Introduction to Operations Research

Operations research

Operations research describes the discipline which deals with the application of scientific methods and techniques to decision making problems. It’s a study of mathematical models for optimal resource allocation. It provides rational bases for decision making in the complex situations. Operations research consists of several fundamental topics such as optimization, stochastic system, simulation, game theory and network analysis. It covers the following techniques.

Linear programming:

 

It is a powerful operations research technique to solve allocation problems. The word linear describes the relationship between decision variables which are directly proportional. For e.g., If doubling or tripling the production of  wheat  will exactly double or triple its  profit and required resources., then it is termed as linear relationship. The word programming means planning of activities to get optimal result with available resources. Thus, it indicates the planning of decision variables which are directly proportional to achieve the optimal solution considering the limitations of the problem. The solution to the linear programming problem can be obtained by graphic method if the number of decision variables is two and by the simplex method if the variables are more than three.

 

Assignment problems :

 

It’s a special type of linear programming.  It is concerned of assigning task to facility on a one to one basis in some optimal way. For e.g., A manager has four persons available for four separate jobs. His job is to assign each person to one and only job in such a way that the time and total cost is minised .

 

Transportation problems:

 

It indicates the amount of consignment to be transported from various sources to different destinations so that the total cost is minimized with available resources. Transportation problems have number of origins and destinations. The origin of a transportation problems is the location from which consignment are transported.  The destination of a transportation problem is the location where consignments are reached
Example: A manager has four factories and four warehouses.  His objective is to ascertain the quantity to be transported from the factories (sources) to different warehouses (destinations) in such a way that the total cost is minised.

 

Queuing theory:

 

Queuing theory is a mathematical study of waiting lines. It’s a tool to make business decisions about the resources provided for services. It has applications in banks, servicing of machines, airports, restaurants etc. Queuing models suggests ways and means to improve the efficiency of the services. Its objective is to find out the optimum service rate and the number of servers so that the average cost of being in queuing system and the cost of service are minimsed.

 

Net work analysis

 

A project will consist of a number of jobs and some jobs can be started only after finishing some other jobs. Net work analysis determines the various sequence of jobs concerning a project and the project completion time .There are two popular methods, CPM and PERT.

 

Game theory:

 

The term game represents a conflict between two or more parties. Theory of games helps to analyze the different situations each player has to face and choose considering the opponent in the business environment. . An important criteria used to develop the theory games is mini max or maxi mini criteria.  Each player wants to maximize his minimum expected gain or minimize his expected loss.
Player: Competitor is called as player
 Strategy: Plan which specifies a player action for every possible action of his opponent.
Zero sum game; one person‘s gain is the loss of the other in a game is referred as zero sum game.

 

Simulation: 

 

Simulations are useful for the problems which cannot be represented mathematically due to its stochastic nature.  
Example: To study the operating characteristics of a new airplane by simulating flight conditions in a wind tunnel.
Simulation enables to get optimal solution by trail and error movement.