Methodology of Operations Research (OR): Phases, Steps and Process

Introduction

Approaches / Phases / Methodology / Stages of Development of Operation Research — Every problem cannot be solved simply by experience or intuition. Modern organizations often face complex problems involving limited resources, multiple alternatives, uncertainty, and conflicting objectives. In such situations, a scientific and systematic approach is required to identify the best possible solution. The methodology of Operations Research is a systematic process used to solve decision-making problems scientifically. This methodology consists of a number of sequential phases or steps. Different authors use the terms phases, steps, process, and methodology interchangeably.

Operations Research (OR) follows a well-defined methodology that guides decision-makers from identifying a problem to implementing the best solution. This methodology ensures that decisions are based on facts, data, and mathematical analysis rather than guesswork.

Understanding the methodology of Operations Research is essential because it explains how OR actually works. It provides a logical sequence of steps that helps managers solve complex business, engineering, production, transportation, and planning problems efficiently.

In this article, we will discuss the complete methodology (phases or steps) of Operations Research in simple language with suitable examples and exam-oriented notes.

What is the Methodology of Operations Research?

The methodology of Operations Research is a systematic and scientific process used to solve complex decision-making problems. It consists of a series of logical phases that help identify a problem, develop a mathematical model, obtain the optimum solution, test its validity, implement it, and continuously monitor its performance.

Different authors use the terms methodology, phases, steps, process, or procedure interchangeably because they all describe the systematic sequence followed in an OR study.

💡 Exam Tip

Methodology of Operations Research is the systematic process of solving decision-making problems scientifically through a sequence of logical phases.

Why is the OR Methodology Important?

Operations Research is not just about solving mathematical equations. A correct solution can only be obtained when the problem is properly understood and solved in a systematic manner.

A well-defined methodology helps to:

Clearly identify the real problem.
Collect relevant and reliable data.
Develop an appropriate mathematical model.
Obtain the optimum solution.
Test the validity of the model.
Successfully implement the solution.
Monitor results and improve the system continuously.

Without following these steps, even advanced mathematical techniques may produce incorrect or impractical results.

Phases (Steps) of Operations Research Methodology

The methodology of Operations Research generally consists of the following phases:

Recognition of the Problem
Problem Formulation (Formulating the problem)
Constructing a mathematical model to represent the system under study
Obtaining the Optimum Solution (Deriving the solutions from the model)
Model Validation and Testing (Testing the Model and the solution derived from it)
Establishing Control and Monitoring (Controlling the solutions)
Implementation of the Solution (Putting the solution to work)

Methodology of Operations Research (OR): Phases, Steps and Process

Phase 0: Recognition of the Problem

Meaning

Every Operations Research study begins with recognizing that a problem actually exists.

Managers first identify situations where performance is below expectations or where improvements are possible. Unless the real problem is recognized, no meaningful analysis can begin.

Typical situations include:

Rising production costs
Declining profits
Delivery delays
Increasing inventory costs
Poor utilization of machines
Customer dissatisfaction

Recognizing the correct problem is the foundation of every successful OR study.

Real-Life Example

A logistics company notices that transportation costs have increased significantly over the past six months. Management recognizes this as a problem requiring scientific analysis.

💡 Exam Tip

Recognizing the correct problem is the first requirement for a successful Operations Research study.

Phase I: Problem Formulation (Formulating the problem)

Meaning

Once the problem has been identified, the next step is to define it clearly and precisely.

Problem formulation is considered one of the most important phases because an incorrectly defined problem will always produce an incorrect solution, regardless of how advanced the mathematical techniques are.

So, before proceeding to find the solution to a problem, first of all, one must be able to formulate the problem in the form of an appropriate model.

During this phase, the decision-maker determines exactly what needs to be achieved and identifies all factors affecting the problem. To do so, the following information will be required:

Who is the decision-maker?
What is the objective?
What are the available alternatives?
Which variables can be controlled?
Which variables cannot be controlled that may affect the possible solution?
What are the restrictions, limitations or constraints?
What information is required?

A clearly formulated problem becomes the foundation for developing an effective mathematical model.

