Alexander L. Kazakov

An approach to optimization in transport logistics

A new approach to some optimization problems arising in the transport logistics was proposed. Consideration was given to the fundamental problems of the today logistics such as the problem of optimal arrangement and that of identification and segmentation of the logistic zones. They are solved using the “wave” method which relies on the analogy between the determination of the global extremum of the integral functional and propagation of light in an optically inhomogeneous medium. A numerical algorithm was developed, and the results of calculations presented.

On segmenting logistical zones for servicing continuously developed consumers

We study the optimal placement problem for several logistical objects. A characteristic feature of this problem is the need for sequential segmentation into servicing zones and accounting for population distributed continuously across the entire region. We reduce this problem to a variational calculus problem in a special form. To study this problem, we develop numerical algorithms that are able to determine the optimal placement of a logistical object inside a given segment. The algorithms are based on constructing wavefronts for a light wave emitted from the boundary of the chosen region. The wave moves inside the region, which lets us account for all inhabitants in this region. In constructing the solution, we have accounted for the loss of smoothness in the wavefront, have developed a software implementation for the computational algorithms, and have conducted a numerical experiment for a number of model problems.

Mathematical model and program system for solving a problem of logistic objects placement

This paper considers a placement problem for logistic objects with logistic zones segmentation in the continuous setting (an object can be placed at any point of a given area). The authors reduce this framework to a calculus of variations problem and suggest a numerical algorithm of solution based on the optical-geometrical approach. And finally, this algorithm is employed to solve the problems of municipal infrastructure optimization.

An intelligent management system for the development of a regional transport logistics infrastructure

This paper presents an intelligent management system realized on the basis of ontologies and formalized expert knowledge, mathematical models and numerical methods. We introduce a complex approach to the analysis of transport logistics systems using an original concept of multilevel modeling. The constructed mathematical models and software modules integrated in the system are described in brief. Modern intellectualization tools are applied for providing interaction among different modules and processing of incomplete statistical data. And finally, we consider some test and applied problems and their solution by the system.

Algorithms for constructing optimal n-networks in metric spaces

We study optimal approximations of sets in various metric spaces with sets of balls of equal radius. We consider an Euclidean plane, a sphere, and a plane with a special non-uniform metric. The main component in our constructions of coverings are optimal Chebyshev n-networks and their generalizations. We propose algorithms for constructing optimal coverings based on partitioning a given set into subsets and finding their Chebyshev centers in the Euclidean metric and their counterparts in non-Euclidean ones. Our results have both theoretical and practical value and can be used to solve problems arising in security, communication, and infrastructural logistics.

The Problem of the Optimal Packing of the Equal Circles for Special Non-Euclidean Metric

The optimal packing problem of equal circles (2-D spheres) in a bounded set P in a two-dimensional metric space is considered. The sphere packing problem is to find an arrangement in which the spheres fill as large proportion of the space as possible. In the case where the space is Euclidean this problem is well known, but the case of non-Euclidean metrics is studied much worse. However there are some applied problems, which lead us to use other special non-Euclidean metrics. For instance such statements appear in the logistics when we need to locate a given number of commercial facilities and to maximize the overall service area. Notice, that we consider the optimal packing problem in the case, where P is a multiply-connected domain. The special algorithm based on optical-geometric approach is suggested and implemented. The results of numerical experiment are presented and discussed.