A Reinforcement Learning Approach to Airline Seat Allocation for ...

53 downloads 116194 Views 383KB Size Report
Jun 11, 2000 - proposed a simple adaptive approach which solves the L ittlewood 's equation .... a new customer arrives to the system requesting a ticket, 2) a ...
  

       !#" $ %& ('&) * +  %'&', -+., / 0 / 21 3'4.56'5 78 :9'!;[N)10-#&9$.68%w*-#'1#[d68*-#9:%_94
[d6EB>6m[q) %d685&*aBs#&%/*aPQ9?PZ6EBg@ š .J#0-)1'1*-5&B #%z*=,()~#@ W)†*=0-94#&*v64%(.U.() @A*=#%(68*=#&9:% )1P –^640-2:#&%d645w"g)E68* )1L:)1%w3()l©S!9g.() 5 I 0-) @C3(5&*-@©#&% 6rJƒ$)1.+}w3d64%G*=#\*aB?94‰†‘Ž4‹g˜ ¢ ™ [d640-64SU)†*=)10-@ nK"$)1'1*=#&9:%

H ' 9:%G*68#%(@f@-9:S!)+'19:%(' 5&3(.(#&%(2~0C) SU640-Vw@W68%(.b64%b64' '19:3(%G*

94 . + ,, "#%#$#$ 

˜" $# !

;~64%(.  9  š   ; C94#%G*X[(0C9$'1) @-@+i  Kl  9$i Ql š

š 

-.,+"#$#$#% ™

 !

þ

i l P,(#&',US!)E64%J@*=,d68*¦*-,()X[(0-9g' )1@-@Ki  Kl“#@¦6 –;640CV49L>0-)1%()1PQ645d[(0C9$'1) @-@1npX,() %!*=,().()1' #&@-#94%![J0-9g' ) @C@ 64@C@-9g' #76t*=) .mP#\*=,Ui  Kl¥#@6X@-)1SU# hA–;640CV49Lm.()1' #&@-#94%m[(0-9g' )1@-@ I 64%(.(

#@6f–;640CV49Lm',d64#&%?3(%(.()10-5&Bg#&%(2

*=,J)+–^640-V89RL0C) %()†PZ685[J0-9g' ) @C@ n pX,()U[(0-9g' )1@-@+*-,d68* *=0=68'Vg@_)1L4) 0CBz@C*=68*=)U',d64%(24)iY#&%(' 5&3(.(#&%(2' 3(@A*=9:S!) 0 0-)1}g3J) @C* I 'E64%J' ) 5&5768*-#9:% I 68%(. …d#&2:,G*.() [(640C*-3(0-)El~#@]0C)1%()†ƒg*?.()1' #&@-#94%$haSU64Vw#%(2~@C*6t*=)/) %J' 9:3(%G*-) 0-)1.€MGB;*-,()>@CBg@C*-) S #@ % n)†*.1i8  %gl .()1%(94*=)f*=,()K*-#S!)f@C[N)1%G*#%~*-,(#@u*=0=68%(@-#\*=#94%U

)1}g3(68*=#&9:%€ik¢:l I ) }w3d68*-#9:%zi :lQ'E64%TMN)mP0C#&*-*-) %T64@ š





~i -8gl*  ;i8  %gl ˜ ( i -8  %gl



}w3d68*=#&9:%

.1i -8  %gl¬S~ 6tƒ  Ui % †l ™ '

i l+) @A*=#SU68*-)+i`)†ƒ$[(564#%()1.





Mq) 59Pfl9464%b6452:940-#&*-,(S

*=,(68*KPv)s,d6EL:)/%(64SU)1.

