# 3.1. Introduction¶

Have you ever wondered how airline companies route their planes to minimize the costs for each trip and maximize the profit made from these trips? Or, how one might minimize the waiting time for people in a customer service phone queue? These questions are examples of optimization problems.

Optimization is the overarching objective of Operations Research, the study of applying mathematics to these types of questions that are important in business operations and in other areas where maximizing or minimizing something is important. The field of Operations Research has many different uses, such as optimizing waiting lines (queue theory) and graph analysis (related to graph theory), but its most frequent use is in linear programming, a technique for solving systems of linear constraints with a linear objective function. In this chapter, you will learn about the optimization model and its three components: the objective function (the variable being optimized), the decision variables (those elements that will change to achieve the optimization), and the constraints (the elements that create limitations).

We will use a tool for linear programming called Solver in Google Sheets. Solver can also be used with Microsoft Excel and many other spreadsheet programs.

## 3.1.1. Learning Goals¶

• Explore the ideas and techniques of optimization.

• Learn how to optimize an objective function under specific constraints.

## 3.1.2. Learning Objectives¶

• Be able to recognize an objective function and any constraints in a specific problem.

• Learn to apply optimization concepts to maximize or minimize an objective function or to set it to a specified value.

• Use Solver as a tool to optimize an objective function for a specific scenario.