# Decision Modeling/Linear Programming

**Topics:**Decision theory, Bayesian probability, Operations research

**Pages:**4 (924 words)

**Published:**November 19, 2005

Linear programming is a modeling technique that is used to help managers make logical and informed decisions. All date and input factors are known with certainty. Linear program models are developed in three different steps: Formulation

Solution

Interpretation

The formulation step deals with displaying the problem in a mathematical form. Once that is developed the solution stage solves the problem and finds the variable values. During the interpretation stage the sensitivity analysis gives managers the opportunity to answer hypothetical questions regarding the solutions that are generated.

There are four basic assumptions of linear programming and they are as follows: Certainty

Proportionality

Additivity

Divisibility

Linear programming is the development of modeling and solution procedures which employ mathematical techniques to optimize the goals and objectives of the decision-maker. Programming problems determine the optimal allocation of scarce resources to meet certain objectives. Linear Programming Problems are mathematical programming problems where all of the relationships amongst the variables are linear.

Components of a LP Formulation are as follows:

Decision Variables

Objective Function

Constraints

Non-negativity Conditions

Decision variables represent unknown quantities. The solutions for these terms are what we would like to optimize. Objective function states the goal of the decision-maker. There are two types of objectives: Maximization

Minimization

Constraints put limitations on the possible solutions of the problem. The availability of scarce resources may be expressed as equations or inequalities which rule out certain combinations of variable values...

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