241Rail Passenger Revenue Management Problem
other classes to c-class is correctly computed, that is, y
c′cjt
= β
c′ct
max{z
c′cjt
− x
c′jt
, 0}.
Specically, if v
c′cjt
= 0, y
c′cjt
has to be 0; otherwise y
c′cjt
= β
c′ct
(z
c′jt
− x
c′jt
). Here, the
smallest value of M
c′cjt
can be computed as follows.
Mn dn
ccjt ccct cttcjt c
t
t
′′ ′′ ′′ ′
′
−
∑
=, 0,
=0
minmaxβα
∀∈ ∀
′
∈∀∈∀∈cCcCcjJtT,{}, ,\ .
(9.9)
Here α
c′t′t
is the demand transaction rate from time t′ to time t for class
c′, and α
′′
cttcjt
d
computes the total accumulated demand from time 0
to time t for class c′ of journey j. Therefore,
x0,
α
′′ ′′ ′
−
cttcjt c
t
is
the maximum possible number of unsatised demand at time t if trip t is
selected in the solution. Therefore ...