Optimal aggregation of production systems with parametric connections - Боровская, Таиса Николаевна (Eastern-European Journal of Enterprise Technologies, 2014)
Today, all conditions for effective functioning and development of production systems, with the exception of effective mathematical models for the new production management problems are provided. Based on the analysis of the state of theory and practice, requirements to models of production systems: absence of restrictions on the type of production functions, except for non-strict monotony and non-strict positivity; eliminating the dimensionality problem for optimization problems; isomorphic mapping of the structure of the production system in the decomposition structure of the optimization problem were formulated. To solve the problem of optimal control, methodology of optimal aggregation of production systems was used. The key point of this methodology is the decomposition of multidimensional nonlinear programming problem in the system of one-dimensional optimization problems. The structure of this system corresponds to the structure of the resource connections in the production system. Solutions for optimal aggregation of typical structures of production systems with parametric connections: “production – development”, “production – warehouse”, “production with recycling” that satisfy the set requirements were first obtained. The properties of this class of models for production systems are insufficiently investigated. Concrete results of modeling for these tasks were presented in the paper. Models are open for modifications and customization to specific segments of the production.