MATHEMATICAL MODELS AND METHODS OF COORDINATED PLANNING

Abstract

Modern processes of globalization and economic competition require a significant increase in the requirements for the professional degree of top-level managers who manage the activities of international corporations, regional economies, branch ministries, etc. Their efficient operation is impossible without the use of basic scientific developments and appropriate software which implement the main qualitative law of complex organizational and production systems management: the law of coordinated management (planning), when management decisions at the top level take into account interests that may not coincide, or even be antagonistic in organizational and production subsystems connected by a certain structure of mutual relations within a single organizational and production complex system. In this work, we consider a two-level organizational and production system, which in terms of the generally known theory of active systems is defined as “decision-making center → elements (of an organizational and production subsystem)”. We consider formal models of elements of two classes, linear continuous and discrete, aggregated production models which belong to the same class of NP-hard single-stage scheduling problems. For both types of element models, we give compromise criteria and corresponding methods of constructing compromise solutions based on the results of Prof. A. A. Pavlov for multi-objective linear programming, as a result of his theoretical research for discrete optimization problems under uncertainty, and the theory of PSC-algorithms created by him and his students, that is, algorithms containing polynomial complexity subalgorithms for constructing feasible solutions that satisfy theoretically substantiated sufficient signs of optimality. In this work, we use the PSC-algorithm for the NP-hard scheduling problem “Minimization of the total weighted completion time of jobs on a single machine with precedence relations given by a directed acyclic graph”.