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Formulating the problem is perhaps the most crucial step in optimization. Problem
formulation requires identifying the essential elements of a conceptual or verbal
statement of a given applicationand organizing them into a prescribed mathematical
form, namely,
1. The objective function (economic criterion)
2. The process model (constraints)
The objective function represents such factors asprofit, cost, energy, and yield
in terms of the key variables of the process being analyzed. The process model and
constraints describe the interrelationships of the key variables. It is importantto
learn a systematic approach for assembling the physical and empirical relations and
data involved in an optimization problem, and Chapters 1, 2, and 3 cover the recommended
procedures. Chapter 1presents six steps for optimization that can serve
as a general guide for problem solving in design and operations analysis. Numerous
examples of problem formulation in chemical engineering arepresented to
illustrate the steps.
Chapter 2 summarizes the characteristics of process models and explains how
to build one. Special attention is focused on developing mathematical models,particularly
empirical ones, by fitting empirical data using least squares, which itself
is an optimization procedure.
Chapter 3 treats the most common type of objective function, the cost or revenuefunction. Historically, the majority of optimization applications have involved
trade-offs between capital costs and operating costs. The nature of the trade-off
depends on a number of assumptions such asthe desired rate of return on investment,
service life, depreciation method, and so on. While an objective function
based on net present value is preferred for the purposes of optimization,discounted
cash flow based on spreadsheet analysis can be employed as well.
It is important to recognize that many possible mathematical problem formulations
can result from an engineering analysis,...
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