Tools and Techniques of Operations Research (OR)
Introduction
Operations Research (OR) uses different mathematical tools and analytical techniques to solve managerial and decision-making problems. Every problem is different, so a single technique cannot solve every type of problem. Depending on the nature of the problem, the O.R. specialist selects the most suitable tool or technique.
Some techniques are used to maximize profit, some minimize cost, while others help in project planning, inventory control, scheduling, transportation, waiting-line analysis, or decision making under competition.
The following are the important tools and techniques used in Operations Research.
1. Linear Programming (LP)
In OR, Linear programming is used to find a solution for optimising a problem or objective. The objective may to maximize or minimize a problem.
Linear Programming is one of the most widely used techniques in Operations Research. It is used to obtain the best solution when the objective is to maximize or minimize a linear objective function subject to a set of linear constraints.
In Linear Programming, both the objective function and all constraints must be expressed in linear expressions (linear equations or inequalities).
Example
A factory manufactures two products using limited labour and raw materials. Linear Programming helps determine how many units of each product should be produced to earn the maximum profit.
ЁЯТбExam Note:
Linear Programming is used only when both the objective function and the constraints are linear.
2. Non-linear Programming (NLP)
These methods are used when either the objective function or some of the constraints are not linear in nature.
Some decision-making problems cannot be represented by linear equations. When the objective function, one or more constraints, or both are non-linear, Non-linear Programming is used.
This technique helps solve optimization problems where the relationship between variables is non-linear.
Example
A company wants to minimize production cost when the cost increases at a changing rate instead of a constant rate.
ЁЯТбExam Note:
Non-linear Programming is used when linear programming assumptions are not satisfied.
3. Integer Programming (IP)
In some practical situations, decision variables cannot have fractional values. They must be whole numbers.
Integer Programming is used when one or more decision variables are restricted to integer values.
In an LPP, if the decision variables are restricted to an integer value, it is known as Integer programming problems. In other words, these methods are used when one or more of the variables can take only integral values.
Example
A company must decide how many trucks or machines to purchase. Since fractional values are not possible, Integer Programming is used.
ЁЯТбExam Note:
Integer Programming is a special type of Linear Programming in which decision variables take only integer values.
4. Transportation Problem
The Transportation Problem is a special type of Linear Programming problem.
In this problem, goods are transported from a set of sources to a set of destinations subject to the supply and demand of the source and destination, respectively, such that the total cost of transportation is minimized.
So, it is used to determine the most economical way of transporting goods from several sources to several destinations while satisfying supply and demand requirements.
Its main objective is to minimize the total transportation cost.
Example
A company has three factories and four warehouses. The Transportation Model determines the least-cost shipping plan.
ЁЯТбExam Note:
The Transportation Problem minimizes transportation cost while satisfying supply and demand constraints.
5. Assignment Problem
The Assignment Problem is a special case of the Transportation Problem.
It is used when a fixed number of persons, jobs, machines, or facilities must be assigned to an equal number of tasks in the best possible way. That is, it is used when the problem involves the allocation of n different facilities to n different tasks.
The objective is usually to minimize time or cost, or to maximize efficiency.
Example
Four employees are assigned to four different jobs so that the total time required is minimum.
ЁЯТбExam Note:
In the Assignment Problem, one resource is assigned to one task.
6. Dynamic Programming (DP)
Dynamic programming is used for solving problems that involve taking decisions over several stages in a sequence.
Some decision-making problems cannot be solved in a single step. They require a series of decisions, where each decision affects the next one. Such problems are solved by Dynamic Programming.
In this technique, a large problem is divided into a number of smaller stages or sub-problems. Each stage is solved separately, and the solutions are combined to obtain the best solution for the original problem.
That is, this method starts by dividing a given problem into stages or sub-problems and then solves those sub-problems sequentially until the solution to the original problem is obtained.
Dynamic Programming is widely used in planning, resource allocation, advertising, expenditures distributing sales effort, production scheduling, equipment replacement, and investment planning.
Example
A company prepares a production plan for the next five years. The decision taken for one year affects the decisions for the following years. Dynamic Programming helps determine the best plan for all years.
ЁЯТбExam Note:
Dynamic Programming is used for solving multi-stage decision-making problems.
