## Tuesday, July 19, 2022

### The inverse of A(i,j) has signature B(j,i)

GAMS has strict domain checking (type checking). This has some interesting consequences. Basically all good: much better protection against errors compared to simply using integer indices $$1,\dots,n$$. Consider the square matrix $$\color{darkblue}A_{i,j}$$:

 set   i /a,b,c,d/   j /1,2,3,4/ ; parameter A(i,j) 'square matrix'; A(i,j) = min(ord(i),ord(j)); display A;

## Tuesday, July 12, 2022

### Linearize min(a,b)>min(x,y)

This question was posed [1]: How to linearize $\min(\color{darkred}a,\color{darkred}b)\gt \min(\color{darkred}x,\color{darkred}y)$ where $$\color{darkred}a,\color{darkred}b,\color{darkred}x,\color{darkred}y$$ are variables. The type of variables is not specified so let's assume they all are continuous variables.

## Monday, July 11, 2022

### Transportation model with some non-existing links

I am again looking at simple models based on the transportation model:

Dense Transportation Model
\begin{align}\min&\sum_{i,j}\color{darkblue}c_{i,j}\cdot\color{darkred}x_{i,j}\\ & \sum_j \color{darkred}x_{i,j} \le \color{darkblue}a_i && \forall i \\& \sum_i \color{darkred}x_{i,j} \ge \color{darkblue}b_j && \forall j \\ & \color{darkred}x_{i,j} \ge 0 \end{align}

## Friday, July 8, 2022

### Artificially creating a large LP model: why is Cplex so efficient

I am teaching some GAMS classes this summer. The first class is about the transportation model. This is model number 1 from the GAMS model library [1]. It is a tiny model, slightly modified from the original model in [2]. I believe the GAMS version has been made dual degenerate.