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Linear Optimization

Linear Optimization

A constrained optimization model takes the form of a constrained performance measure to be optimized over a range of feasible values of the decision variables.

The feasible values of the decision variables are determined by a set of inequality constraints. constraints Values of the decision variables must be chosen such that the inequality constraints are all satisfied while either maximizing or minimizing the desired performance variable.

These models can contain tens, hundreds, or thousands of decision variables and constraints.

Linear Optimization

Very efficient search techniques exist to optimize constrained linear models. constrained These models are historically called linear programs linear (LP). In this chapter we will:

1. Develop techniques for formulating LP models

2. Give some recommended rules for expressing LP models in a spreadsheet that facilitates application of Excel’s Solver

3. Use Solver to optimize spreadsheet LP models

Formulating LP Models

Every linear programming model has two important features: Objective Function

Constraints

A single performance measure to be maximized or minimized

(e.g., maximize profit, minimize cost)

Constraints are limitations or requirements on the set of allowable decisions.

Constraints may be further classified into physical, economic, or policy limitations or requirements. Formulating LP Models

The first step in model formulation is the development of the constraints.

For example:

Investment decisions are restricted by the amount of capital and government regulations.

Management decisions are restricted by plant capacity and availability of resources.

Staffing and flight plans of an airline are restricted by the maintenance needs of the

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