### 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

### 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