**INTRODUCTION TO OPERATION RESEARCH**

**Def: OPERATION RESEARCH:-**

Â Â Â Â Â Â Â Â Â Operation research is the application of scientific methods, techniques and tools to problemsÂ involving the operations of systems so as provide those in control of operations with optimum solutions to the problems.

**FEATURES OF OR:-**

**1)Â Â Â Â Â Â ****Decision making:Â **OR is used for obtaining numerical solutions to problems. Based on these numerical solutions, the manager can make decision making.

**2)Â Â Â Â Â Â ****Scientific nature:Â **OR is quantitative in nature, not qualitative. Hence, it is not judgemental in nature. The problem is clearly defined. Numerical data is collected. This data is analyzed using the appropriate technique and the solution is obtained.

**3)Â Â Â Â Â Â ****Well defined goals and objectives:Â **A computer program can be created for a particular OR technique to solve problems involving large set of data.

**METHODOLOGY OF OPERATION RESEARCH:-**

The application of OR generally involves following steps:

**1)Â Â Â Â Â Â ****Problem formulation:Â **The first step is to identify the problem and then representing it precisely. This includes steps starting from the problem discovery and ending in problem definition.

**2)Â Â Â Â Â Â ****Model construction:Â **After defining the problem, a model needs to be developed to represent the problem. Models can be-

**(a)Â Â Â ****Physical model:Â **It is a physical representation of the real situation. E.g. model of a proposed building.

**(b)Â Â Â ****Symbolic model:Â **Symbolic model use symbols, letters, and numbers etc. to represent things associated with real life situations. Symbolic model can be verbal or mathematical.

E.g. In words, area of a rectangle is the product of its length and breadth

Â Â In Symbols, A=l.b

Â Â Where- A=area, l=length, b=breadth.

**3)Â Â Â Â Â Â ****Data collection:Â **After formulating the model, we need collect the data related with value of variables. This data will determine the final solution. Hence data collection is extremely important. Inaccurate or insufficient data will result in poor solution.

**4)Â Â Â Â Â Â ****Substitute data in the model:Â **Then we substitute the data in the model, apply the appropriate mathematical technique and solve the model to get solution.

**5)Â Â Â Â Â Â ****Interpretation of solution:Â Â **Interpretation of solution is subjective in nature. How one manager interprets a solution can differ from how another manager reads the same situation. Past experience, attitude, bias influence of surrounding etc. are some of the factors which can affect interpretation.

**6)Â Â Â Â Â Â ****Decision making:Â **Based on the interpretation of the solution, the final decision will be taken. The manager may completely accept the solution, completely rejecte the solution or accept it partly.Â

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**OPERATION RESEARCH TECHNIQUES:-**

**1. STATISTICAL TECHNIQUES: **Statistical techniques are applied in statistics for data collection, data organisation and data analysis. Some of the examples are:

**1)Â Â Â Â Â Â **Mean, median and mode.

**2)Â Â Â Â Â Â **Mean deviation and standard deviation.

**3)Â Â Â Â Â Â **Probability theory.

**4)Â Â Â Â Â Â **Regression analysis and correlation analysis.

**5)Â Â Â Â Â Â **Sampling.

**2. PROGRAMMING TECHNIQUES: **These are OR techniques. These techniques involve problem formulation , building mathematical models, substituting data in mathematical models, testing the model, using appropriate OR technique to solve the problem, obtaining optimal solution. Some examples are:

**1)Â Â Â Â Â Â **Linear programming.

**2)Â Â Â Â Â Â **Transportation problems.

**3)Â Â Â Â Â Â **Assignment problems.

**4)Â Â Â Â Â Â **Critical path method.

**5)Â Â Â Â Â Â **Decision theory.

**6)Â Â Â Â Â Â **Inventory management.

**APPLICATION AREAS FOR OPERATION RESEARCH TECHNIQUES:-**

Or techniques are applied to a variety of business problems. Some examples are:

**1. Production management:**

**Â Â Â Â Â 1)Â **To calculate loss of time due to waiting time, queuing time etc.

**Â Â Â Â Â 2)Â **To decide optimum allocation of jobs and optimum sequence in which job should be sequenced.

**2. Personal management:**

Â Â Â Â Â **1)Â **To study labour turnover.

**Â Â Â Â Â 2)Â **To do human resource planning.

**Â Â Â Â Â 3)Â **To decide number of personnel required to be kept on standby in case of demand for higher manpower.

**3. Inventory management:**

Â Â Â Â Â **1)Â **To study economic lot size to be ordered.

**4. Marketing management:**

Â Â Â Â Â **1)Â **To decide optimal product mix for maximum profit.

**Â Â Â Â Â 2)Â **Media selection for advertising for maximum reach.

**Â Â Â Â Â 3)Â **Sales forecasting.

**5. Transportation management:**

Â Â Â Â Â **1)Â **To determine transportation schedule for minimum cost or minimum time.

**6. Project management:**

Â Â Â Â Â **1)Â **To identify critical and non-critical activities of a project.

**Â Â Â Â Â 2)Â **To determine minimum project completion time.

**Â Â Â Â Â 3)Â **To determine optimal project cost.

**7. Financial management:**

Â Â Â Â Â **1)Â **To decide investment portfolio to maximize return on investment.

**Â ****LIMITATIONS OF OPERATIONS RESEARCH TECHNIQUES:-**

Some of the major limitations of OR techniques are:

**1)Â Â Â Â Â Â **In construction of mathematical models, something assumptions are necessary to simplify model construction. But over simplification of a model or too many assumptions can make the model un realistic.

**2)Â Â Â Â Â Â **OR techniques are quantitative in nature. Hence these techniques do not consider qualitative or intangible factors such as customer perceptions, employee motivation levels, quality of executives, advantage of experience etc.

**3)Â Â Â Â Â Â **All business situations cannot be responded with quantitative techniques. Some business situations require gut feeling, initiative or managerial judgment. OR techniques cannot be applied in such situations.