A basis factorization method for multi-stage linear programming problems with an application to optimal operation of an energy plant

An algorithm for solving multi-stage linear programming problems is presented, which is based on a basis factorization method. It is shown that the correction factor of the basis means the interchange of the columns between the original and the working bases. Using this fact, the relative cost factor is calculated and the correction factor is updated by a set of column operations. A program code using the above idea is developed and applied to an in-plant energy operating system. The preliminary study shows that the proposed algorithm reduces both computational storage and computing time by less than a half of a general purpose LP code (MPS-II).