Linear Programming Assumptions

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Assumptions of Linear Programming

We now elearly state the assumptions that distinguish a linear programming problem form other mathematical problems. These assumptions are:

1.    Proportionality. This assumption means that if the value of a variable is multiplied by a constant, then its contribution to the objective function and to each constraint is also multiplied by that constant. In actual situations, this is not always the case. For example, the law of diminishing returns, where a unit of activity contributes less than the previous unit, may be operating in a situation.

2.    Additively. This assumption means that the total value of the objective function is sum of the individual contributions and total impact on each constraint is the sum of the individual impacts of the decision variables. In other worlds, there is no “interaction” between the decision variables. To understand the concept of additively better, consider the situation where a certain amount of water s to be mixed with a certain amount of alcohol. Since water and alcohol are partially miscible, the resulting amount will actually be much less partially miscible, the resulting amount will actually be much less than the sum of the amounts of the water and alcohol and thus the amount of the mixture is not additive.

3.    Divisibility. Divisibility simply means that the decision variables can take any non-negative values, i.e., fractional values of the decision variable are permitted. This is not always desirable. For example, it is impossible to produce one-third of an aeroplane. When it is necessary to have integer variables, a technique known as integer programming could be used.

4.    Certainty. This assumption means that all parameters are known with certainty and do not change during the period being studied. Unfortunately, we will be solving problems about the future, not the past, and thus all data will be certain.

Remark. The proportionality and the additivity assumptions automatically imply that all the constraints in the problem are either linear equations or inequalities. They also imply that the objections functions are linear.

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