Analysis of the Preference Shift of. Customer Brand Selection. and Its Matrix Structure. -Expansion to the second order lag
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1 Jourl of Compuo & Modellg vol. o. 6-9 ISS: (pr) (ole) Scepre Ld l of he Preferece Shf of Cuomer Brd Seleco d I Mr Srucure -Epo o he ecod order lg Kuhro Teu rc I ofe oerved h coumer elec he upper cl rd whe he u he e me. Suppoe h he former ug d d he curre ug d re ghered. lo uppoe h he upper rd loced upper he vrle rr. The he ro mr ecome upper rgle mr uder he uppoo h he former ug vrle re e pu d he curre ug vrle re e oupu. The good of he me rd group would compoe he Bloc Mr he ro mr. Codeg he vrle of he me rd group o oe l ecome eer o hdle d he ro of Brd Seleco c Tooh Uver. E-ml: eu@f.ooh-u.c.p rcle Ifo: Receved : ugu 8. Reved : Sepemer 9. Pulhed ole : Decemer.
2 66 l of he Preferece Shf of Cuomer Brd Seleco e el grped. I h pper equo ug ro mr ed he Bloc Mr epded o he ecod order lg d he mehod of codeg he vrle ed ove lo ppled o h ew model. Pler for produc eed o ow rd poo wheher her rd upper or lower h oher produc. Mr rucure me pole o cer h clculg coumer cve for rd eleco. Thu h propoed pproch me pole o eecue effecve mreg pl d/or elhg ew rd. Mhemc Suec Clfco: C8 Keword: rd eleco mr rucure rd poo uomole dur rd group Iroduco I ofe oerved h coumer elec he upper cl rd whe he u he e me. Focug he ro mr rucure of rd eleco her cve m e led. I he p here re m reerche ou rd eleco [-]. Bu here re few pper cocerg he l of he ro mr rucure of rd eleco. I h pper we me l of he preferece hf of cuomer rd eleco. The good of he me rd group would compoe he Bloc Mr he ro mr. Codeg he vrle of he me rd group o oe l ecome eer o hdle d
3 Kuhro Teu 67 he ro of Brd Seleco c e el grped. The we cofrm hem he queore vego for uomole purchg ce. If we c def he feure of he mr rucure of rd eleco c e uled for he mreg reg. Suppoe h he former ug d d he curre ug d re ghered. lo uppoe h he upper rd loced upper he vrle rr. The he ro mr ecome upper rgulr mr uder he uppoo h he former ug vrle re e pu d he curre ug vrle re e oupu. If he op rd were eleced from he lower rd umpg w correpodg pr he upper rgulr mr would e. Thee re verfed he umercl emple wh mple model. Pler for produc eed o ow rd poo wheher her rd upper or lower h oher produc. Mr rucure me pole o cer h clculg coumer cve for rd eleco. Thu h propoed pproch me pole o eecue effecve mreg pl d/or elhg ew rd. quve l cocerg rd eleco h ee eecued [ ]. [] emed purchg proce Mrov Tro Prol wh he pu of dverg epee. [] mde l he Brd Seleco Prol model ug logc druo. The good of he me rd group would compoe he Bloc Mr he ro mr. Codeg he vrle of he me rd group o oe
4 68 l of he Preferece Shf of Cuomer Brd Seleco l ecome eer o hdle d he ro of Brd Seleco c e el grped. I h pper equo ug ro mr ed he Bloc Mr epded o he ecod order lg d he mehod of codeg he vrle ed ove lo ppled o h ew model. Such reerch co e foud log erched. The re of he pper orged follow. Mr rucure clrfed for he eleco of rd eco. loc mr rucure led whe rd re hdled group eco. Epo of he loc mr rucure o he ecod order lg eecued eco. loc mr rucure whe codeg he vrle of he me rd group led eco. I epo o he ecod order lg ed eco 6. umercl clculo eecued eco 7. Seco 8 ummr. Brd Seleco d I Mr Srucure. Upper Shf of Brd Seleco I ofe oerved h coumer elec he upper cl rd whe he u he e me. ow uppoe h he mo upper cl rd he ecod upper rd d he lowe rd. Coumer ehvor of elecg rd would e ec. mgh e few. Suppoe h he curre ug vrle d he prevou ug vrle. Shf o eecued from or. Therefore ed he followg equo.
