Modeling the interaction of resource flows in the foreign trade system

The article investigates the relationship of flows of various types (transport, cargo, information, financial, energy, legal and others) between themselves and elements in the delivery system of foreign trade cargo. A hierarchical scheme of points of interaction of various types of flows is proposed. It is note that optimization of flow control will create more favorable conditions for rhythmic work and coordination of transportation with other modes of transport, and a correctly calculate supply of goods to ports and border crossings will provide an opportunity for the economical use of rolling stock. The solution to this problem at a new level has become possible due to the widespread introduction of digital information technologies. A model of the topology of their interaction has been develop with the definition of an integral quality indicator of a particular route or delivery option. An algorithm for assessing the interdependence of various types of elements, flows, legal ties and the degree of complexity of the structure of the system for the delivery of foreign trade goods.


Introduction
Freight owners are constantly face with a number of problems: on what basic conditions to conclude an agreement for the purchase or sale of goods, how to choose a transportation route, how to pay the minimum price for transportation, and others. It is know that the commercial success of a product or transport service depends on not only the ratio of price and quality, investment in advertising, but also on how well the delivery, payment, transportation and storage schemes are chose [1,2]. The advantages of an integrated, systemic or, as it is now customary to call, -a logistics approach to managing the movement of transport, cargo, information, financial and energy flows served as one of the reasons for

