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Would anyone be able to provide me with some general guidelines that could help me determine when to use a particular method to solve a Linear Programming problem? For example to know when I should use Primal Simplex/Dual Simplex/2-Phase/Big M/Cutting Plane? So far I have a list of guidelines which tell me how to solve a standard maximization problem, if the following conditions are satisfied:

• It’s to maximize an objective function

• All variables are non-negative (i.e. ≥0)

• Constraints should all be ≤ a non-negative value

Could anyone provide me with similar conditions for when you have a standard minimization problem, e.g. what way should the constraints and variables be to be able to find the optimal solution using the Primal Simplex method?

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    Do you mean on paper, or with a computer? – 2017-01-15
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    On paper! It's all by hand – 2017-01-15
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    If you have a primal basic feasible solution, use primal simplex. If you have a dual basic feasible solution, use dual simplex. Otherwise use either two 2-phase or the Big-M method. If you have integers, use a cutting plane method in addition to the aforementioned. – 2017-01-15
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    I know this is going to sound silly but how exactly do you know if you're going to have a primal basic feasible solution or not? Could you give me any guidelines (like the ones mentioned above) that could help me to determine which method to use? – 2017-01-15
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    Practically you often only consider trivial solution. If $x=0$ is feasible for the primal, you have a primal feasible solution (considering of all slack or excess variables). If $y=0$ is feasible for the dual, you have a dual feasible solution. – 2017-01-15
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    I still don't think I completely understand what you mean... For example, I have a question which is to minimize z = 2x1 + 3x2 + 4x3 + 5x4 subject to 3 constraints which are all ≥ a non-negative value and x1, x2, x3, x4 are all ≥0. What simplex method do I use to solve this? How do I know that's it's the right method to use? – 2017-01-15
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    Depends. If the rhs is nonpositive, $x=0$ is primal feasible and the primal simplex method is a good choice. If the rhs is nonnegative, $y=0$ is dual feasible and the dual simplex method is a good choice. – 2017-01-15
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    So is that irrespective of the inequality signs? Or is that just if they're ≥0 in the constraints? – 2017-01-15

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