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Business Modeling

Business Modeling. Lecturer: Ing. Martina Hanová, PhD. Stochastic Processes Xj (t) j = 1, 2, ...n - the realization stochastic process. Stochastic Modeling. E1, E2, .... Em - random phenomena - states Markov property

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Business Modeling

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  1. Business Modeling Lecturer: Ing. Martina Hanová, PhD.

  2. Stochastic Processes Xj(t) j = 1, 2, ...n - the realization stochastic process Stochastic Modeling

  3. E1, E2, .... Em - randomphenomena -states Markov property thedistributionforthevariabledependsonly on thedistributionoftheprevious state Markov chain – Finite Markov chain Markov model

  4. Company placed on the market a new product and explores its success, in terms of sales which can be characterized as follows:- product is considered to be successful if in specified time sells more than 70% of the production- product is deemed to have failed, if in specified time sell less than 70% of production. Model of business policy decision-making

  5. E1 - the product is successful E2 - the product is unsuccessful Changes to the success oftheproduct examineafter months, or step = 1 month. Suppose that it is a finite Markov chain with states E1, E2, ... Em.

  6. If the product is successful in the first month, with probability 0.5 and remain successful in the next month. If not, with probability 0.2 will become successful in the next month. Transition matrix: E1 E2 homogeneous Markov chain

  7. transition matrix of conditional probabilities after k-steps: States: 1. transient 2. recurrent (refundable): - periodic (with regular return)- aperiodic (irregular return) 3. absorbent (non-refundable) Markov chains in terms Analysis the development of systems

  8. ergodic Markov chains absorbing Markov chain Example: At the beginning in the first month, found 75% of the success of the product ergodic Markov chains

  9. vector of the absolute probabilities after 1-month: vector of the absolute probabilities after 2-month: vector of the absolute probabilities after 3-month:

  10. Asymptotic behavior of the ergodic Markov chains

  11. revenue matrix R mean values ​​of the immediate revenue expected total revenue after k-steps Markov chains with the revenues

  12. Markov chains with alternatives

  13. mean values ​​of the immediate revenue • Total expected revenue on the optimal path: • 1 step: • 2 step:

  14. Final step: determine the optimal path vector ofcorresponding alternatives Markov chains with alternatives

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