Markov Analysis Overview A probabilistic decision analysis Does
Markov Analysis
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
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 Month This month P N P 0. 6 0. 4 N 0. 8 0. 2
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
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 month 1 =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 month 1 =0. 24+0. 32=0. 56 • Use the following decision tree 1 – Given that N is the starting state in month 1, the probability of a customer’s purchasing gas from N in month 3: 0. 08+0. 64=0. 72 – Given that N is the starting state in month 1, the probability of a customer’s purchasing gas from P in month 3: 0. 12+0. 16=0. 28
Month 3 -Result Month 3 This month P N P 0. 44 0. 56 N 0. 28 0. 72 • Easy for month 3, but not for month 10 or 15 • Follow the notes in class
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