7. Goal Programming (GP)
In many practical situations, an organization has more than one objective. Sometimes these objectives conflict with one another. For example, a company may want to increase profit, reduce cost, improve product quality, and maintain customer satisfaction at the same time.
Goal Programming is used to deal with such multiple objectives. It helps management decide the order of importance of different goals and then finds a solution that satisfies them as much as possible.
Goal Programming is a powerful tool to tackle multiple and incompatible goals of an enterprise. In other words, it is used when there is more than one goal, i.e., several objectives (a real-life situation) and these several objectives have their own goals to complete.
Example
A manufacturing company wants to increase profit, reduce overtime, and improve product quality. Goal Programming helps achieve these goals according to their priority.
ЁЯТбExam Note:
Goal Programming is used when a problem has multiple objectives or goals.
8. Game Theory
Business organizations often face competition. The decision taken by one competitor influences the results of the other competitors.
Game Theory is used to study such competitive situations. It helps decision-makers choose the best strategy when two or more competitors have conflicting objectives.
That is, it is used for decision making under conflicting situations where there are one or more players. In the game theory, we consider two or more persons with different objectives, each of whose actions influence the outcomes of the game. The game theory provides solutions to such games, assuming that each of the players wants to maximize his profits and minimize his losses.
In most cases, each player tries to maximize gains and minimize losses.
Example
Two companies manufacturing the same product are deciding whether to reduce prices or keep them unchanged. The profit of one company depends on the decision taken by the other company. Such situations can be analysed using Game Theory.
ЁЯТбExam Note:
Game Theory deals with decision making under competitive or conflicting situations.
9. Inventory Control
Every organization must maintain sufficient inventory to continue its operations smoothly. However, keeping too much inventory increases storage costs, while keeping too little may interrupt production or sales.
Inventory Control helps determine:
- When an order should be placed.
- How much quantity should be ordered or produced.
Its main objective is to maintain the required inventory at the minimum possible cost. It is used in determining when and how much production or purchase.
Example
A supermarket decides how many grocery items should be ordered every month so that customer demand is met without keeping unnecessary stock.
ЁЯТбExam Note:
Inventory Control determines the economic order quantity and the appropriate time for replenishment.
10. PERT and CPM
PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method) are two network analysis techniques used for planning, scheduling, and controlling complex projects which can be characterized as networks.
These techniques help managers identify the sequence of activities, estimate project completion time, and monitor the progress of the project.
Although both techniques are used in project management, PERT is generally applied to projects where activity times are uncertain, whereas CPM is mainly used when activity times are known.
Example
Construction of a bridge, hospital, highway, or factory can be planned and controlled using PERT and CPM.
ЁЯТбExam Note:
PERT and CPM are used for planning, scheduling, and controlling projects.
11. Simulation
Some real-life problems are too complex to be solved by mathematical models alone. In such cases, Simulation is used.
Simulation is a very powerful technique for solving many complex models which cannot be solved otherwise and thus it is being extensively applied to solve a variety of problems.
Simulation creates a model that behaves like the real system. Different situations are then tested on the model to study their possible outcomes before making actual decisions.
Simulation is useful when obtaining an exact mathematical solution is difficult or impossible. In fact, such models are solved by simulation techniques where no other method is available for its solution.
Example
Before opening additional service counters at an airport, different passenger traffic situations can be tested using a simulation model.
ЁЯТбExam Note:
Simulation is used when exact mathematical solutions are difficult or not available.
12. Queuing Theory
Many organizations provide services where customers have to wait in a queue. Examples include banks, hospitals, railway reservation counters, supermarkets, and call centres.
Queuing theory works out the expected number of people in the queue, expected waiting time in the queue, expected idle time for the server etc. These calculations then help in deciding the optimum number of service facilities under given constraints.
Queuing Theory studies waiting-line problems. It helps estimate:
- The average waiting time.
- The average number of customers in the queue.
- The idle time of service facilities.
- The optimum number of service counters required.
The main objective is to provide satisfactory customer service while keeping operating costs as low as possible.
Example
A bank uses Queuing Theory to decide how many cash counters should remain open during busy hours.
ЁЯТбExam Note:
Queuing Theory helps determine the optimum level of service facilities by analysing waiting-line systems.
