USING PERIODIC FUZZY GRAPHS IN PRODUCTION EQUIPMENT CONTROL PROBLEMS

Abstract

Monitoring equipment wear is an important and urgent task that requires constant attention
and monitoring. This is due to the fact that wear and tear on equipment can lead to a decrease in
its operating efficiency, an increased likelihood of accidents or breakdown. The task of replacing
equipment is a systemic production task, in solving which it is necessary to take into account many factors that influence the efficiency of the enterprise. This paper proposes a concept for solving the
problem of timely replacement of equipment using periodic fuzzy graphs. Periodic fuzzy graph
models make it possible to adequately reflect types of uncertainty, reflect the specifics of relationships
between modeled objects, and optimization constraints; solve various cyclic problems, network
planning and management problems. In this work, the use of the mathematical apparatus of
periodic fuzzy graphs allowed a problem of a dynamic nature, which depended on two time variables,
to be reduced to a problem that depended only on the operating time of the equipment. At the
same time, it is proposed to take into account the age of equipment when determining the wear
coefficient, determined by the degree of belonging to a particular wear class. This aspect made it
possible to reduce the task to study the wear of all equipment involved in the technological process
and consider the purchase of used (not new) equipment. When determining the membership function,
it is possible to consider 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 recurring periods. The article contains a literature review, justifying
the relevance of the problem considered. The problem of replacing equipment considering
dynamic components is considered. Temporal graphs have been proposed to reflect the dynamics
of the production process. The use of a graph model provides a clear display of the state of equipment
during its operation. The use of periodic fuzzy graphs allows the problem of replacing
equipment to be simplified by reducing one time component and to scale the classical dynamic
problem considering uncertain initial data.