The mathematical models and methods for planning and decision making in complex systems under uncertainty

1. Номер государственной регистрации темы – 0111U000740, НТУУ «КПИ» – 2400-ф.
2. Научный руководитель – д.т.н., проф. Pavlov Alexander A.
3. Суть розробки, основні результати.

The mathematical models, methods and information technology have been developed for hie-rarchical planning and decision-making in complex organizational and economic systems of the network representation of technological processes and limited resources. The work is a continuation of original new direction that has no analogues in the world to create the exact PDC-algorithms (al-gorithms with polynomial and decompositional components) for solving intractable combinatorial optimization problems (ICOP). New methods and based on these new theoretically grounded exact PDC-algorithms was created for the known classical ICOP “Minimizing total weighted tardiness of jobs on one machine” (TWT) and “Minimizing total earliness and tardiness of jobs on one machine” (TET), which will significantly expand the class of polynomially solvable problems. Modified the PDC-algorithms for ICOP “Minimizing total tardiness of jobs on one machine” (TT), “Minimizing the total weighted completion time of jobs on one machine with respect to the order given by oriented acyclic graph” (TWCTG) and “Minimizing total tardiness of jobs on parallel machines” (TTP). The effective methods created of multivariate polynomial regression by excessive description with randomly distributed error with limited variance using an active experiment; the effective methods of building the regularity that is given by the description which is linear of an excessive number of unknown coefficients by a limited set of experimental data obtained by passive experi-ment in the case if the number of experiments is less than the number of unknown coefficients. The upper bound of measurement error variance is obtained. A new formal models was developed that allowed Saaty analytic hierarchy process method to be extended to the case of poorly due partly filled empirical pairwise comparisons matrices of arbitrary dimensions; the formal models and methods of determining the global goal; hierarchy tree to select the best plan generated from the set of 31 optimality criteria in relation to informal global goals based on the modified method of analytic hierarchy process. Complexes of interrelated models was created for hierarchical planning and management of job shop, “on demand” production planning, small-scale type production planning, hierarchical planning of batch productions, planning building productions, project management. The result of work is the new information technologies for the proposed models and methods as integrated software packages that implement the solution of multistage planning problem for 31 optimality criterion in complex organizational and economic systems with the network representation of technological processes and limited resources and the decision making problem solution.

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