Practical Optimization: A Gentle Introduction

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The content has good explanatory videos that are useful for understanding the basics of optimization topics. All content is freely available and copyright-free.

Chapter 1: Introduction

Practical optimization is the art and science of allocating scarce resources to the best possible effect. Optimization techniques are called into play every day in questions of industrial planning, resource allocation, scheduling, decision-making, etc. For example, how does a global petroleum refiner decide where to buy crude oil, where to ship it for processing, what products to convert it to, where to sell those products, and at what prices? A maximum-profit optimization model is used to solve this problem. How does an airline know how to route its planes and schedule its crews at minimum cost while meeting constraints on airplane flight hours between maintenance and maximum flight time for crews? A minimum-cost optimization model is used.

Many of the large scale optimization techniques in general use today can trace their origins to methods developed during World War II to deal with the massive logistical issues raised by huge armies having millions of men and machines. Any techniques that promised to improve the effectiveness of the war effort were desperately needed, especially in the face of limited numbers of people, machines, and supplies. What is the optimum allocation of gasoline supplies among competing campaigns? What is the best search and bombing pattern for anti-submarine patrols?

The fundamentals of the first practical, large-scale optimization technique, the simplex method, were developed during the war. The simplex method was perfected shortly after the war when the first electronic computers were becoming available. In fact, the early history of computing is closely intertwined with the history of practical optimization. In the early years, the vast majority of all calculation on electronic computers was devoted to optimization via the simplex method!

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