Abstract
This chapter is dedicated in its entirety to Linear Programming, a well-known mathematical procedure which has an enormous diffusion in hundreds of applications around the world. This technique, using a practical example, is explained in a way for everybody to understand it. It aims at making the DM aware of how to use this tool, and more important, how to interpret its results. Linear Programming as is explained here deals with a sole objective which is common in many applications and in different fields. Its greatest advantage can be synthesized on three counts: (a) It permits one to approximately represent an actual situation – no matter its nature – in a mathematical context, that allows for applying an algorithm to solve it, (b) it yields a unique and optimal solution, and (c) it lets to perform an extensive analysis of “What if….?” scenarios which is a valuable tool for sensitivity analysis.
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Notes
- 1.
There could be a non-linear objective function, originating non-linear programming problems. Pioneered and investigated by Kuhn and Tucker (1950).
- 2.
Legend has it that Archimedes set Roman warships afire using ‘a burning glass’ during the siege of Syracuse.
- 3.
Algorithm developed by George Dantzig to solve Linear Programming problems.
- 4.
In most multicriteria publications the inverse system is normally used, in which the alternatives are in rows while the criteria are in columns, but naturally, this difference does not alter results. It is probable that in LP, alternatives are in columns due to the set of ‘xj’ variables representing them, which are always in columns in mathematics literature.
- 5.
To invoke, go to the large button located upper left, then hit Excel options, next Excel complements, after that, mark in the box for Solver and finally, back in the Excel spreadsheet hit ‘Data’. A question mark along with the word ‘Solver’ will appear in the upper right corner with the word ‘Solver’. Double click it and you are on.
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Munier, N. (2011). Linear Programming for a Single Objective. In: A Strategy for Using Multicriteria Analysis in Decision-Making. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1512-7_4
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