Markov Chains in Logistics

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MAGAZINE №4(87) August 2018


CATEGORY Optimization and mathematical modelling Warehouse logistics



The paper examines application of homogeneous discrete-time Markov chains to logistics and features a problem of a logistics center (warehouse) state. Under the statement of problem, the warehouse can have different states, and transition from one state to another is not determined but random (indeterminate warehouse state). It is expected that on the basis of statistical inquiry were obtained evaluations (approximate values) of probabilities of such transitions. In such conditions of indeterminacy arises a problem of assessment of warehouse profit and tenant’s costs within a certain time.

The article presents calculation of average time of a warehouse state in each of its possible states with the method of Markov ergodic theorem in order to forecast average profit and average tenant’s costs.

In conclusion it is noted that all solution reasoning on the problem of a warehouse remains valid if we substitute a warehouse with any logistics chain, if each link of which is influenced by a number of factors, which results in chain transformation from one state to another and these processes are random. Therefore, in certain conditions (conditions of Markov theorem) it is possible to calculate average time of a chain state in each of its possible states, which is particularly useful in general evaluation of effectiveness of a logistics chain.

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