5 Kuhro Teu 69 Smlrl d Thee re re-wre follow. Se : () he repreeed follow. Here () R R R upper rgulr mr. To eme h geerg he followg d whch re ll coed he upper rd hf d
6 7 l of he Preferece Shf of Cuomer Brd Seleco () () prmeer c e emed ug le qure mehod. Suppoe ε () d M J T ε ε (6)  whch emed vlue of oed follow. ˆ T T (7) I he d group of he upper hf rd emed vlue  hould e upper rgulr mr. If he followg d h hve he lower hf rd re dded ol few equo () d ()  would co mue em he lower pr rgle.
7 Kuhro Teu 7. Sorg Brd Rg Re-rrgg Row I geerl d vrle m o e order. I h ce lrge d mll vlue le cered Â. Bu re-rrgg h we c e order hfg row. The lrge vlue pr re ghered upper rgulr mr d he mll vlue pr re ghered lower rgulr mr. Â Â ε ε ε Shfg row ε ε ε (8). I he ce h rd eleco hf ump I ofe oerved h ome coumer elec he mo upper cl rd from he mo lower cl rd d p elecg he mddle cl rd. e uppoe v w rd (uppoe he re ld from he upper poo o he lower poo v > w > > > ). I he ove ce he eleco hf would e v v Suppoe here o hf from o correpodg pr of he ro mr (.e. ). Smlrl f here o hf from o from o w from o form o w from o w he he mr rucure would e follow.
8 7 l of he Preferece Shf of Cuomer Brd Seleco w v w v (9) Bloc Mr rucure Brd Group e we eme he ce rd group. Mrce re compoed Bloc Mr. () Brd hf group - he ce of wo group Suppoe rd eleco hf from Coroll cl o Mr II cl cr. I h ce doe o mer whch comp cr he chooe. Thu eleco of cr re eecued group d rd hf codered o e doe from group o group. Suppoe rd group me re follow. co of p vree of good d co of q vree of good. p q () Here
9 Kuhro Teu 7 p R ( ) q R ( ) p p R p q R q q R Me oe more ep of hf he we o followg equo. () Me oe more ep of hf g he we o followg equo. () Smlrl () () Fll we ge geerled equo for -ep hf follow. () If we replce equo () we c me -ep forec. () Brd hf group - he ce of hree group Suppoe rd eleco eecued he me group or o he upper group d lo uppoe h rd poo > > ( upper poo). The rd eleco ro mr would e epreed
10 7 l of he Preferece Shf of Cuomer Brd Seleco Z Z (6) here p q Z r Here p R ( ) q R ( ) r Z R ( ) p p R p q R R p r q q R q r R R r r Thee re re-ed (7) where Z Z Herefer we hf ep doe prevou eco. I he geerl decrpo we e () (8) Here
11 Kuhro Teu 7 () () () () () () () Z From defo () (9) I he ce we o () () e he ce we o () Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α Α () I he ce equo ecome wde-pred o we epre ech Bloc Mr follow. ( ) () () ( ) () () () I he ce we o he followg equo mlrl.
12 76 l of he Preferece Shf of Cuomer Brd Seleco () () () () () () I he ce 6 we o 6 (6) (6) () e ge geerled equo for -ep hf follow. ) ( ) ( ) ( S ) ( ) ( ) ( K ) ( Α Α Α ) ( () Epreg hem mr follow.
13 Kuhro Teu 77 S ) (K ) ( Α Α Α Α Α ) ( (6) Geerlg hem o m group he re epreed ) ( () () ) ( () () m m mm m m m m (7) ) ( R ) ( R m m R ) ( R ( )( ) m m Epo of he Bloc Mr rucure o he ecod order lg Epo of he ove ed Bloc Mr model o he ecod order lg eecued he followg mehod. Here we e hree group ce. Geerg Eq.(6) d Eq.(8)we e he model follow. Here we e P. Z J H G F E D C B Α Z (8) here
14 78 l of he Preferece Shf of Cuomer Brd Seleco Z (9) Here ( ) ( ) ( ) R R Z R } { BC DEFG H J R. Thee re re-ed P () Z () J H G F E D C B P () Z () f mou of d e we c derve he followg he equo mlrl Eq.() ( ) ε P () d M J T ε ε () P whch emed vlue of P oed follow.
