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2. Markov Analysis and it’s
Applications

3. CONTENTS
 MARKOV PROCESS
 MARKOV CHAIN
 EXAMPLES
 APPLICATIONS
 ADVANTAGES
 LIMITATIONS

4. MARKOV PROCESS
A Markov analysis looks at a sequence of events, and
analyzes the tendency of one event to be followed by
another. Using this analysis, you can generate a new
sequence of random but related events, which will
look similar to the original.

5. MARKOV CHAIN
 A Markov system (or Markov process or Markov
chain) is a system that can be in one of several
(numbered) states, and can pass from one state to
another each time step according to fixed
probabilities. If a Markov system is in state i, there is
a fixed probability, pij, of it going into state j the next
time step, and pij is called a transition probability

6. MARKOV CHAIN
 A Markov process is useful for analyzing dependent
random events -that is, events whose likelihood depends
on what happened last. It would NOT be a good way to
model a coin flip, for example, since every time you toss
the coin, it has no memory of what happened before. The
sequence of heads and tails are not inter-related. They
are independent events.
 But many random events are affected by what happened
before. For example, yesterday's weather does have an
influence on what today's weather is. They are not
independent events

7. EXAMPLE
 Markov Analysis In an industry with 3 firms we
could look at the market share of each firm at any
time and the shares have to add up to 100%. If we
had information about how customers might change
from one firm to the next then we could predict
future market shares. This is just one example of
Markov Analysis. In general we use current
probabilities and transitional information to figure
future probabilities.

8. PROBLEM
 A petrol station owner is considering the effect on his business
of a new petrol station (at Goaves)
Currently (of the total market shared between Shahapur and
Goaves) Shahapur has 80% of the market and Goaves has
20%
Analysis over the last week has indicated the following
probabilities for customers switching the station they stop at
each week:
Shahapur Goaves
Shahapur 0.75 0.25
Goaves 0.55 0.45
 What will be the expected market share for Shahapur and
Goaves after another two weeks have passed?
 would be the long-run prediction for the expected market
share for Shahapur and Goaves?

9. STATE DIAGRAM

10. SOLUTION
 Letting
 state 1 = Shahapur
 state 2 = Goaves
 we have the initial system state s1 given by s1 = [0.80, 0.20] and the transition
matrix P given by
 P = 0.75 0.25
0.55 0.45
Hence after one week has elapsed the state of the system s2 = s1P = [0.71, 0.29]
so after two weeks have elapsed the state of the system = s3 = s2P = [0.692, 0.308]
and note here that the elements of s2 and s3 add to one (as required).
Hence the market shares after two weeks have elapsed are 69.2% and 30.8% for
Shahapur and Goaves respectively.
Assuming that in the long-run the system reaches an equilibrium [x1, x2] where [x1,
x2] = [x1, x2]P and x1 + x2 = 1
we have that x1 = 0.75x1 + 0.55x2 (1)
x2 = 0.25x1 + 0.45x2 (2) and
x1 + x2 = 1 (3)

11.  From (3) we have that x2 = 1-x1
so substituting into (1) we get
x1 = 0.75x1 + 0.55(1-x1)
i.e. (1-0.75+0.55)x1 = 0.55
i.e. x1 = 0.55/0.80 = 0.6875
 Hence x2 = 1-x1 = 1-0.6875 = 0.3125
 Note that as a check we have that these values for x1
and x2 satisfy equations (1) - (3) (to within rounding
errors).
 Hence the long-run market shares are 68.75% and
31.25% for Shahapur and Goaves respectively.

12. Markov Chain Analysis Applied To FMCG
Product

13.  QUESTION - Given these conditions about brand
switching, assuming no further entry or exit and
given further that the market share for these three
brands for the Month March is 30%,45%,25% for
Good Day, Monaco, Marie respectively. Determine :
1) What would be the market share of these three
brands in May (Short Run)?

14. GD MO MA
P = GD 0.60 0.30 0.10 (Transition matrix)
MO 0.20 0.50 0.30
MA 0.15 0.05 0.80
 P(0) = | 0.30 0.45 0.25 | (Initial state)
P(2) = p(o) * p2
P(2) = | 0.30 0.45 0.25 | * 0.60 0.30 0.10 2
0.20 0.50 0.30
0.15 0.05 0.80
 P(2) = | 0.30475 0.27425 0.42100 |
 The market shares of three brands Good day, Monaco and Marie are
expected to be 30.47 %, 27.42%, and 42.10% respectively in May.

15. APPLICATION OF MARKOV CHAIN
 Frequently used to describe consumer behavior
 Used for forecasting long term market share in an
oligopolistic market
 Brand loyalty and consumer behavior in the same
can be analyzed
 Useful in prediction of brand switching and their
effect on individual’s market share
 Sales forecasting

16. ADVANTAGES
 Markov models are relatively easy to derive (or infer) from
successional data
 Does not require deep insight into the mechanisms of dynamic
change
 Can help to indicate areas where deep study would be valuable
and hence act as both a guide and stimulator to further
research
 Transition matrix summarizes all the essential parameters of
dynamic change
 The results of the analysis are readily adaptable to graphical
presentation and hence easily understood by resource
managers and decision-makers
 The computational requirements are modest and can easily be
met by small computers or for small numbers of states by
simple calculators

17. LIMITATIONS
 Customers do not always buy products in certain
intervals and they do not always buy the same
amount of a certain product
 Two or more brands may be bought at the same time
 Customers always enter and leave markets, and
therefore markets are never stable
 The transition probabilities of a customer switching
from an i brand to an j brand are not constant for all
customers

18. LIMITATIONS
 These transitional probabilities may change
according to the average time between buying
situations
 The time between different buying situations may be
a function of the last brand bought
 The other areas of the marketing environment such
as sales promotions, advertising, competition etc.
were not included in these models