Introduction

A model is an abstraction or mathematical representation of a problem of interest and is an essential part of the process of solving that problem optimally. However, it is difficult, and sometimes impossible, to develop a mathematical model that addresses all aspects of the problem and its planning environment, since most real-world problems are too complex and involved. As a result, researchers and practitioners attempt to formulate either a simplified version of the problem or make numerous assumptions and approximations. As the modelling approach provides solutions to the simplified or approximated problem, there may exist a significant discrepancy between those solutions and the subjectively expected realistic solution to the original problem. This discrepancy may lead to an inappropriate decision being made if the decision is made based solely on the solutions of the simplified model. This may happen in many practical decision-making or design processes. As can be seen in most books, journal articles, and conference proceedings on optimization, a tremendous effort has been put into the development of solution approaches over the past half-a-century. However, the appropriateness of modelling and appropriate techniques have received little attention. In fact, mathematical modelling may be considered an art that has its own domain and has not been generally explored by problem-solving practitioners. So, instead of solution techniques, the emphasis of this book is on the modelling aspects such as

. Importance of modelling in the decision-making process

. Modelling techniques

. Influence of modelling in decision making

. Linking of the mathematical model to the other components of a decision-making process

In this introductory chapter, we present a brief history of optimization, the nature of the optimization problem, the nature of the mathematical

basic concept of optimization, and the classification of optimization problems. The general structure of the book is also discussed.