*=,J) .J)1*68#5@Q94L46853()1@ 98< 645&2:9:0-#\*=,(S!@Q' 64%TMN)m2:)1%() 0-68*=)1. n

'

I 6P,(9:5&)>&

. &+*!,  i 8  # -l

   

5 !ti Tl I

5!Ri # l#@u6 *-,()K5&)E640C%(#%(2

P,()10-)

0=68*-)4n



5&@-) I

%) #   % `n

"g)1*

 ¡ l_)15) S!) %G*-@#&%T6455¥*-,()?@-)†*=@ "    €64%(. # #

iY.dlef.(.^*-,()Ui

 #   

iY)El’”
@A*68*-) Rl I

5 

*=,()1%T) S![J*aB@-)†*=@1n

5&@-) I

@C)1*

@C)1*

~i 458 4El '

P,J) 0-)?*=,J) ;J*=,*=) S![q9:0=645N.(#&xN) 0C) %('1) <
3(@-)1.z*=,J0-9:3(24,(9:3J*?9:3J0m)†ƒ$[N)10-#&SU)1%w*-@ 640-)>64@mMq)m*=,() 0-)1' 3(0C0-) %G*f@C*=68*=)0_S!) %G*=#&9:%()1.T#&%^"$) '†*=#94%^Ÿ(n ;#&@X@-)1**=9 *=,() m  hŠL46853()1@9:3J*-[(3J* 576EB:)10m' 9:%G*=64#%(@W*-,()>9:3J*-[(3J* %(9g.()4n/pX,()>9:3$*=[(3J*?%J9$.()>#&%9:3(0m'E68@-)!#@W*=,J)

Wh”L86453J)Q64%J.+*=,()Q#%([(3$*“%(9g.()1@.()

%J94*=)u*=,()QL8640C#764MJ5) @3(@C) .s*=9f.()1r(%()Z*=,()v@C*=68*=)oha@-[(64' )8n W3(0“%()13(0-94%(@

,d6EL:)m*aPv9U#&%([(3J*%J9$.()1@X)E64',jiY@C) ) c“#&2:3(0-) ¡ l†n W%()?%(9g.()m#@v*=,()?M(#64@Z3(%(#\*XP,(#',#&@645&PQ6EB$@Z*-3(0-%J) . 9:%z64%(.O,d64@_64%O#%([(3$*_98
#%([J3J*?#@W%J9:0-SU645#&| )1.bMN)†*aPQ)1) %j£T68%(.

n+ª

,()1% I 64@?6

.() '1#@-#&9:%$h”S~64Vw#&%(2s@C*=68*=) I *=,() m  hŠL86453()W%()†P

*=,J)64'1*-#9:%j*=64V4)1%#&%j*=,J)9:5.€.J) ' #&@-#&9:%$haSU64Vw#%J2;@C*=68*=),(64@s*=9Mq)3([q.d68*=)1. nOpX,()%()1*>@A*=9:0C) @/*=,J)

Wh”L86453J)+*-,()?@CBg@C*-) S

¡ 

i



l

@



pX,()?[(0C9:Md64MJ#5#\*aB~98i ¡ l

þ

)†ƒ$[q) 0C#S!) %G*_PQ64@s'19:%(.(3J'1*=)1.jP#&*-,€6T@-#%J2:5)>0-)1[(5#&'E68*-#9:%¥n]’”*+0C) }w3(#&0-) @+6T*-94*645¦94
64%  O6452:940-#&*-,(STn“–T9:@C*0C)E645q5#\'E64%('1) 5&5768*-#9:%(@©PQ)10-)' 9:%J@-#.J) 0-)1.>#%s*=,J)S!9g.() 5g*=,()10-) MGB/SU64Vw#%J2

*=,J)S!9g.() 5J6?'159:@C)0-) [J0-) @C) %G*6t*=#&L4)f98*-,(#@¦680-)E6$neK%~"(–



S!9$.()15N,J#%(2:)1@Z9:%6>–;680-V49Lg#768%64@-@C3(SU[$*=#94% npX,()m3(@C)m94' 5&)E640C5&B]6>*-9:[(#'W5)E680-%(#&%(2 I 6@-3(0AL:)1B4n

n

2† 

' 9:%G*-0-9:5f94