Introduction to Modeling and Simulation

8Optimization

8.1 Introduction

In this chapter we present concepts and methods from optimization theory. The notation and derivations of the main concepts in this chapter are based largely on the books [16, 49], to which the reader can refer for additional details.

Optimization methods are used in many areas of science and engineering, including:

• operations research;
• supply‐chain management;
• risk management;
• reliability;
• economics and game theory;
• financial engineering;
• optimal control;
• neural networks and machine learning.

In most problems in design, decision‐making, or control we want to find the best solution. For example:

• in business, we may want to maximize profit, minimize loss, or minimize risk;
• in mechanical design, we may want to maximize strength, minimize weight, or minimize cost;
• in transportation, we may want to minimize travel time, or minimize fuel consumption.

Often a decision‐making process involves constraints, such as:

• a speed should not exceed a value ;
• a temperature should be held at a constant value ;
• cost cannot exceed a fixed budget amount.

Example 8.1

Let us begin with a simple example. Suppose you own a large apartment complex with 500 units. You know that if you charge $1000 per month rent you will have occupancy. Historical data suggest that ...