1. Markov Chains Applications

2. Brand Switching 100 customers currently using brand A
84 will stay with A, 9 will switch to B, 7 will switch to C
100 customers currently using brand B
78 will stay with B, 14 will switch to A, 8 will switch to C
100 customers currently using brand C
90 will stay with c, 4 will switch to A, 6 will switch to B

3. Brand Switching States Time Period Transition Probabilities
Brands of product
Time Period
Interval between purchases
Transition Probabilities A B C P = 84 09 07 14 78 08 04 06 90 .

4. Brand Switching If the current market share is given by:
What is the market share after one time period ?
What is long term market share ? P ( ) . 39 32 29 =

5. Brand Switching Assumptions Markovian Property
Brand switching might take into consideration more than just the past brand; e.g. customer dissatisfaction with brand A led to B, marketing lead in led to C
Stationarity Property
Marketing strategies may change transition probabilities over time

6. Stock Market Analysis
Transition Probabilities 1 P = 4 2

7. Stock Market Analysis Assumptions Markovian Property
Stationarity Property

8. Equipment Replacement
States
State 1: New Filter
State 2: One year old, no repairs
State 3: Two years old, no repairs
State 4: Repaired once
Time Period
One year
Transition Probabilities
Repaired filter will be replaced after one year
Filters scrapped after 3 years use

9. Equipment Replacement
Transition Probabilities 1 3 2 4

10. Equipment Replacement
Transition Probabilities 1 3 2 4 P = 7 3 4 6 5 1 .

11. Equipment Replacement= F H G I K J 7 3 4 6 5 1 .
Steady State Probabilities p 1 3 4 2 5 7 6 = + . p 1 2 3 4
352
246
098
304 = .

12. Equipment Replacement

13. Equipment Replacement
Suppose that the following costs apply
New Filters $ 500
Repair Filter $ 150
Scrap filters ($ 50) (scrap salvage)
For a pool of 100 filters, on average, what is the expected cost of our repair policy ?

14. Population Mobility Forest consists of 4 major species Aspen Birch Oak
Maple A B O M P = . 05 08 03 84 00 80 20 35 53 10 85 A B O M

15. Population Mobility States Time period Transition Probabilities
State 1: No movement
State 2: Movement within region
State 3: Movement out of a region
State 4: Movements into a region
Time period
Transition Probabilities

16. Population Mobility States: Movement at SDSM&T Time period
State 1: Student remains in major
State 2: Student switches major
State 3: Student leaves school (transfer out, matriculates)
State 4: Student enters school (transfer in, first year studs.)
Time period
Semester
Transition Probabilities

17. Population Mobility States: Movement at SDSM&T Time period
State 1: Student in IE
State 2: Student in other major
State 3: Student leaves school (transfer out, matriculates)
State 4: Student enters school (transfer in, first year studs.)
Time period
Semester
Transition Probabilities P = 85 05 10 3 4 9 1 20 70 .