Every Operations Research study begins with identifying and clearly defining the problem. Unless the problem is properly formulated, even the most advanced mathematical techniques cannot produce a useful solution.

Real-Life Example

A manufacturing company wants to maximize profit by producing two products using limited labour hours and raw materials.

The problem is formulated as:

"Determine the quantity of Product A and Product B that should be produced to maximize profit without exceeding the available resources."

💡 Exam Tip

Problem formulation is the most important phase of Operations Research because a wrongly defined problem can never produce the correct solution. Since the wrong formulation cannot yield the right decision (solution), one must be considerably careful while executing this phase.

Phase II: Constructing a mathematical model to represent the system under study:

Meaning

After defining the problem, it is converted into a mathematical model. A mathematical model is a simplified mathematical representation of a real-life problem. It helps analyze different alternatives objectively and scientifically.

Hence, the second phase of OR is to construct a mathematical model representing the system under study. A mathematical model should include the following three important basic factors:

1. Decision Variables and parameters

These are the unknown values that must be determined.

Example:

Quantity of Product A and Product B to be produced.

2. Objective Function

This represents the goal of the problem.

The objective may be:

Maximize Profit
Minimize Cost
Minimize Time
Maximize Production
Maximize Customer Satisfaction (where measurable)

3. Constraints or Restrictions

Constraints represent the limitations under which decisions must be made.

Examples include:

Limited labour hours
Limited raw materials
Budget limitations
Machine capacity
Storage space

Only after identifying these three components can a complete mathematical model be developed.

Real-Life Example

Suppose a factory manufactures two products.

The mathematical model may include:

Decision Variables → Number of units of Product A and Product B
Objective Function → Maximize total profit
Constraints → Labour hours, machine hours, and raw material availability

That is,

Decision Variables

↓

Objective Function

↓

Constraints

↓

Mathematical Model

💡 Exam Tip

Every mathematical model in Operations Research contains Decision Variables, Objective Function, and Constraints.

📌 Remember This

Every OR study begins with recognizing the real problem.
A well-formulated problem is half solved.
A mathematical model converts a real-life problem into mathematical form.
Every OR model contains Decision Variables, Objective Function, and Constraints.

Phase III: Obtaining the Optimum Solution (Deriving the solutions from the model)

Meaning

After constructing the mathematical model, the next step is to solve it and determine the optimum (best) solution.

The objective of this phase is to find the values of the decision variables that either maximize or minimize the objective function while satisfying all the given constraints.

Hence, this phase is devoted to the computation of those values of decision variables that maximize or minimize the objective function. Such a solution is called an optimal solution.

Depending on the nature of the problem, different Operations Research techniques are used to obtain the optimum solution.

Some commonly used techniques are:

Linear Programming (LP)
Simplex Method
Transportation Model
Assignment Model
Dynamic Programming
Queuing Theory
Inventory Models
Network Analysis (PERT & CPM)
Simulation

The selected technique depends on the type and complexity of the problem.

Real-Life Example

A furniture company manufactures chairs and tables. After developing the mathematical model, the Simplex Method is used to determine how many chairs and tables should be produced to earn the maximum profit without exceeding the available wood, labour, and machine hours.

💡 Exam Tip

The purpose of this phase is to obtain the optimum solution, not just any feasible solution. The optimum solution provides the best possible result within the given constraints.

Phase IV: Model Validation and Testing (Testing the Model and the solution derived from it)

Meaning

Obtaining a mathematical solution does not guarantee that it will work in real life. Therefore, before implementation, the model and its solution must be carefully tested.

So, after completing the model, it is once again tested as a whole for the errors if any. A model may be said to be valid if it can provide a reliable prediction of the system’s performance.

That is, Model validation checks whether the mathematical model accurately represents the real-world system and whether its predictions are reliable.

A good practitioner of OR realizes that his model be applicable for a longer time and thus he updates the model from time to time by taking into account the past, present and future specifications of the problem.

During this phase, managers verify:

Is the model realistic?
Does the model represent the real problem correctly?
Are assumptions valid? Are all assumptions reasonable?
Is the solution practical? Does it predict correctly?
Does the model produce realistic results?
Can the solution be applied under actual working conditions?

