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Linear programming

Linear programming. Linear programming…. …is a quantitative management tool to obtain optimal solutions to problems that involve restrictions and limitations (called constrained optimization problems).

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Linear programming

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  1. Linear programming

  2. Linear programming… • …is a quantitative management tool to obtain optimal solutions to problems that involve restrictions and limitations (called constrained optimization problems). • …consists of a sequence of steps that lead to an optimal solution to linear-constrained problems, if an optimum exists.

  3. Typical areas of problems • Determining optimal schedules • Establishing locations • Identifying optimal worker-job assignments • Determining optimal diet plans • Identifying optimal mix of products in a factory (!!!) • etc.

  4. Linear programming models • …are mathematical representations of constrained optimization problems. • BASIC CHARACTERISTICS: • Components • Assumptions

  5. Components of the structure of a linear programming model • Objective function: a mathematical expression of the goal • e. g. maximization of profits • Decision variables: choices available in terms of amounts (quantities) • Constraints: limitations restricting the available alternatives; define the set of feasible combinations of decision variables (feasible solutions space). • Greater than or equal to • Less than or equal to • Equal to • Parameters. Fixed values in the model

  6. Assumptions of the linear programming model • Linearity: the impact of decision variables is linear in constraints and the objective functions • Divisibility: noninteger values are acceptable • Certainty: values of parameters are known and constant • Nonnegativity: negative values of decision variables are not accepted

  7. Model formulation • The procesess of assembling information about a problem into a model. • This way the problem became solved mathematically. • Identifying decision variables (e.g. quantity of a product) • Identifying constraints • Solve the problem.

  8. Graphical linear programming • Set up the objective function and the constraints into mathematical format. • Plot the constraints. • Identify the feasible solution space. • Plot the objective function. • Determine the optimum solution. • Sliding the line of the objective function away from the origin to the farthes/closest point of the feasible solution space. • Enumeration approach.

  9. Lets solve some exercises…

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