Optimal resource allocation is an extremely important part of many human activities, including reliability engineering. One of the first problems that arose in this engineering area was optimal allocation of spare units. Then it came to optimization of networks of various natures (communication, transportation, energy transmission, etc.) and now it is an important part of counter-terrorism protection.

Actually, these questions have always stood and still stand: How can one achieve maximum gain with limited expenses? How can one fulfill requirements with minimum expenses?

In this book is an overview of different approaches of optimal resource allocation, from classical LaGrange methods to modern heuristic algorithms.

This book is not a tutorial in the common sense of the word. It is not a reliability “cookbook.” It is more a bridge between reliability engineering and applied mathematics in the field of optimal allocation of resources for systems' reliability increase. It supplies the reader with basic knowledge in optimization theory and presents examples of application of the corresponding mathematical methods to real world problems. The book's objective is to inspire the reader to visit the wonderful area of applied methods of optimization, rather than to give him or her a mathematical course on optimization.

Examples with sometimes tedious and bulky numerical calculations should not frighten the reader. They are given with the sole purpose of demonstrating “a kitchen” of calculations. All these calculations have to be performed by a computer. Optimization programs themselves are simple enough. (For instance, all numerical examples were performed with the help a simple program in MS Office Excel.) At the very end of the book there is a complete enough list of monographs on the topic.

Who are potential readers of the book? First of all, engineers who design complex systems and mathematicians who are involved in “mathematical support” of engineering projects. Another wide category is college and university students, especially before they take classes on optimization theory. Last, university professors could use the material in the book, taking numerical examples and case studies for illustration of the methods they are teaching.

In conclusion, I would like to say a few words about references at the end of chapters. Each of them is not a list of references, but rather a bibliography presented in a chronological order. The author's belief is that such a list will allow the reader to trace the evolution of the considered topic. The lists, of course, are not full, for which the author apologizes in advance. However, as Kozma Prutkov (a pseudonym for a group of satirists at the end of the 19th century) said: “Nobody can embrace the unembraceable.”

I would like to express my deep gratitude to my friend and colleague Dr. Gregory Levitin, who supplied me with materials on genetic algorithms and optimal redundancy in multi-state systems. I also would like to thank my friend Dr. Simon Teplitsky for scrupu­lously reading the draft of the book and giving a number of useful comments.

This book is in memory of my friend and colleague Dr. John D. Kettelle, a former mariner who fought in WWII and later made a significant input in dynamic programming. His name was known to me in the late 1960s when I was a young engineer in the former Soviet Union. I had been working at one of the R&D institutes of the Soviet military–industrial establishment; my duty was projecting spare stocks for large scale military systems.

I met Dr. J. Kettelle in person in the early 1990s when I came to the United States as Distinguished Visiting Professor at The George Washington University. After two years at the university, I was invited by John to work at Ketron, Inc., the company that he established and led. We became friends.

I will remember John forever.