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Linear programing

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linear pragramming ppt

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Linear programing

1. 1. LINEAR PROGRAMING OPERATIONS RESEARCH BY- Anam Katmale…… MMS-I
2. 2. Meaning & Definition Linear programming is the two word phrase. It means 1. The word linear refer to any linear relationship among variables in a model. It means that any change in one variable will result into a proportional change in other variables. 2. Programming refers to any problem that can be modelled and solved mathematically. According to William M Fox, “Linear programming is a planning technique that permits some objective functions to be minimized or maximized within the framework of given situational restrictions”.
3. 3. Components of Linear Programming Problem  Objective Function:  It is linear function and can work either by maximization or minimization process. It includes all possible components of a problem to optimize the solution. Decision Variables:  The variables that help to decide the outcome are called ‘Decision Variables’ OR ‘Activity Variables’. Constraints: • Constraints are a part of every practical situation • The mathematically program stated in a algebraic form will also specify constraints.
4. 4. Assumptions of Linear Programming Problem Certainty:  All the variables and parameters in an LP model should be assumed to be constant or known.  For the best optimal solution, parameters such a availability and consumption of resource or the profit/cost contribution variable should be assumed to be certainty.  Divisibility:  It is assumed that decision variables and resources have solution values which are either whole number or mixed numbers .  For eg machines,employees etc.
5. 5. Assumptions of Linear Programming Problem conti… Additive:  This means that the function value is the sum of the contributions of each term, i.e., when two or more activities are used , the total product is equal to the sum of the individual products where there is no interaction effect between the activities. Linearity:  Liner programming requires linearity in the equations, i.e., the relationship in both objective function and constraints must be linear.
6. 6. Advantages of Linear Programming Problem Improve Quality Decision Cost- Benefit Analysis Flexibility Number of Possible Solutions Use of Productivity Factors Scientific Approach
7. 7. Disadvantages of Linear Programming Linear Programming Coefficients & Constraints Fractional Solutions Complexity Possibility for More Than One Objective Time Effect