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

ABSTRACT of Theory

(1) From the total problem matrix (TPM) partial problems (PP) are taken arbitrarily.

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

(3) The optimized solutions of the PP´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 acual values of the variables of the to-be-optimized function as per item (3), starting a new cycle of the algorithm.

The full text of the thesis in German language you can find under:

http://www.decomposition-algorithm-linear-optimization.com/ 

or in pdf-format under:

http://mpra.ub.uni-muenchen.de/28842/3/MPRA_paper_28842.pdf