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Mathematical Programming (MP) or Optimization

a field of management science that finds the optimal, or most efficient way of using limited resources to achieve the objectives of an individual or a business. For this reason, mathematical programming often is referred to as optimization.

Constraints

Restrictions that are placed on the alternatives available to the decision maker:


A "less than or equal to" constraint


A "greater than or equal to" constraint


An "equal to" constraint

Characteristics of Optimization Problems

Decisions


Constraints


Objective

Decision Variables

The decisions in an optimization problem are represented in a mathematical model by decision variables, or symbols X1, X2, X3...Xn.

Objective Function

The objective function identifies some function of the decision variables that the decision maker wants to either MAXimize or MINimize