Alexander G. Madera - Professor, Department of Mathematics of the Faculty of Economics, National Research University Higher School of Economics
Address: 20, Myasnitskaya Street, Moscow, 101000, Russian Federation
E-mail: amadera@hse.ru

      This paper is devoted to mathematical modeling and optimization of business processes and process systems under conditions of uncertainty. At present, modeling of business processes is mainly descriptive, which does not allow quantitative modeling and optimization in the design of processes and process systems. In addition, the existing methods of decision-making in business processes are based on the assumption that the decisive factors are deterministic. Despite uncertainty of the real processes caused by the uncertainty of future costs of resources, the market environment, economy, finances, etc,, the factors of an uncertain future are either not taken into account, or are believed to be the same as those observed  currently.
      In this paper, a stochastic interval mathematical optimization model is developed. This model allows us to simulate in a quantitative way the business processes and process systems in which they take place, taking into account the uncertainties of the future state of the economy, finances, market environment, costs of resources, as well as future realization of chances and risks related to the productive, supporting, and service processes. The criterion for optimality of the model is the maximization of the smallest deviation of the projected chances and risks, which makes it possible to make the best decision in the case that the most unfavorable conditions for the business process occur in the future. The criterion of optimality adopted in the mathematical model takes into account not only the uncertainty of the future state of the economy, finance, and market environment, but also the psychology of decision-making and the subjective nature of  judgments and estimates. We present a concept and method for estimating the inductive (logical, subjective) probabilities of the occurrence of uncertain predicted business process factors.
      The models and methods developed in the paper make it possible to carry out mathematical modeling and optimization of business processes in a variety of activities without restrictions on the complexity of the structural model of the business process, the qualitative and quantitative composition of the connections in the process systems. On their basis, a software package for the quantitative design of business processes and process systems under conditions of uncertainty can be developed.