Abstract
This chapter will cover the fundamentals of modeling problems such as the one introduced in the previous chapter but now with a view to modeling and solving much larger problems. By modeling we mean taking all the features of the original industrial or commercial problem and encapsulating the ideas in it as a mathematical programming problem. We aim for a one-to-one correspondence between the original problem and the model.
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Notes
- 1.
In the LP community variables are also called activities or just columns.
- 2.
Maple is a registered trademark of Waterloo Maple Inc.
- 3.
MathCAD is a registered trademark of MathSoft, Inc.
- 4.
Conventionally variables with zero coefficients are omitted from the expression, so not all variables are necessarily present in the expression. Also a coefficient of 1.0 is conventionally not shown next to its associated variable, i.e., 1x is written as x.
- 5.
Modelers in the refinery industry call these constraints quality constraints. Quality constraints describe concentrations, sulfur content in streams and similar quantities. These constraints, which are always related to properties of streams or materials, might also be called property constraints.
- 6.
A minimization problem has been chosen as the standard form; since any maximization problem can be formulated as a minimization problem, this is not a limitation.
- 7.
Often a feasible point is also called feasible solution. We do not want to do this in this book because the aim of optimization is to determine the optimal point, or in case of ambiguity also optimal points, and therefore only those can be regarded as a solution.
- 8.
LOTUS 1-2-3 is a registered trademark of Lotus Development Corp.
- 9.
EXCEL is a registered trademark of Microsoft Corp.
- 10.
What’s Best? is a registered trademark of Lindo Systems Inc.
- 11.
LINDO is a registered trademark of Lindo Systems Inc.
- 12.
MS-EXCEL is a registered trademark of Microsoft Corp.
- 13.
The DISKDATA command for reading text data is supported by mp-model’s successor FICO Xpress Mosel by FICO. Just LOTUS is probably not much used these days.
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Kallrath, J. (2021). From the Problem to its Mathematical Formulation. In: Business Optimization Using Mathematical Programming. International Series in Operations Research & Management Science, vol 307. Springer, Cham. https://doi.org/10.1007/978-3-030-73237-0_2
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