It is clear that the model can get very quick, very fast. Fortunately, models this large have a lot of internal structure. Therefore, most linear programs contain a tremendous number of 0s. By the way, linear programming packages solve a number of individual pieces much faster than the linear program consisting of all of them. We will concentrate on block angular systems.
Similar methods hold for staircase and other large scale, structured systems.
Block angular systems consist of some common rows which contain nearly all the variables. The remaining rows are divided into sets with corresponding variables that are contained in the rows. Each variable is in exactly one set. These sets define subproblems . To solve this sort of linear program, we create one master problem .