15 Kuhro Teu 79 T T P (6) ow we epd Eq.() o he ecod order lg model follow. ε P P (7) Here J H G F E D C B P J H G F E D C B P (8) I we e ( ) P P P (9) he P c e emed follow. T T P () e furher develop h equo follow.
16 8 l of he Preferece Shf of Cuomer Brd Seleco P ( P P ) B C B C D E F D E F G H J G H J T T T T T T T T T T T T ( ) ( ) T T T T T T ( ) ( ) T T T T T T ( ) ( ) T T T T T T T T T T T T T T T T T T
17 Kuhro Teu 8 T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T () e e h : M M M M M M K K K L L L M M M P K K K L L L Q Q Q R R R K K K L L L Q Q Q R R R Q Q Q R R R () The whe ll co of he me level hf or he upper level hf (uppoe > > Z) K K 7 K 8 L L 7 L 8 M M M R R R re ll. M M T M 7 M T M 8 M 6 T R 6 R T R 7 R T R 8 R 6 T Q T Q 7 T Q 6 8 T herefore he re ll. M M M 9 R R R 9 ecome dgol Mrce.
18 8 l of he Preferece Shf of Cuomer Brd Seleco Ug mol dgol mr P ecome follow ug he relo ed ove. K K K L L L Q K L9 Q Q P K K L L Q7 Q8 Q9 () Mr Srucure he Codeg he Vrle of he Sme Cl Suppoe he cuomer elec Ber from Coroll (Ber upper cl rd uomole h Coroll.) whe he/he u e me. I h ce here re uch rd uomole luerd Gll gm d 7 coupe for he correpodg me rd cl group wh Ber oher compe. Someoe m elec oher uomole from he me rd cl group. There lo he ce h he coumer elec oher comp uomole of he me rd cl group whe he/he u e me. Mr rucure would e he follow. Suppoe w he me rd cl group he emple of.. If here e followg hf:
19 Kuhro Teu 8 w w v v v w w w w v he ro equo epreed follow. w v w v () Epreg hee Bloc Mr form ecome follow. Α () here R R R R R w re he me cl rd group codeg hee vrle o oe d epreg w he Eq.() ecome follow.
20 8 l of he Preferece Shf of Cuomer Brd Seleco v v w w (6) fe he followg equo : ( ) (7) Codeed vero of Bloc Mr re follow where um of ech em of Bloc mr e d he re dvded he umer of vrle. (8) (9) Geerlg h ecome follow. () r r r r rr () where p p p p r r ( r)( r) R R R he he vrle of ech Bloc Mr re codeed o oe ro mr epreed follow.
21 Kuhro Teu 8 r rr r r r () here p p l l p ( ) ( ) r r () Here ( ) ) ( l P l P me he em of. Tg hee opero he vrle of he me rd cl group re codeed o oe d he ro codo mog rd cl c e grped el d clerl. Judgme whe d where o pu he ew rd ecome e d m e eecued properl. 6 Epo o he Secod Order Lg Here we e up Eq. (7) (8) (9) d epd he mehod ed eco. he he vrle of ech mr re codeed o oe ro mr epreed follow he me w ed eco. h g f e d c h g f e d c () here
22 86 l of he Preferece Shf of Cuomer Brd Seleco Here re em of ech Bloc Mr B B repecvel d re he codeed vrle of ech Bloc Mr B B. 7 umercl Emple e coder he ce h rd eleco hf o he me cl or upper cle. ove-refereced ro mr mu e upper rgulr mr. Suppoe followg eve occur. o o () L L eve L L eve () L L eve L L eve () L L eve L L eve () L L eve L L eve () L L eve L L eve (6) L L eve L M eve (7) L L eve L M eve (8) L L eve L M eve (9) L L eve L M eve
