Markov Chains Applications
Brand Switching Ø 100 customers currently using brand A 84 will stay with A, 9 will switch to B, 7 will switch to C Ø 100 customers currently using brand B 78 will stay with B, 14 will switch to A, 8 will switch to C Ø 100 customers currently using brand C 90 will stay with c, 4 will switch to A, 6 will switch to B
Brand Switching Ø States Brands of product Ø Time Period Interval between purchases Ø Transition Probabilities A B C 0. 84 0. 09 0. 07 P = 014 0. 78 0. 08. 0. 04 0. 06 0. 90
Brand Switching • If the current market share is given by: P ( 0) = (0. 39 0. 32 0. 29) a. What is the market share after one time period ? b. What is long term market share ?
Brand Switching Ø Assumptions ØMarkovian 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 ØStationarity Property Marketing strategies may change transition probabilities over time
Stock Market Analysis w Transition Probabilities 1 0 0 0 1 1 1 0 4 2 4 1 1 1 P= 0 4 2 4 1 1 0 0 4 2 1 0 0 0 2 0 0 0 1 4 1 2
Stock Market Analysis w Assumptions w Markovian Property w Stationarity Property
Equipment Replacement "States State 1: State 2: State 3: State 4: New Filter One year old, no repairs Two years old, no repairs Repaired once "Time Period One year "Transition Probabilities Repaired filter will be replaced after one year Filters scrapped after 3 years use
Equipment Replacement "Transition Probabilities 2 3 1 4 4 1 1 1
Equipment Replacement "Transition Probabilities 2 3 1 4 1 P= 0. 0 0. 7 0. 0 0. 3 0. 0 0. 4 0. 6 0. 5 0. 0 0. 5 10 0. 0. 4 4 1 1 1
Equipment Replacement F G. 0 0 P=G 0 G. 5 G 10. H I 0. 6 J J 0. 5 J 0. 0 J K "Steady State Probabilities 0. 0 0. 7 0. 0 0. 3 p 1 =. 5 p 3 + p 4 p 2 =. 7 p 1 p 3 =. 4 p 2 p 4 =. 3 p 1 +. 6 p 2 +. 5 p 3 0. 0 0. 4 0. 0 p 1 = 0. 352 p 2 = 0. 246 p 3 = 0. 098 p 4 = 0. 304
Equipment Replacement
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 ?
Population Mobility v. Forest consists of 4 major species v. Aspen v. Birch v. Oak v. Maple A B O M A • P= . 05. 08. 03. 84 B . 00. 80. 20 O . 00. 08. 35. 53 M. 05. 00. 10. 85
Population Mobility v. States State 1: State 2: State 3: State 4: No movement Movement within region Movement out of a region Movements into a region v. Time period v. Transition Probabilities
Population Mobility v. States: Movement at SDSM&T 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. ) v. Time period Semester v. Transition Probabilities
Population Mobility v. States: Movement at SDSM&T 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. ) v. Time period Semester v. Transition Probabilities 0. 85 0. 3 P= 0. 0 0. 20 0. 05 0. 4 0. 0 0. 70 010. 0. 3 0. 9 01. 0. 0 01. 0. 0
Скачать презентацию Markov Chains Applications Brand Switching Ø 100
c1c84871d770376134847d520d962ed0.ppt