Management Science Chapter 1 and 2 notes.docx

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making a small adjustment on the spreadsheet, as will be illustrated in Section 3.2 . Characteristic 5 describes the so-called proportionality assumption of linear programming, which states that each term in an output cell must be proportional to a particular changing cell. This prohibits those cases where the Excel equation for an output cell cannot be expressed as a SUMPRODUCT function. To illustrate such a case, suppose that the weekly profit from producing Wyndor’s new windows can be more than doubled by doubling the production rate because of economies in marketing larger amounts. This would mean that this weekly profit is not simply proportional to this production rate, so the Excel equation for the objective cell would need to be more complicated than a SUMPRODUCT function. Consideration of how to formulate such models will be deferred to Chapter 8 . Additional examples of formulating linear programming models on a spreadsheet are provided in Section 2.7 and in both of this chapter’s solved problems presented at the end of the chapter. (All of these examples also will illustrate the procedure described in the next section for using algebra to formulate linear programming models.) Summary of the Formulation Procedure The procedure used to formulate a linear programming model on a spreadsheet for the Wyndor problem can be adapted to many other problems as well. Here is a summary of the steps involved in the procedure. 1. Gather the data for the problem (such as summarized in Table 2.1 for the Wyndor problem). 2. Enter the data into data cells on a spreadsheet. page 33 3. Identify the decisions to be made on the levels of activities and designate changing cells for displaying these decisions. 4. Identify the constraints on these decisions and introduce output cells as needed to specify these constraints. 5. Choose the overall measure of performance to be entered into the objective cell. 6. Use a SUMPRODUCT function to enter the appropriate value into each output cell (including the objective cell). This procedure does not spell out the details of how to set up the spreadsheet. There generally are alternative ways of doing this rather than a single “right” way. One of the great strengths of spreadsheets is their flexibility for dealing with a wide variety of problems. Review Questions 1. What are the three questions that need to be answered to begin the process of formulating a linear programming model on a spreadsheet? 2. What are the roles for the data cells, the changing cells, the output cells, and the objective cell when formulating such a model? 3. What is the form of the Excel equation for each output cell (including the objective cell) when formulating such a model? 2.3 THE MATHEMATICAL MODEL IN THE SPREADSHEET There are two widely used methods for formulating a linear programming model. One is to formulate it directly on a spreadsheet, as described in the preceding section. The other is to use algebra to present the model. The two versions of the model are equivalent. The only difference is whether the language of spreadsheets or the language of algebra

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is used to describe the model. Both versions have their advantages, and it can be helpful to be bilingual. For
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