If any errors or unrealistic assumptions are found, the model is revised and tested again.

Why is Validation Important?

Business conditions change continuously. A model that works today may become unsuitable in the future due to changes in technology, customer demand, government policies, or market conditions.

Therefore, Operations Research models should be reviewed and updated whenever necessary.

Real-Life Example

A supermarket develops a demand forecasting model. Before using it, the predicted demand is compared with actual sales from previous months. If the results closely match the real data, the model is considered valid.

💡 Exam Tip

A mathematical model is useful only if it provides reliable and realistic predictions under actual conditions.

Phase V: Establishing Control and Monitoring (Controlling the solutions)

Meaning

Even after a model has been validated, its performance must be monitored continuously.

This phase establishes a control system to ensure that the implemented solution continues to produce the desired results.

This phase establishes control over the solution with any degree of satisfaction. The model requires immediate modification as soon as the controlled variables (one or more) change significantly, otherwise the model goes out of control.

Managers regularly compare actual performance with the expected performance suggested by the model.

As the conditions are constantly changing in the world, the model and the solution may not remain valid for a long time.

If significant changes occur, such as:

Customer demand
Production capacity
Raw material prices
Government regulations
Technology

the mathematical model should be modified accordingly.

Without proper monitoring, an OR model may gradually become outdated and ineffective.

Real-Life Example

An airline uses an OR model to schedule flights. During the holiday season, passenger demand increases significantly. The company reviews and updates the scheduling model to accommodate the increased traffic.

💡 Exam Tip

Operations Research is a continuous process. Models should be monitored and updated whenever operating conditions change.

Phase VI: Implementation of the Solution (Putting the solution to work)

Meaning

Finally, the tested results of the model are implemented to work. This would basically involve a careful explanation of the solution to be adopted and its relationship with the operating realities.

Implementation is the final and most practical phase of the Operations Research methodology. After the solution has been tested and approved, it is put into practice.

A scientifically correct solution is valuable only when it is successfully implemented.

Successful implementation generally requires:

Management support
Employee cooperation
Proper communication
Adequate training
Continuous supervision

Managers should also monitor the implementation process to identify practical difficulties and make necessary adjustments.

Real-Life Example

A logistics company develops an optimized vehicle routing plan using Operations Research. After testing the plan, the company introduces the new routes into its daily delivery operations, resulting in lower transportation costs and faster deliveries. That is, after developing the optimum transportation schedule, the company applies the recommended routes in its daily logistics operations.

💡 Exam Tip

The effectiveness of Operations Research depends not only on finding the best solution but also on implementing it successfully.

Flowchart of Operations Research Methodology

The complete methodology of Operations Research can be represented as follows:

Recognition of the Problem
            ↓
Problem Formulation
            ↓
Construction of Mathematical Model
            ↓
Obtaining the Optimum Solution
            ↓
Model Validation and Testing
            ↓
Establishing Control and Monitoring
            ↓
Implementation of the Solution

This flowchart shows that Operations Research follows a logical and systematic process, where each phase builds upon the previous one to achieve the best possible decision.

📌 Remember This

Recognition identifies the problem.
Problem formulation defines the problem clearly.
Mathematical modelling converts the problem into mathematical form.
Optimization identifies the best solution.
Validation ensures that the model is realistic.
Control keeps the model effective over time.
Implementation converts the solution into practical action.

Real-Life Example of Operations Research Methodology

To understand the methodology of Operations Research more clearly, let us consider a simple real-life example.

Problem

A furniture manufacturing company produces Tables and Chairs. The company wants to earn the maximum profit, but it has limited raw materials, labour hours, and machine time.

Instead of making decisions based on guesswork, the company applies the Operations Research methodology.

Step 1: Recognition of the Problem

The company realizes that profits are not increasing even though demand is high.

Step 2: Problem Formulation

The problem is defined as:

"How many tables and chairs should be produced to maximize profit without exceeding the available resources?"

Step 3: Mathematical Model

The OR team develops a mathematical model containing:

Decision Variables → Number of tables and chairs.
Objective Function → Maximize total profit.
Constraints → Labour hours, machine hours, and raw materials.

