Using the Max Flow Problem for Business Processes

Abstract

The article is devoted to the use of optimization methods for managing business processes. Problems of synthesizing the structure and choosing parameters of systems, as well as problems of optimal control of them, are most often solved by reducing them to problems of finding a number of parameters so that the extremum of the quality function is achieved under a set of restrictions. A separate group of problems related to the choice of topology can be solved using the apparatus of graph theory. Problems of choosing channel capacity can be reduced to classical optimization problems, such as linear programming, transport problem, nonlinear programming, etc. The minimum flow problem is a special case of the transport problem, which is related to linear programming problems. The paper analyzes the use of the maximum flow problem in economic systems, namely for planning business processes. The use of tasks to optimize business processes in various industries, such as logistics, production and finance, and personnel management, is described. A review of the developments and research of the maximum flow problem is carried out, a number of algorithms for solving this problem and their main points are given. The problems, the mathematical formulation of the problem, the algorithm for placing marks and the calculation of arc flows for each iteration are described in detail. An example of the flagging algorithm shows how maximum flow models can be used to analyze and optimize production processes. Maximum flow problems can identify bottlenecks in a production chain, optimize resource utilization, and plan production. Using the maximum flow problem when planning business processes will improve efficiency and increase production, help reduce costs and improve profitability, and ensure that products are in stock to meet demand.