Page 31 - IMDR JOURNAL 2020-21

IMDR’s Journal of Management Development and Research 2020-21

= 75% of A + 50% of ( 6400-A ) = 4266 approx.
A B Thus B=6400-A=6400-4266= 2134
The results obtained are nearly close to those
3200 3200 obtained in method 1 described above.
X 3. Finding probability that B will have a share in
A B the market.
75% 25% Let us assume that share of B is 1 and no share
50% 50% for A.
= [ 0 1 ] X [ 75% 25% ] [ 75% 25% ] [ 75% 25% ]
A B 50% 50% 50% 50% 50% 50%
4000 2400 = [ 0.65625 .34375 ]
Thus the probability that supplier B will have a
share is 34.37%. Obliviously the probability of A
The multiplication of Consumer matrix by would be 65.63.
Transition matrix given a consumer matrix having It can be realized from the above example how
different share of suppliers A and B i.e. [4000, 2400] Markov Chains are simple but quite effective.
in place of our initial assumption of [3200 3200] However, the things become more complex
market share. This is the first iteration. In a second when the number of fields involved are more. For
iteration, the newly obtained Consumer matrix is instance more number of markets, large number of
multiplied by the Transition matrix as shown below. consumers, large number of suppliers and variety of
products would complicate the issue. Under these
A B circumstances, it would be difficult to form model,
4000 2400 create matrices, perform computations and analyze
X the results obtained. This problem can be tackled
A B by new technologies such as Python Programming,
Data Science and Cloud Computing. This paper
75% 25% presents the Python programming based approach
50% 50% to handle complexity and implement Markov Chin
= technique.
A B III ALGORITHM FOR MARKOV CHAIN
4200 2200 IMPLEMENTATION
An algorithm is a step by step method of solving
In second iteration A = 4200 and B=2200 are a problem. Like flowchart, algorithm is common
obtained as worked out above. In third iteration for all programming languages. The algorithm for
share of A and B is found out in a similar manner. Markov Chain analysis is illustrated below.
The procedure is continued till the constant values At first, the consumer matrix [C] is created from
of A and B are obtained. If the Consumer matrix is data available to us. The total number of consumers
multiplied by Transition matrix as a third iteration, attending the market for purchasing a product
the constant values of A and B are obtained. This
is called convergence. Thus in this example, the
convergence is obtained at second iteration. In case
the convergence is not obtained despite undergoing
number of iterations, the situation is called
divergence.
2. Finding share of suppliers A and B out of 6400
consumers using algebraic expression .
Let A and B are the shares of products A and B
respectively . Then the following expression can be are given. These are bifurcated into suppliers A
formed :- and B. Initially it is assumed that equal number of
A = 75% of A + 50% of B consumers are corresponding to suppliers A and B.
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