1 An Introduction to Model Building

1 An Introduction to Model Building - An Introduction to...

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± ± ± ± ± ± ± ± ± ± ± An Introduction to Model Building 1.1 An Introduction to Modeling Operations research (often referred to as management science ) is simply a scientific approach to decision making that seeks to best design and operate a system, usually un- der conditions requiring the allocation of scarce resources. By a system, we mean an organization of interdependent components that work together to accomplish the goal of the system. For example, Ford Motor Company is a system whose goal consists of maximizing the profit that can be earned by producing quality vehicles. The term operations research was coined during World War II when British military leaders asked scientists and engineers to analyze several military problems such as the de- ployment of radar and the management of convoy, bombing, antisubmarine, and mining operations. The scientific approach to decision making usually involves the use of one or more mathematical models. A mathematical model is a mathematical representation of an ac- tual situation that may be used to make better decisions or simply to understand the ac- tual situation better. The following example should clarify many of the key terms used to describe mathematical models. Eli Daisy produces Wozac in huge batches by heating a chemical mixture in a pressur- ized container. Each time a batch is processed, a different amount of Wozac is produced. The amount produced is the process yield (measured in pounds). Daisy is interested in understanding the factors that influence the yield of the Wozac production process. De- scribe a model-building process for this situation. Solution Daisy is first interested in determining the factors that influence the yield of the process. This would be referred to as a descriptive model, because it describes the behavior of the actual yield as a function of various factors. Daisy might determine (using regression methods discussed in Chapter 24) that the following factors influence yield: container volume in liters (V) container pressure in milliliters (P) container temperature in degrees Celsius (T) chemical composition of the processed mixture If we let A, B, and C be percentage of mixture made up of chemicals A, B, and C, then Daisy might find, for example, that (1) yield ± 300 ² .8V ² .01P ² .06T ² .001T*P ³ .01T 2 ³ .001P 2 ² 11.7A ² 9.4B ² 16.4C ² 19A*B ² 11.4A*C ³ 9.6B*C Maximizing Wozac Yield EXAMPLE 1
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To determine this relationship, the yield of the process would have to be measured for many different combinations of the previously listed factors. Knowledge of this equation would enable Daisy to describe the yield of the production process once volume, pres- sure, temperature, and chemical composition were known.
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This note was uploaded on 11/02/2010 for the course ORIE 1101 taught by Professor Trotter during the Fall '10 term at Cornell University (Engineering School).

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1 An Introduction to Model Building - An Introduction to...

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