Table 4. Open in new tab The parameters...

Notation

Definition

Set of stations, S = {1, …, i, …, |S|}, i∈S, |S| is the total number of stations on the high-speed rail line.

Set of trains, k∈K, k = 1, 2, …, |K|. |K| is the total number of trains.

Set of time periods, t∈T, t = 1, 2, …, |T|. |T| is the total number of time periods

Set of OD pairs, w∈W.

Section set between two adjacent stations, a∈A, a = 1, 2, …, |A|. |A| is the total number of sections.

C_k

Maximum seat capacity of train k.

p_ij

Ticket price of OD(i, j)∈W.

〈k, (i, j), t〉

Product, which represents train k serving passengers travelling between the OD(i, j) in the |$t$|-th time period.

q_ijt

Stochastic variable, passenger demand of OD(i, j) during the t-th time period, which follows a Poisson distribution with parameter λ_ωt.

|$q_{ijt}^k$|

Intermediate variable, passenger demand assigned to train k in the t-th time period between the OD(i, j).

M₁

Maximum number of stops.

M₂

Minimum number of stops.

N_s

Service frequency requirements at station s.

DF_s

Maximum arrival and departure capacity of station s.

Cost of one train stops at a station.

t_ij(k)

Travel time of train k between OD(i, j).

t′

Expected departure time of passengers, which is taken as the intermediate value of time period t.

|$d_s^k$|

Actual departure time of train k at station s.

θ₁

Deviation coefficient between the expected departure time and actual departure time of passengers.

θ₂

Unit time value coefficient of passenger travel time.

Parameter for the MNL model which indicates the familiarity of passengers with each product.

|$b_{ijt}^k$|

Decision variable, seats of train k allocated to product 〈k, (i, j), t〉, which represents the booking limit of product 〈k, (i, j), t〉.

x_ks

Decision variable, x_ks = 1, train k stops at station s; x_ks = 0, train k does not stop at station s.

Table 4.

Open in new tab

The parameters related to the studied problem.

Notation	Definition
S	Set of stations, S = {1, …, i, …, \|S\|}, i∈S, \|S\| is the total number of stations on the high-speed rail line.
K	Set of trains, k∈K, k = 1, 2, …, \|K\|. \|K\| is the total number of trains.
T	Set of time periods, t∈T, t = 1, 2, …, \|T\|. \|T\| is the total number of time periods
W	Set of OD pairs, w∈W.
A	Section set between two adjacent stations, a∈A, a = 1, 2, …, \|A\|. \|A\| is the total number of sections.
C_k	Maximum seat capacity of train k.
p_ij	Ticket price of OD(i, j)∈W.
〈k, (i, j), t〉	Product, which represents train k serving passengers travelling between the OD(i, j) in the \|$t$\|-th time period.
q_ijt	Stochastic variable, passenger demand of OD(i, j) during the t-th time period, which follows a Poisson distribution with parameter λ_ωt.
\|$q_{ijt}^k$\|	Intermediate variable, passenger demand assigned to train k in the t-th time period between the OD(i, j).
M₁	Maximum number of stops.
M₂	Minimum number of stops.
N_s	Service frequency requirements at station s.
DF_s	Maximum arrival and departure capacity of station s.
u	Cost of one train stops at a station.
t_ij(k)	Travel time of train k between OD(i, j).
t′	Expected departure time of passengers, which is taken as the intermediate value of time period t.
\|$d_s^k$\|	Actual departure time of train k at station s.
θ₁	Deviation coefficient between the expected departure time and actual departure time of passengers.
θ₂	Unit time value coefficient of passenger travel time.
θ	Parameter for the MNL model which indicates the familiarity of passengers with each product.
\|$b_{ijt}^k$\|	Decision variable, seats of train k allocated to product 〈k, (i, j), t〉, which represents the booking limit of product 〈k, (i, j), t〉.
x_ks	Decision variable, x_ks = 1, train k stops at station s; x_ks = 0, train k does not stop at station s.

Notation	Definition
S	Set of stations, S = {1, …, i, …, \|S\|}, i∈S, \|S\| is the total number of stations on the high-speed rail line.
K	Set of trains, k∈K, k = 1, 2, …, \|K\|. \|K\| is the total number of trains.
T	Set of time periods, t∈T, t = 1, 2, …, \|T\|. \|T\| is the total number of time periods
W	Set of OD pairs, w∈W.
A	Section set between two adjacent stations, a∈A, a = 1, 2, …, \|A\|. \|A\| is the total number of sections.
C_k	Maximum seat capacity of train k.
p_ij	Ticket price of OD(i, j)∈W.
〈k, (i, j), t〉	Product, which represents train k serving passengers travelling between the OD(i, j) in the \|$t$\|-th time period.
q_ijt	Stochastic variable, passenger demand of OD(i, j) during the t-th time period, which follows a Poisson distribution with parameter λ_ωt.
\|$q_{ijt}^k$\|	Intermediate variable, passenger demand assigned to train k in the t-th time period between the OD(i, j).
M₁	Maximum number of stops.
M₂	Minimum number of stops.
N_s	Service frequency requirements at station s.
DF_s	Maximum arrival and departure capacity of station s.
u	Cost of one train stops at a station.
t_ij(k)	Travel time of train k between OD(i, j).
t′	Expected departure time of passengers, which is taken as the intermediate value of time period t.
\|$d_s^k$\|	Actual departure time of train k at station s.
θ₁	Deviation coefficient between the expected departure time and actual departure time of passengers.
θ₂	Unit time value coefficient of passenger travel time.
θ	Parameter for the MNL model which indicates the familiarity of passengers with each product.
\|$b_{ijt}^k$\|	Decision variable, seats of train k allocated to product 〈k, (i, j), t〉, which represents the booking limit of product 〈k, (i, j), t〉.
x_ks	Decision variable, x_ks = 1, train k stops at station s; x_ks = 0, train k does not stop at station s.

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