An approach to solving the problem of equipment replacement using periodic fuzzy graphs

Abstract

Monitoring equipment wear is an important problem that requires constant attention, since this process can lead to a decrease in its efficiency, accidents or breakdown. The problem of replacing equipment is a production problem, in which it is necessary to consider many factors that influence the efficiency of the enterprise itself. This paper examines various formulations of the equipment replacement problem: in the classical formulation of dynamic programming, in the stochastic formulation and fuzzy graph representation. The idea to solve the problem using periodic fuzzy graphs is proposed. We also consider the age of equipment when determining the wear coefficient, determined by the degree of belonging to a particular class of parameters defined in the formulation of the problem. Periodic fuzzy graphs allow considering the problem of replacing equipment not for one type of equipment, but for a complex of machines, which ensures the scalability of the classical dynamic programming problem under uncertain initial data. When determining the membership function, it is possible to consider those factors that may influence the solution of the optimization production problem. Setting the problem in a fuzzy form makes it possible to forecast and plan the activities of an enterprise for future periods.