# Tagged Questions

is a discipline to apply analytical methods for better decisions. It has many synonyms such as management science, decision science and system science.

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### Variable leaving basis in linear programming - when does it happen?

In the simplex algorithm in linear programming, what are conditions for a variable to leave a basis (not necessarily basis for the/an optimal solution)? I'm supposed to list as many sufficient and ...
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How do I prove an optimal solution to dual is not unique if an optimal solution to the primal is degenerate and unique? What I tried: Let the primal be $$\max z=cx$$ subject to $$Ax \... 2answers 31 views ### Is Reliability Component a vertex? The term component has a distinct definition in graph theory from vertex while the terms components and vertices can be mostly the same in Realiability Engineering, my intuition. So how is the term ... 2answers 99 views ### Under what conditions does (I-N)^{-1} exist? Given an nxn matrix N and I=I_n, under what conditions does (I-N)^{-1} exist? On one hand (I-N)(I + N + N^2 + ...) = (I + N + N^2 + ...) - (N + N^2 + ...) = I? On the other hand, (I-N)(I + N +... 1answer 86 views ### How to solve this operation research problem using dual simplex method? Maximize$$ z = 2x_1 -x_2 +x_3$$Subject to constraints$$2x_1 + 3x_2 -5x_3 \ge 4-x_1 +9x_2 -x_3 \ge 34x_1 +...
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for somebody having a quite strong background in Mathematics, which are some good books for the domain of Operations research? I guess there are textbooks covering topics like linear and nonlinear ...