Introductory Case on How to Solve Markov Chain.

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Unit No.3.
DECISION SCIENCE
Presented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Dean, EDP & Associate Professor MBA
1
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in

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302-DECISION SCIENCE
Unit No.3 Marko Chain & Simulation
3.1.2 Introductory Case: Markov
Chain
Presented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Dean EDP & Associate Professor MBA
2
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in

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MARKOV CHAIN & SIMULATION
 At the End of the Session Student will be able to
understand-
A. Introductory Case: Markov Chain

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MARKOV CHAIN
Consider the case where the present market shares of three
brands of soft drinks A, B and C are 60%, 30% and 10%
respectively. Also, let their transition probability matrix (on
the basis of the shifting pattern for a year) be-
P =
A B C
A 0.7 0.2 0.1
B 0.2 0.6 0.2
C 0.1 0.1 0.8

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MARKOV CHAIN
Here we have, for the present year (n=0)
R0 = 0.6 0.3 0.1 - Initial Condition
Hence, their market share after 1 year i.e. for n=1 is
R1 = R0 * P
0.7 0.2 0.1
R1 = 0.6 0.3 0.1 * 0.2 0.6 0.2
0.1 0.1 0.8
R1 = 0.42+0.06+0.01 0.12+0.18+0.01 0.06+0.06+0.08
R1 = 0.49 0.31 0.20

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MARKOV CHAIN
The market share of A, B and C in the next year will be 49%,
31% & 20% respectively.
Similarly, market share after 2 years i.e. for n=2 will be-
R2 = R1 * P
0.7 0.2 0.1
R2 = 0.49 0.31 0.2 * 0.2 0.6 0.2
0.1 0.1 0.8
R2 = 0.425 0.304 0.271

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MARKOV CHAIN
Alternatively, we know that-
R2 = R0 * P2
0.7 0.2 0.1 0.7 0.2 0.1
P2 = 0.2 0.6 0.2 * 0.2 0.6 0.2
0.1 0.1 0.8 0.1 0.1 0.8
0.54 0.27 0.19
P2 = 0.28 0.42 0.30
0.17 0.16 0.67

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MARKOV CHAIN
Hence, R2 will be-
i.e. for n=2 will be-
R2 = R0 * P2
0.54 0.27 0.19
R2 = 0.6 0.3 0.1 * 0.28 0.42 0.30
0.17 0.16 0.67
R2 = 0.425 0.304 0.271

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EXERCISE
 Solve the Explanatory Case of Markov Chain in the
Notebook as a practice Exercise.

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For More Details Contact
Dr. V M Tidake
tidkevishal@gmail.com
tidkevishalmba@sanjivani.org.in

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Thank You