Linear programing
- 1. LINEAR PROGRAMING OPERATIONS RESEARCH BY- Anam Katmale…… MMS-I
- 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. 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. 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. 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. Advantages of Linear Programming Problem Improve Quality Decision Cost- Benefit Analysis Flexibility Number of Possible Solutions Use of Productivity Factors Scientific Approach
- 7. Disadvantages of Linear Programming Linear Programming Coefficients & Constraints Fractional Solutions Complexity Possibility for More Than One Objective Time Effect