# Ein allgemeines Dekompositionsverfahren fuer lineare Optimierungsprobleme

Heinemann, Hergen H. (1971): Ein allgemeines Dekompositionsverfahren fuer lineare Optimierungsprobleme. Published in: Zeitschrift fuer betriebswirtschaftliche Forschung No. 22 (1970): pp. 302-317.

## Abstract

A Really GENERAL Decomposition Algorithm for Very Large Linear Optimization Problems

Proven theory as Regards Optimality and Finality

Advantageous for very large problems with a rather small percentage of real variables in the optimal solution - Simplex method is used as a calculating sub-routine -

NO SPECIAL STRUCTURE OF MATRIX REQUIRED - Method applicable without change for non-structures as well as for any and all structures of matrix.

Maximum necessary problem size to be calculated with simplex method procedure: a bit more than a matrix of optimal-solution original variables and optimal solution restrictions - single-stage or double-stage decomposition possible - parametric-programming-similar re-calculations possible. For consultancy on slight extensions in theory as well as on important extensions in calculation tactics you may contact Dr. Hergen Heinemann: Hergen.Heinemann"et"alumni.insead.edu

Detailed ABSTRACT of Theory

(1) From the total problem matrix (TPM) partial problems (PP) are taken arbitrarily, but every variable should be represented in at least one of them.

(2) PPA´s are equipped with suitable functions for optimization and are optimized with the simplex method procedure.

(3) The optimized solutions of the PPA´s serve to obtain variables for an auxiliary problem (AP), which is then optimized to reflect an optimal combination of the optimized PP`s.

(4) With the optimal dual values of the AP the actual values for every variable of the to-be-optimized function of the TPM are calculated.

(5) With the actual values for every variable of the to-be-optimized function of the TPM a test is done to check whether the optimal solution of the TPM is already reached.

(6) Is the optimum solution of the TPM reached, then the algorithm is at the end. If not, the algorithm continues with item (2) above with a new set of variables and using the actual values of the variables of the to-be-optimized function as per item (3), starting a new cycle of the algorithm.

Original copy may be available at:

Titel: Ein allgemeines Dekompositionsverfahren fuer lineare Optimierungsprobleme (in English: A General Decomposition Algorithm for Linear Optimization Problems) ( To obtain a copy of this operations research on linear programming paper e-mail to Technische Universitaet, Braunschweig:) fernleihe@tu-bs.de

Author: Heinemann, Hergen Published: 1971 No. of pages: III, 80 S. ; 8º Doctoral Degree Paper: Saarbruecken, University, Diss., 1971 Signature: 2400-3106 / Tiefmagazin, 2. UG