Linear Programming
Linear Programming is a technique for making decisions under certainty i.e.; when all the courses of options available to an organisation are known & the objective of the firm along with its constraints are quantified. That course of action is chosen out of all possible alternatives which yield the optimal results. Linear Programming can also be used as a verification and checking mechanism to ascertain the accuracy and the reliability of the decisions which are taken solely on the basis of manager's experience without the aid of a mathematical model. Linear Programming is the analysis of problems in which a linear function of a number of variables is to be optimized (maximized or minimized) when whose variables are subject to a number of constraints in the mathematical near inequalities.
The characteristics or the basic assumptions of linear programming are as follows:
- Decision or Activity Variables & Their Inter-Relationship. The decision or activity variables refer to any activities which are in competition with other variables for limited resources.
- Finite Objective Functions. Such objectives can be: cost-minimization, sales, profits or revenue maximization & the idle-time minimization etc
- Limited Factors/Constraints. These are the different kinds of limitations on the available resources e.g. important resources like availability of machines, number of man hour’s available, production capacity and number of available markets.
- Presence of Different Alternatives. Different courses of action or alternatives should be available to a decision maker, who is required to make the decision which is the most effective.
- Non-Negative Restrictions. Since the negative values of (any) physical quantity has no meaning, therefore all the variables must assume non-negative values.
- Linearity Criterion. The relationship among the various decision variables must be directly proportional Le.; Both the objective and the constraint, $ must be expressed in terms of linear equations or inequalities
- Additively. It is assumed that the total profitability and the total amount of each resource utilized would be exactly equal to the sum of the respective individual amounts
- Mutually Exclusive Criterion. All decision parameters and the variables are assumed to be mutually exclusive in other words, the occurrence of anyone variable rules out the simultaneous occurrence of other such variables
- Divisibility. Variables may be assigned fractional values. i.e.; they need not necessarily always be in whole numbers. If a fraction of a product cannot be produced, an integer programming problem exists. Not hold good at all times.
Advantages of Linear Programming
- Scientific Approach to Problem Solving. Linear Programming is the application of scientific approach to problem solving. Hence it results in a better and true picture of the problems-which can then be minutely analyzed and solutions ascertained.
- Evaluation of All Possible Alternatives. Most of the problems faced by the present organizations are highly complicated - which cannot be solved by the traditional approach to decision making. The technique of Linear Programming ensures that’ll possible solutions are generated - out of which the optimal solution can be selected.
- Helps in Re-Evaluation. Linear Programming can also be used in. revaluation of a basic plan for changing conditions. Should the conditions change while the plan is carried out only partially, these conditions can be accurately determined with the help of Linear Programming so as to adjust the remainder of the plan for best results?
- Quality of Decision. Linear Programming provides practical and better quality of decisions’ that reflect very precisely the limitations of the system i.e.; the various restrictions under which the system must operate for the solution to be optimal. If it becomes necessary to deviate from the optimal path, Linear Programming can quite easily evaluate the associated costs or penalty.
- Focus on Grey-Areas. Highlighting of grey areas or bottlenecks in the production process is the most significant merit of Linear Programming. During the periods of bottlenecks, imbalances occur in the production department. Some of the machines remain idle for long periods of time, while the other machines are unable toffee the demand even at the peak performance level.
- Flexibility. Linear Programming is an adaptive & flexible mathematical technique and hence can be utilized in analyzing a variety of multi-dimensional problems quite successfully.
- Creation of Information Base. By evaluating the various possible alternatives in the light of the prevailing constraints, Linear Programming models provide an important database from which the allocation of precious resources can be don rationally and judiciously.
- Maximum optimal Utilization of Factors of Production. Linear Programming helps in optimal utilization of various existing factors of production such as installed capacity, Labour and raw materials etc.
Limitations of Linear Programming
- Linear Relationship. Linear Programming models can be successfully applied only in those situations where a given problem can clearly be represented in the form of linear relationship between different decision variables.
- Constant Value of objective & Constraint Equations. Before a Linear Programming technique could be applied to a given situation, the values or the coefficients of the objective function as well as the constraint equations must be completely known.
- No Scope for Fractional Value Solutions. There is absolutely no certainty that the solution to a LP problem can always be quantified as an integer quite often, Linear Programming may give fractional-varied answers,
- Degree Complexity. Many large-scale real life practical problems cannot be solved by employing Linear Programming techniques even with the help of a computer due to highly complex and Lengthy calculations.
- Multiplicity of Goals. The long-term objectives of an organisation are not confined to a single goal. An organisation, at any point of time in its operations has a multiplicity of goals or the goals hierarchy - all of which must be attained on a priority wise basis for its long-term growth.
- Flexibility. Once a problem has been properly quantified in terms of objective function and the constraint equations and the tools of Linear Programming are applied to it, it becomes very difficult to incorporate any changes in the system arising on account of any change in the decision parameter.
0 Comments