Comparison of Major OR Techniques
| Technique | Main Purpose |
|---|---|
| Linear Programming | Maximize profit or minimize cost under linear constraints |
| Non-linear Programming | Solve optimization problems involving non-linear relationships |
| Integer Programming | Solve problems where decision variables must be whole numbers |
| Transportation Problem | Minimize transportation cost |
| Assignment Problem | Assign resources to tasks in the best possible way |
| Dynamic Programming | Solve multi-stage decision problems |
| Goal Programming | Solve problems with multiple objectives |
| Game Theory | Analyse competitive decision-making situations |
| Inventory Control | Decide when and how much to order or produce |
| PERT and CPM | Plan, schedule, and control projects |
| Simulation | Study complex systems using a model |
| Queuing Theory | Analyse waiting-line problems and service facilities |
Applications of OR Techniques
Different OR techniques are used in different fields according to the nature of the problem.
Some common applications are:
- Production planning and scheduling
- Transportation and logistics
- Inventory management
- Project management
- Financial planning
- Marketing decisions
- Hospital management
- Airline scheduling
- Supply chain management
- Banking and insurance
- Defence planning
How Is the Appropriate OR Technique Selected?
There is no single technique that can solve every problem.
The selection of an OR technique depends on several factors, such as:
- Nature of the problem
- Objective of the study
- Availability of data
- Type of decision variables
- Assumptions of the mathematical model
- Time and computational requirements
The O.R. specialist studies the problem carefully before selecting the most suitable technique.
Summary
Operations Research provides several mathematical tools and analytical techniques for solving different types of managerial problems.
Each technique has a specific purpose. Some techniques are used for optimization, some for project management, some for inventory control, while others help analyse competition, waiting lines, transportation, or complex decision-making situations.
Therefore, selecting the appropriate technique is an important step in every Operations Research study.
Frequently Asked Questions (FAQs)
1. What are the tools and techniques of Operations Research?
Tools and techniques of Operations Research are mathematical methods and analytical procedures used to solve managerial and decision-making problems.
2. Which is the most widely used technique in Operations Research?
Linear Programming is one of the most widely used techniques because it helps maximize profit or minimize cost under given constraints.
3. What is the difference between the Transportation Problem and the Assignment Problem?
The Transportation Problem determines the least-cost transportation plan from sources to destinations, whereas the Assignment Problem allocates one resource to one task in the most efficient way.
4. Why is Simulation used in Operations Research?
Simulation is used when a problem is too complex to obtain an exact mathematical solution or when testing the real system is difficult or expensive.
5. Which OR technique is used for project management?
PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method) are used for planning, scheduling, and controlling projects.
6. Which OR technique is used for waiting-line problems?
Queuing Theory is used to analyse waiting-line problems and determine the optimum number of service facilities.
7. Is every OR technique suitable for all problems?
No. Each technique is designed for a particular type of problem. The appropriate technique is selected according to the nature of the problem.
8. Difference Between Tools and Techniques of Operations Research
Students often ask whether Tools and Techniques in Operations Research are different.
In most standard Operations Research books, these two terms are used interchangeably. Both refer to the mathematical methods and analytical procedures used to solve decision-making problems.
However, for better understanding, the difference can be explained as follows:
| Tools | Techniques |
|---|---|
| Mathematical models used to solve problems. | Methods or procedures used to apply those models. |
| Example: Linear Programming Model | Example: Simplex Method used to solve an LPP |
Exam Note: In most OR textbooks, the terms Tools and Techniques are used with the same meaning.
Conclusion
Operations Research offers a wide range of tools and techniques for solving managerial problems scientifically. Each technique is designed for a specific type of problem and helps managers make better decisions by using mathematical models and analytical methods.
A proper understanding of these techniques enables organizations to improve planning, utilize resources efficiently, reduce costs, and achieve organizational objectives more effectively.
Read Next
References
- Hamdy A. Taha, Operations Research: An Introduction, Pearson.
- Kanti Swarup, P. K. Gupta & Man Mohan, Operations Research, Sultan Chand & Sons.
- J. K. Sharma, Operations Research: Theory and Applications, Macmillan India.
- Frederick S. Hillier & Gerald J. Lieberman, Introduction to Operations Research, McGraw-Hill.
- H. M. Wagner, Principles of Operations Research, Prentice Hall.
Comments
Post a Comment