Мathematical model of the problem of optimizing logistics networks under conditions of interval determination of input data

Abstract

Problem. In the conditions of rapid changes in demand and supply in transportation markets, there is a need for corresponding changes in logistics technologies and networks, which are carried out through their reengineering. Existing mathematical models for the optimization of logistics networks are designed for conditions with point-wise, clearly defined input data, which does not allow obtaining solutions resistant to changes in the external environment. This determined the relevance of the scientific and applied task of developing mathematical models of multi-criteria optimization problems of logistics networks for the conditions of interval submission of input data. Goal. The goal is to increase the efficiency of the logistics network optimization technology at the stage of re-engineering by developing a mathematical model of the multi-criteria optimization problem for the conditions of interval submission of input data. Methodology. According to the results of the decomposition of the problem of system optimization of logistics networks as the most complex defined task of their structural and topological optimization. When developing the model, the methodology of system design of territorially distributed objects, methods of multi-criteria optimization, theories of utility and decision-making were used. The apparatus of interval mathematics was used to compare solution options with vaguely specified input data. The results. The result are the formulated and completed formalization of the task of optimizing logistics networks as territorially distributed objects. The relationship for the objective function and constraints of the optimization task of topological structures of centralized three-level logistics networks is proposed. Originality. A mathematical model of the task of reengineering topological structures of centralized three-level logistics networks according to cost and efficiency indicators for interval defined input data and values of local criteria using comparison indices based on the Hukuhara difference has been developed. Practical value. The obtained results make it possible to increase the reliability of optimization results in the processes of design, development planning and reengineering of logistics networks, to obtain variants of the construction of their topological structures that are resistant to changes in external conditions.