Proof of Strong Duality Theorem

Let be Then is The theorem states: Suppose B is an optimal basis for the primal .  Then is an optimal solution to the dual.  Also where * indicates optimal value. Proof Advertisements

Minimum Cost Flow Problem Formulation

Supposed you have several locations, indexed These locations have demands and supplies.  We’ll denote as the supply from location .  A negative indicates a demand at location . The arc set A contains arcs for directed arcs from location to .  The node set N contains the location indices Define amount of commodity moved from … Continue reading

MikTex. Vista. Problems!

I am not a latex pro.  I use TexnicCenter as an IDE, and I use pretty basic functionalities.  Every once in awhile, I have to use packages, and today, I was having major problems installing packages. Each time I tried to build the .tex file, my screen would go dark, and a window would appear, … Continue reading

Proof Bonferroni’s Inequality

Let be an event that occurs with probability for .  Then   where is the intersection of non-independent events . Proof by induction on n Base case, By additivity law and probability axiom Inductive hypothesis Suppose relation is true for , that is Inductive Step Let .  Then as required.

Order Lists on AutoMod

I’ve been trying to simulate a bottling facility using AutoMod.  This is a lesser known simulation program playing with big-time competitors like Simul8 and ARENA.  Regardless, this is the program directed by my professor, so I have struggled through it. One feature I’ve been using extensively is the Order List, which is quite powerful, but … Continue reading

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