Results
In the process of reforming, the vertical of management of the transportation process and its constituent structural units underwent hierarchical and abbreviated changes in names, as a result of which, for convenience and completeness of perception [3,4], Figure 1 shows the previous and existing abbreviations of structural units involved in the management of train and shunting operations on railway stations, sections, tracks, landfills, etc.
Based on the above, a hierarchical scheme of points of interaction of various types of flows is propose, including dispatch, information, situational and other control centers for freight traffic in the mixed message system, shown in Figure 1.
The entire structure of the system for the delivery of foreign trade cargo (SDFTG) can be represent as a set of elements X = loading station (port), consignor, cargo owner, railway lines, stations for disbanding or forming trains, unloading station (port), consignee, forwarder, etc.) and a set of flows (transport -T, cargo -G, information -Y, financial -F, energy -E and legal ties -P) interacting with each other. In turn, each element, flow and legal connection can be categorize -attributed to one category or another [5,6].
Each element or subsystem of the SDFTG must be assignee a dynamic array consisting of constant and variable parameters of the current forecast and archive states. The parameters are not only the normative and reference information of the rules for the carriage of goods, tariff guides and various standards, but also the functional properties of the elements, determined by customer passports, technical and administrative acts of the stations, the train formation plan, codes of customs of seaports, charters of enterprises, licenses, certificates, etc. [7,8].
Each parameter characterizing the elements (performance of handling equipment, storage capacity, span length, availability of licenses or the right to provide various types of services in the field of transport business, the procedure for handling arriving and departing trains at stations, the procedure for delivering / cleaning wagons to / from the port, the right for payment of the tariff according to the 10-01 price list and at the rates of the tariff policy, the bank in which the current account of the subject of the regional customs administration is located, the basic conditions of foreign trade contracts, etc.) has its own functional purpose and affects both the state and functioning separately taken element or subsystem of SDFTG, and the order of interaction of elements with flows of various types and categories, flows of various types among themselves, elements and flows with legal connections -that is, on the state and functioning of SDFTG as a whole. One of the most important (qualitative) properties of SDFTG lies mainly in the strength of the connectivity of its elements, transport, cargo, information, financial and energy flows with a certain technology and legal basis for their interaction, or, in other words, this is the topological state space in which qualitative property of SDFTG [9,10]. It is a space that can be called the space of the structure of elements, structures of all types of flows and the structure of legal relations of various categories, since it is the structure of the relationship of elements, flows and the legal framework or individual subsystems of the SDFTG that determines its functioning. With a change (disappearance or weakening) of the connectivity between individual elements (closure of lines, natural disasters, wars, interstate conflicts, seizure of a current account, termination of sales and purchase agreements, forwarding contracts, chartering, declaration, revocation of licenses, power outages, etc. .) there is either the disappearance of SDFTG itself, or a change in its functional properties (quality).
Information about the qualitative state of SDFTG in statics given by its description in terms of incidence relations.
In general, a saturated linear plan in k-dimensional space is a collection of M + 1 points located in this space in such a way that they do not simultaneously belong to any subspace of dimension less than M. Such points define the vertices of a geometric figure that is call a k-dimensional simplex. A. Poincaré considered figures made up of simplexes (the so-called polyhedral) in the construction of homology theory -one of the sections of topology [11].
The notion "simplex" is formulate as follows: a simplex is the convex hull of linearly independent points in Euclidean space or a homeomorphism image; these points are call vertices of the simplex, and their number reduced by one is call the dimension of the simplex. Any subset of vertices of a simplex also defines a simplex -a face of the original simplex. Correct adjoining of simplexes in a polyhedron means that simplexes can intersect only along their common face.
However, according to computer terminology, there is also an excellent concept. In it is said, "between the vertices of the simplex, data can move in only one direction and it is impossible for the data flow to move in the opposite direction." In this case, only the information flow meant. In SDFTG, not only information flows, but all other types of flows move in both directions (exchange of information, return of incorrectly accrued sums of money, return of rolling stock to its owner, return of cargo to the departure station due to a commercial malfunction, etc.), therefore this the term for modeling the corresponding processes is unacceptable. The term "duplex", which characterizes the possibility of simultaneous transmission of data (movement of information flow) in both directions, is also not entirely appropriate, since between the same elements of the SDFTG and the subjects of regional customs departments (railway stations, ports, forwarders, etc.) move flows of various types. Therefore, the most suitable for formalizing interactions between elements, flows and legal ties in SDFTG seems to be the term "multiplex", which characterizes the movement of all types of flows in any direction, their interaction with elements, legal ties and among themselves [12,13].
To simulate the interaction of elements х , flows , , , f , e and legal relations ( , , , , , , ) on products and , and , and , and , and , and , as well as all the others, the relations λ × , λ × , λ × , λ × , λ × , λ × , etc., which exist between the sets and , and , At the same time, each multiplex means a certain interaction of elements, flows of various types and legal relations between themselves (for example, "cargo shipment ↔ ship", "transit car with processing ↔ sorting station", "customs payments ↔ bank", "navigator's receipt ↔ fuel and energy complex "," a document confirming the export of goods ↔ VAT refund "," agreement for the provision of information services ↔ dislocation of a wagon or cargo "," energy flow ↔ railway line "," set of shipping documents ↔ commodity office ", etc.), and the totality of such multiplexes constitutes the structure of the entire SDFTG [14]. Table 1 shows the designations of relations and incidence matrices, as well as multiplicative complexes for the corresponding products of element structures, flows and legal relationships. 2. Each of the multiplexes ∈ , ∈ , ∈ , ∈ , ∈ , ∈ , etc. are defined by some subsets of ( + 1) different , , , , R and , for each of which there is at least one ∈ , ∈ , ∈ , ∈ , ∈ , ∈ и ∈ , such that ( ; ) ∈ , ( ; ) ∈ , ( ; ) ∈ , ( ; ) ∈ , ( ; ) ∈ , ( ; ) ∈ etc. for each of the ( + 1) values , , , , R and .   Table 2 shows the designations of relations and transposed incidence matrices, as well as conjugate multiplicative complexes for the corresponding products of elements, flows of various types and legal relationships.
Thus, the structure of the SDFTG is consider as consisting of 21 interacting complexes (21 direct and 21 reverse): complexes of elements, complexes of flows of various typestransport, cargo, information, financial, energy and complexes of legal ties.
Co-evolutionary interaction, considered from the point of view of its organization, is a chain link of conjugating complexes, which is characterize by asymmetry and the presence of a link. Breaking the bond in co-evolutionary interaction entails either disorganization or the emergence of separate independent complexes.
Let us consider some of the features of the use of multiplicative complexes for assessing the structure of SDFTG.