Mikhail Ivlev – Associate Professor, Department of Computer Technologies in Design and Manufacturing, Institute of Radio Electronics and Information Technologies, Nizhniy Novgorod State Technical University n.a. R.E. Alekseev. Address: 24, Minina str., Nizhny Novgorod, 603950, Russian Federation. E-mail: ivlev-ma@yandex.ru

Issue concerning mathematical models for optimization of company output subject to its customers preferences is still cental to production and consumption theory. Models are based on finite directed graph (digraph) with flows which formalizes optimal selection in terms of type, quality and cost of product.

Based on digraph analysis objective functions for optimization problem solving were determined. Particularly objective functions and limitations necessary and sufficient for optimal solutions were specified. Moreover production and consumption theory allows intuitive designing and manufacture of differentiated products in accordance with customer needs. This paper describes logic and process of parameterization through optimization model, which refers to nonlinear integer programming (objective function is nonlinear, limitations are linear). Additionally method of minimal graph partition into set of independent arcs.

Usefulness of this paper is proved by the fact that it offers method for minimal edge separation which takes into account generation of paths in digraph with flows as compared to traditional edge separation in network models. Digraph nodes are classified and rules on which calculation of flows to outer vertexes is based are set up.

Production and consumption theory and its chain binary structure interpretation allow choice and validation of relevant mathematical model (the first step of modeling process). After analysis of such model objective function is made up, limitations are determined and algorithm is developed.

If necessary, this mathematical model could be extended to those objective functions which are determined by more than two factors. In this case graph would be m-dimensional where m is a number of factors.

Citation:
Ivlev M. A (2013) Matematicheskie osnovy teorii proizvodstva-potrebleniia: opredelenie vida, struktury i parametrov modelei. [Mathematical bases of the production-consumption theory: definition of a type, structure and parameters of models.] Biznes-informatika, 1(23), pp. 10-18 (in Russian)