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Vladimir O.

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Vladimir O.

D.Sc., Prof.

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DOI: 10.17586/2226-1494-2015-15-3-538-545

DOI: 10.17586/2226-1494-2015-15-3-538-545

## MATHEMATICAL MODEL FOR CALCULATION OF INFORMATION RISKS FOR INFORMATION AND LOGISTICS SYSTEM

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**Article in**English

**For citation:**Korobeynikov A.G., Grishentsev A.Yu., Komarova I.E., Ashevsky D.Yu., Aleksanin S.A., Markina G.L. Mathematical model for calculation of information risks for information and logistics system.

*Scientific and Technical Journal of Information Technologies, Mechanics and Optics*, 2015, vol.15, no. 3, pp. 538–545.

**Abstract**

**Subject of research.** The paper deals with mathematical model for assessment calculation of information risks arising during transporting and distribution of material resources in the conditions of uncertainty. Meanwhile information risks imply the danger of origin of losses or damage as a result of application of information technologies by the company. **Method. **The solution is based on ideology of the transport task solution in stochastic statement with mobilization of mathematical modeling theory methods, the theory of graphs, probability theory, Markov chains. Creation of mathematical model is performed through the several stages. At the initial stage, capacity on different sites depending on time is calculated, on the basis of information received from information and logistic system, the weight matrix is formed and the digraph is under construction. Then there is a search of the minimum route which covers all specified vertexes by means of Dejkstra algorithm. At the second stage, systems of differential Kolmogorov equations are formed using information about the calculated route. The received decisions show probabilities of resources location in concrete vertex depending on time. At the third stage, general probability of the whole route passing depending on time is calculated on the basis of multiplication theorem of probabilities. Information risk, as time function, is defined by multiplication of the greatest possible damage by the general probability of the whole route passing. In this case information risk is measured in units of damage which corresponds to that monetary unit which the information and logistic system operates with. **Main results. **Operability of the presented mathematical model is shown on a concrete example of transportation of material resources where places of shipment and delivery, routes and their capacity, the greatest possible damage and admissible risk are specified. The calculations presented on a diagram showed that risk value under the specified conditions becomes lower than permissible if the demanded time of material resources transportation determined by the customer is more than 50 minutes. This calculation provides additional information for the person making the decision about the offer acceptance or refusal on transportation of material resources to the specified points. **Practical significance. **Results of work are usable in the fully functional information and logistic systems for calculation of the information risks arising during the transporting or distribution of material resources. It will increase competitiveness of the logistic companies operating in the conditions of the modern market relations.

**Keywords:**digraph, weight matrix, adjacency matrix, transportation problem, mathematical model, logistics information system, information risks, Kolmogorov equations, Dejkstra algorithm, system of ordinary differential equations.

**References**