ABSTRACT
This chapter discusses the decomposition method for a special class of linear programming (LP) multidimensional problems. This optimization method is applicable to a wide lass of problems such as in Refs. In large-scale systems, a special class of linear programming problems is posed as multidimensional problems and is represented by the decomposition principle, streamlined version of the LP simplex method. The decomposition principle has special characteristic features in that its formulation exploits certain matrices with distinct structures. These matrices, representing the formulated problems, are generally divided into two parts, namely, one with the easy constraints and the other with the complicated constraints. The partitioning is done such that the desired diagonal submatrices and identity matrices are obtained in the reformulation of the problem. Finally, successive iterations are performed until the optimal solution is found and the best value of ?jk is used to replace the value of xj for the optimal solution to conform with that of the original problem.
