MATHEMATICAL MODELS OF DECISION SUPPORT IN THE PROBLEMS OF LOGISTICS NETWORKS OPTIMIZATION

Abstract

The subject of research in the article is the process of decision support in the problems of logistics networks optimization. The goal of the work is to develop a set of mathematical models of logistics network optimization problems to increase the efficiency of decision support systems by coordinating the interaction between automatic and interactive procedures of computer-aided design systems. The following tasks are solved in the article: review and analysis of the current state of the problem of decision support in the problems of logistics networks optimization; decomposition of the problem of decision support for the optimization of logistics networks; development of a mathematical model of the general problem of network optimization in terms of economy, efficiency, reliability and survivability; development of a set of technological mathematical models for the correct reduction of many effective options for building logistics networks for the final choice, taking into account difficult to formalize factors, knowledge and experience of the decision maker (DM). The following methods are used: systems theory, utility theory, optimization and operations research. Results. Analysis of the current state of the problem of logistics networks optimization has established the existence of the problem of correct reduction of a subset of effective options for their construction for ranking, taking into account difficult to formalize factors, as well as knowledge and experience of DM. The decomposition of the problem into tasks is performed: definition of the principles of network construction; network structure selection; determination of the topology of network elements; choice of network operation technology; determination of parameters of elements and communications (means of cargo delivery); multi criteria evaluation and selection of the best option for building a network. A mathematical model of the general problem of network optimization in terms of economy, efficiency, reliability and survivability is proposed. To coordinate the interaction between automatic and interactive network optimization procedures, it is proposed to use a combined method of ranking options, which allows you to identify and correctly reduce the subset of effective options for ranking DM. To implement the method, mathematical models of problems of the procedure of ranking options in the technologies of project decision support have been developed, which allow to combine the advantages of the technologies of the ordinalistic and cardinalistic approaches. Conclusions. The developed set of mathematical models expands the methodological bases of automation of processes of support of multi criteria decisions on optimization of logistic networks, allows to carry out correct reduction of set of effective options of their construction for the final choice taking into account factors, knowledge and experience of DM. The practical use of the proposed models and procedures will reduce the time and capacity complexity of decision support technologies, and through the use of the proposed selection procedures - to improve their quality across a variety of functional and cost indicators.