Markov Analysis
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Transcript of Markov Analysis
![Page 1: Markov Analysis](https://reader035.fdocuments.in/reader035/viewer/2022081813/56812ad0550346895d8eaddc/html5/thumbnails/1.jpg)
Markov Analysis
![Page 2: Markov Analysis](https://reader035.fdocuments.in/reader035/viewer/2022081813/56812ad0550346895d8eaddc/html5/thumbnails/2.jpg)
Overview• A probabilistic decision analysis• Does not provide a recommended decision• Provides probabilistic information about a
decision situation that can aid the DM• Applicable to systems that exhibit probabilistic
movement from one state to another, over time– Probability that a machine will be running one day and
broken down the next– Probability that a customer will change her
department store to the next, called brand switching
![Page 3: Markov Analysis](https://reader035.fdocuments.in/reader035/viewer/2022081813/56812ad0550346895d8eaddc/html5/thumbnails/3.jpg)
Brand Switching Example• Customers are usually royal to a particular brand or store, or
supplier• Two gas stations in a community , P and N• Study indicates customers are not royal to either one• Willing to change based on advertisement factors• If a customer bought gas from P in any given month, there was 0.6
probability that the customer would buy from P and 0.4 probability from N the next month
• If a customer traded with N in any given month, there was 0.8 probability that the customer would buy from N and 0.2 probability from N the next month
Next MonthThis month P N
P 0.6 0.4N 0.8 0.2
![Page 4: Markov Analysis](https://reader035.fdocuments.in/reader035/viewer/2022081813/56812ad0550346895d8eaddc/html5/thumbnails/4.jpg)
Terminology
• Gas station that a customer trades at a given month is called state of the system (two states of system)
• Probabilities of various states are called transition probabilities– Transition probability sum to one– Probabilities apply to all participants– Probabilities are constant over time– States are independent over time
![Page 5: Markov Analysis](https://reader035.fdocuments.in/reader035/viewer/2022081813/56812ad0550346895d8eaddc/html5/thumbnails/5.jpg)
What Information MA Provides?
• Answers the probability of being in a state at some future time period
• Determining the probability that a customer would trade with them in month 3 given that the customer trades with them this month
• Use the following decision tree 1– The probability of a customer’s purchasing gas from P in month 3 given
that the customer traded with P in month1 =0.36+0.08=0.44
– The probability of a customer’s purchasing gas from N in month 3 given that the customer traded with N in month1 =0.24+0.32=0.56
• Use the following decision tree 1– Given that N is the starting state in month1, the probability of a
customer’s purchasing gas from N in month3: 0.08+0.64=0.72
– Given that N is the starting state in month1, the probability of a customer’s purchasing gas from P in month3: 0.12+0.16=0.28
![Page 6: Markov Analysis](https://reader035.fdocuments.in/reader035/viewer/2022081813/56812ad0550346895d8eaddc/html5/thumbnails/6.jpg)
Month 3-Result
Month 3
This month P N
P 0.44 0.56N 0.28 0.72
• Easy for month 3, but not for month 10 or 15• Follow the notes in class