16.1.1 Definitions and Formulas

Constraint

Anything (such as time, money or budget, personnel or other resources) that limits your options regarding possible values of the variables in your model

Inequality

An expression similar to an equation, except the quantities are related by either be less than (<), greater than (>), less than or equal to or greater than or equal to (<= or >=) each other, rather than requiring them to be exactly equal. For example, the inequality

10*(Labor Hours) + 2*(Items made) <= $1000

Could be used to express the situation where we pay $10/hour for labor and each item we make uses $2 of raw goods, electricity and equipment time. If we must keep daily costs below $1000, then the total cost spent of labor (=$10/hour * number of hours used) plus the total cost in materials (=$2/item * number of items made) must be less than or equal to the budget, in this case $1000.

Objective function

This is the quantity (or quantities) that you are trying to optimize. It is sometimes referred to as a target or target cell in spreadsheets.

Optimization variables

These are the variables you can change (sometimes called the changing variables) in order to achieve your optimum solution.

Maximize

In some optimization problems, you seek to make the objective function as large as possible. Such problems are maximization problems.

Minimize

In some optimization problems, you seek to make the objective function as small as possible. Such problems are minimization problems.

Explicit constraint

Explicit constraints describe those items that clearly given to you as goals during your optimization process. For example, limitations on resources (materials, labor) and limitations on demand are often stated explicitly.

Implicit constraint

Implicit constraints refer to those quantities that you must recognize are also constraints on your optimization process. For example, in optimizing company profits by producing different quantities of different goods, the number of units of each good to produce might need to be an integer (unless it’s measured in pounds). The quantity produced must also be non-negative. You must learn to recognize these types of constraints as well.