23 Kuhro Teu 87 o o () L L eve L M eve () L L eve L M eve () L L eve L M eve () L L eve L M eve () L L eve L M eve () L L eve L M eve (6) L L eve L M eve (7) L L eve L M eve (8) L L eve L M eve (9) L L eve L M eve () L L eve L M eve () M M eve M M eve () M M eve M M eve () M M eve M M eve () M M eve M M eve () M M eve M M eve (6) M M eve M M eve (7) M M eve M U eve (8) M M eve M U eve (9) M M eve M U eve () M M eve M U eve o o () M M eve M U eve () M M eve M U eve () M M eve M U eve () M M eve M U eve () M M eve M U eve (6) M M eve M U eve (7) M M eve M U eve (8) M M eve M U eve (9) M M eve M U eve () M M eve M U eve
24 88 l of he Preferece Shf of Cuomer Brd Seleco () M M eve M U eve () M M eve M U eve () M M eve M U eve () U U eve U U eve () U U eve U U eve (6) U U eve U U eve (7) U U eve U U eve (8) U U eve U U eve (9) U U eve U U eve () U U eve U U eve () U U eve U U eve () U U eve U U eve () M M eve M M eve () M M eve M M eve () M M eve M M eve (6) M M eve M M eve (7) M M eve M M eve (8) L L eve L L eve (9) L L eve L L eve (6) L L eve L L eve (6) L L eve (6) L L eve (6) L L eve (6) L M eve (6) L M eve (66) L L eve (67) L L eve (68) L L eve (69) L M eve (7) L U eve (7) L U eve (7) M M eve
25 Kuhro Teu 89 o (7) L L eve (7) M M eve (7) M M eve (76) M M eve (77) M U eve (78) M U eve (79) M U eve (8) U U eve (8) U U eve (8) U U eve (8) U U eve (8) U U eve (8) U U eve (86) U U eve (87) U U eve (88) U U eve (89) L L eve (9) M L eve Vecor Z hee ce re epreed follow. Z Z e how () d () ce for emple.
26 9 l of he Preferece Shf of Cuomer Brd Seleco () Z Z Z () Z Z Z Suug hee o equo () we o he followg emed Mr P
27 Kuhro Teu The Bloc Mrce me upper rgulr mr uppoed. e c cofrm h K K 7 K 8 L L 7 L 8 M M M M 6 M 7 M Q Q Q 6 R R R R 6 R 7 R 8 re ll. M M M 9 R R R 9 ecome dgol Mrce we hve umed.
28 9 l of he Preferece Shf of Cuomer Brd Seleco Codeg he vrle o oe ed eco 6 we o he followg equo Th fr mple oe compred wh he reul oed o fr. The vrle of he me rd cl re codeed o oe. The mr of P d P re 9 9 repecvel u he codeed vero ecome Mr. Therefore he rd ro codo mog rd cl c e grped el d clerl. 8 Cocluo I ofe oerved h coumer elec he upper cl rd whe he u he e me. Suppoe h he former ug d d he curre ug d re ghered. lo uppoe h he upper rd loced upper he vrle rr. The he ro mr ecome upper rgle mr uder he uppoo h former ug vrle re e pu d curre ug vrle re e oupu. If he op rd re eleced from he lower rd umpg w correpodg pr upper rgle mr would e. The good of he me rd group would compoe he Bloc Mr he ro mr. Codeg he vrle of he me rd group o oe l
29 Kuhro Teu 9 ecome eer o hdle d he ro of Brd Seleco c e el grped. I h pper equo ug ro mr ed he Bloc Mr epded o he ecod order lg d he mehod of codeg he vrle ed ove lo ppled o h ew model. Ule pler for produc doe o oce rd poo wheher upper or lower h oher produc mr rucure me pole o def hoe clculg coumer cve for rd eleco. Thu h propoed pproch ele o me effecve mreg pl d/or elhg ew rd. Vrou feld hould e emed herefer. Referece [] er D.. Mgeme Brd Equ Smo & Schuer US 99. [] Khr H. Mreg Scece (I Jpee) Too Uver Pre 987. [] Khr H. Sug Curre moveme of Mreg Scece (I Jpee) Opero Reerch (99) [] Thh. d T. Thh Buldg Brd Seleco Model Coderg Coumer Rol o Brd (I Jpee) Jp Idurl Mgeme oco () () -7. [] m H. Quve Reerch Cocerg dverg d Brd Shf (I Jpee) Mreg Scece Chr-Shoo Pulhg 98.
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