system can be gathered, and whose occurances can be imitated.

Simulation models do not need explicit mathematical functions to relate variables to each other and to the objective. Accordingly, more complex relationships can be modeled.

Solution of Models

In some cases it is sufficient to find just a feasible solution. In some cases, however, it is desired to find the best solution satisfying all the constraints, which is called the optimal solution.

Tools Available for Building and Solving Mathematical Models in Operations Research:

Deterministic Models

Linear Programming
Integer Programming
Dynamic Programming
Network Techniques Deterministic Models
Nonlinear Programming
CPM/PERT

Probabilistic Models

Queuing Theory
Inventory Theory
Reliability and Quality Control
Game Theory
Simulation Probabilistic Models
Markovian Decision Processes
Regression
Forecasting

The Bottom Line

Operations research is the science of planning and executing an operation to make the most economical use of the resourses available. It is the application of the methods of science to complex problems arising in the management of large systems of men, machines, materials and money, in industry, business, government and defense.

The distinctive approach is to develop a mathematical model of the system, incorporating measurements of factors such as chance and risk, with which to predict and compare the outcomes of alternative decisions and strategies. The purpose is to help management determine its policy and actions scientifically.