How to solve Linear Programming with variables that have 2, 3 and 4 dimensions and are time dependent?

Hi, my problem is about a Mixed Integer Linear Programming model. The solution approach that I plan to use, is to solve the binary variable first with GA and in the fitness function insert the LP model.

However I'm very new with Matlab, and I haven't figure out how to solve this model using the "linprog" Toolbox. All examples in the tutorial are very simple.

I have variables that has 2, 3 and 4 dimensions. Can somebody give a light in how to start modeling this equations? In the figure is attached the first part of the model. Thanks!

[Patty]

2nd part of the model.

The y_ljn is the binary variable that is going to be solved with Genetic Algoritmn.

The other variables are: Q_jln, idt_lt, z_lijn, I_jt

The others are known data.

Answer 1

[John D'Errico]

Why cannot you treat those multi-dimensional arrays of unknowns as simply a vector of unknowns? Unroll the arrays.

Admittedly, it forces you to think about where things fall in memory when you do that. But sub2ind and ind2sub will help you there. Little active thought will be needed, beyond understanding the equations you have formulated. But you are lost anyway if you don't understand your own equations, so there is no serious problem.