How is it possible to formulate the convex hull of a linear programming (LP) problem to be integral? Are there any general techniques to perform this?
To add a bit to Martin answer above (I think this is too long for a comment):
There is a general procedure that I know of, called Chvátal-Gomorry procedure, which allow to ultimately describe the convex hull by adding Gomorry cuts. This is very interesting theoretically; however, there is a well-known example where this procedure takes n step (a parameter in the LP) for a problem with two variables and two constraints, i.e. the number of cuts added cannot be bounded by the size of the problem.
Totally unimodular matrix are common in problems arising in graph theory, but it is certainly not a "general" method: you can convince yourself just by the definition that the coefficient of the A matrix must be 0, 1 or -1 in a TU matrix, which is usually not the case in a ILP of course.
Of course, since solving an LP is polynomial and solving an ILP is NP-complete, one cannot expect that there is a general efficient method to do what you expect, since that would almost reduce ILP to LP!
But if you are studiying a problem in particular, especially if it has a simple structure, it could be one of the "special cases" where one of the two methods above are effective.
I can provide further references at the end of the week if you are interested.