Step 4: Obtaining the Optimum Solution

The model is solved using the Simplex Method, and the best production plan is obtained.

Step 5: Model Validation

The solution is compared with previous production data to verify that it is realistic and practical.

Step 6: Control and Monitoring

The company regularly monitors changes in demand, labour availability, and raw material prices. If these factors change, the model is updated.

Step 7: Implementation

The optimized production plan is implemented in the factory, resulting in higher profits and better resource utilization.

Why Should We Follow the OR Methodology?

Following a systematic methodology helps organizations make better decisions and avoid costly mistakes.

Some important benefits are:

Ensures a systematic approach to problem-solving.
Reduces the chances of incorrect decisions.
Improves the quality and accuracy of decisions.
Optimizes the utilization of limited resources.
Saves time and operational costs.
Increases productivity and efficiency.
Helps managers make objective decisions.
Provides reliable and practical solutions.

Common Mistakes Students Make

Many students lose marks in examinations because of the following mistakes:

❌ Mistake 1

Writing only the names of the phases without explaining them.

✔ Correct Approach

Explain the purpose of each phase in 3–5 lines.

❌ Mistake 2

Confusing Problem Recognition with Problem Formulation.

✔ Correct Approach

Problem Recognition means identifying that a problem exists.
Problem Formulation means defining the problem clearly.

❌ Mistake 3

Thinking that obtaining the solution is the final step.

✔ Correct Approach

The solution must also be validated, monitored, and implemented successfully.

❌ Mistake 4

Ignoring the flowchart.

✔ Correct Approach

Always draw the OR methodology flowchart in university examinations whenever possible. It improves presentation and often helps in scoring better marks.

📌 Remember This

Operations Research follows a scientific and systematic methodology.
Every phase is important because each phase depends on the previous one.
A well-formulated problem leads to a better mathematical model.
A mathematical model is useful only if it is validated and implemented successfully.
Operations Research is a continuous process, not a one-time activity.

Frequently Asked Questions (FAQs)

1. What is the methodology of Operations Research?

The methodology of Operations Research is a systematic process used to solve complex decision-making problems through problem identification, mathematical modelling, optimization, validation, control, and implementation.

2. What are the phases of Operations Research?

The major phases are:

Recognition of the Problem
Problem Formulation
Construction of the Mathematical Model
Obtaining the Optimum Solution
Model Validation and Testing
Establishing Control and Monitoring
Implementation of the Solution

3. Why is problem formulation considered the most important phase?

Because an incorrectly defined problem leads to an incorrect mathematical model and an incorrect solution. Therefore, a clear problem formulation is essential for the success of an OR study.

4. Why is model validation necessary?

Model validation ensures that the mathematical model accurately represents the real-world system and produces reliable and practical results before implementation.

5. Can an Operations Research model be used forever?

No. Business conditions change over time. Therefore, OR models should be monitored regularly and updated whenever significant changes occur.

The methodology of Operations Research provides a scientific and systematic framework for solving complex decision-making problems. Instead of relying on intuition or trial-and-error methods, it guides decision-makers through a logical sequence of phases, beginning with problem recognition and ending with the implementation and continuous monitoring of the solution.

Each phase plays a vital role in the success of an OR study. A carefully formulated problem leads to an appropriate mathematical model, while proper validation and implementation ensure that the recommended solution produces practical results. Therefore, understanding the methodology of Operations Research is essential for students, researchers, managers, and professionals who wish to make informed and effective decisions.

About the Author

Lata Agarwal

Mathematics, Science and Astronomy professional, M.Sc. and M.Phil. in Maths with 10+ years of experience as Assistant Professor and Subject Matter Expert.

Author at Prinsli.com

References

Kanti Swarup, P. K. Gupta & Man Mohan, Operations Research, Sultan Chand & Sons.
J. K. Sharma, Operations Research: Theory and Applications, Macmillan India.
Hamdy A. Taha, Operations Research: An Introduction, Pearson Education.
Frederick S. Hillier & Gerald J. Lieberman, Introduction to Operations Research, McGraw-Hill Education.
H. M. Wagner, Principles of Operations Research, Prentice Hall.