Markov chain analysis

This PPT is made by collecting information from various slides made previously by others.

1. GKV HARIDWAR FACULTY OF MANAGEMENTSTUDIES BBA v SEMESTER Quantitative technique in management presentation By- Divyandu P andey

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

19. THANKYOU