Difference: LinearProgramming (2 vs. 3)

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Linear Programming

The simplest type of mathematical programme is a linear programme.

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Linear expressions are any expression of the form

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%BEGINLATEX% \begin{equation*} a_1 x_1 + a_2 x_2 + ... + a_n x_n \left\{ \begin{matrix} \leq \\ = \\ \geq \end{matrix} \right\} b \end{equation*}

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%BEGINLATEX% \begin{equation*} a_1 x_1 + a_2 x_2 + ... + a_n x_n \left\{ \begin{matrix} \leq \\ = \\ \geq \end{matrix} \right\} b \end{equation*}

%ENDLATEX%

where $a_1, a_2, \ldots, a_n$ and are known quantities and $x_1, x_2, \ldots, x_n$ are variables.

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??? Mike to add general form of a linear programme

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The general form of a linear programme is

$\begin{array}{rr@{}l} \min & c^\top & x \\ \text{subject to} & A & x \left\{ \begin{matrix} \leq \\ = \\ \geq \end{matrix} \right\} b \end{array}$

The process of solving a linear programme is called linear programming. Linear programming is done via the Revised Simplex Method (also known as the Primal Simplex Method), the Dual Simplex Method or an interior point method. Some software packages, such as CPLEX, allow you to specify which method you use, but we won't go into further detail here.

To see linear programming in action, check out some of the linear programming case studies:

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The process of solving a linear programme is called linear programming. Linear programming is done via the Revised Simplex Method (also known as the Primal Simplex Method), the Dual Simplex Method or an Interior Point Method. ??? Mike to add links to Wikipedia or ENGSCI 391 ENGSCI 768). Some software packages, such as CPLEX, allow you to specify which method you use, but we won't go into further detail here.

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Results from OpsRes web retrieved at 19:25 (GMT)

AmericanSteelPlanningProblem

r8 - 2009-10-06 - 07:38 MichaelOSullivan

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AmericanSteelTransshipmentProblem

r24 - 2014-05-22 - 15:38 MichaelOSullivan

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BlendingModels

r5 - 2019-11-11 - 02:53 MichaelOSullivan

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BreweryProblem

r10 - 2008-04-02 - 11:30 MichaelOSullivan

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CokeSupplyChain

r20 - 2018-11-23 - 01:32 TWikiAdminUser

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ForestryProblem

r9 - 2008-04-03 - 01:38 MichaelOSullivan

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HerdFeedingProblem

r16 - 2009-10-06 - 07:44 MichaelOSullivan

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WhiskasCatFoodProblem

r56 - 2019-07-20 - 05:53 TWikiAdminUser

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WinstoneAggregatesProblem

r3 - 2008-04-02 - 09:49 MichaelOSullivan

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Number of topics: 9

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-- MichaelOSullivan - 16 Feb 2008

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