 the results to guide our design and upgrade of real-world sys- items. The principles used in making general business and engineering decisions also apply to the design of mathematical models, but the optimization models also have more stringent requirements. Mathematicians also have a unique skill at picturing systems in ways that might appear counterintuitive but which make problems easier to solve. In the first section of this chapter we will look at some business and engineering tools that help us define problems and improve systems as we plan them or modify them. The business models are important because, more and more, engineers are expected to be able to present business cases, express value in business terms, and commit to busi- ness requirements and goals. The engineering tools are valuable because organizations such as the Institute for Operations Research and the Management Sciences (INFORMS) and the Institute of Electrical and Electronics Engineers (IEEE) have developed approaches that can save us time and improve the quality of our work. These conceptual tools allow us achieve better results simply because we do not have to reinvent the wheel if we use them. When it is possible to create models of systems and quantify the parameters, we can engage in optimization. We use the term optimization to refer to the mathemati- cal process of finding the best solution in a model of a system that can then be used to guide real-world implementation. After our discussion of business and engineering tools, we will define quantitative optimization and then discuss several elements of optimization, including tradeoffs, network flows with pipes, bottlenecks, and alter- nate routes, constrained optimization, optimization variables, quality, capacity, and cost. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Capacity and Quality Tradeoffs Capacit