The purposeful transformation of mathematical models based on strategic reflection

The study of complex processes in various spheres of human activity is traditionally based on the use of mathematical models. In modern conditions, the development and application of such models is greatly simplified by the presence of high-speed computer equipment and specialized tools that allow, in fact, designing models from pre-prepared modules. Despite this, the known problems associated with ensuring the adequacy of the model, the reliability of the original data, the implementation in practice of the simulation results, the excessively large dimension of the original data, the joint application of sufficiency heterogeneous mathematical models in terms of complexity and integration of the simulated processes are becoming increasingly important. The more critical may be the external constraints imposed on the value of the optimized functional, and often unattainable within the framework of the constructed model. It is logical to assume that in order to fulfill these restrictions, a purposeful transformation of the original model is necessary, that is, the transition to a mathematical model with a deliberately improved solution. The new model will obviously have a different internal structure (a set of parameters and their interrelations), as well as other formats (areas of definition) of the source data. The possibilities of purposeful change of the initial model investigated by the authors are based on the realization of the idea of strategic reflection. The most difficult in mathematical terms practical implementation of the author's idea is the use of simulation models, for which the algorithms for finding optimal solutions have known limitations, and the study of sensitivity in most cases is very difficult. On the example of consideration of rather standard discrete-event simulation model the article presents typical methodological techniques that allow ranking variable parameters by sensitivity and, in the future, to expand the scope of definition of variable parameter to which the simulation model is most sensitive. In the transition to the “improved” model, it is also possible to simultaneously exclude parameters from it, the influence of which on the optimized functional is insignificant, and vice versa — the introduction of new parameters corresponding to real processes into the model.