In order to avoid infeasibility when breaking and reorga
nizing the groups, one can solve (3) after each modification.
For efficiency, we have found that it was sufficient to apply
both operators until either there was no change in the groups
or the groups resulted in an infeasible schedule.
input:
A subset of groups
G
t
∈ G
output:
A fragmented set
H
t
with same passengers
1
Set
H
t
←
G
t
2
foreach
g
∈
G
t
do
3
if

H
t

<
C
& MGWT
(
g, g
(1)
)
>
MPWT
(
g
(1)
)
then
4
for
i
←
2
, . . . ,

g

do
5
if
MPWT
(
g
(
i
)
)
>
MPWT
(
g
(1)
)
then
6
Set
g
0
← {
g
(1)
, . . . , g
(
i

1)
}
7
Set
g
00
← {
g
(
i
)
, . . . , g
(

g

)
}
8
Set
H
t
←
(
H
t
\ {
g
}
)
∪ {
g
0
, g
00
}
9
break
10
end
11
end
12
if

H
t

=
C
then
13
break
14
end
15
end
16
end
Algorithm 3:
Breaks groups with copassenger delays
Experiments
We present numerical experiments in the setting of Figure 1.
The passengers originate from a set of 4 stations and desire
to reach one of the buildings in B1B10 within a specified
timewindow.
U
consists of MT services that reach
T0
ev
ery 15 minutes and the travel time between stations is 5 min
utes. We assume that the CVs are all parked at
T0
and return
back to
T0
after dropping off all passengers. The CVs take 1
minute to go between
T0
B1,
T0
B10, and all pairs of build
input:
A subset of groups
G
b
∈ G
output:
A reorganized set
H
b
with same passengers
1
Set
H
b
← ∅
,
h
←
g
b
1
2
for
i
←
2
, . . . ,

G
b

do
3
if

h

=
CV
max
then
4
Set
H
b
←
H
b
∪ {
h
}
,
h
←
g
b
i
5
end
6
if

h

< CV
max
then
7
for
j
←
1
, . . . ,
min
{
CV
max
 
h

,

g
b
i
}
do
8
Set
p
←
g
b
i
(
j
)
9
if
rel
(
p
)
≤
ded
(
h
(1)
)
&
MGWT
(
h
∪ {
p
}
, h
(1)
)
=
MGWT
(
h, h
(1)
)
then
10
Set
h
←
h
∪ {
p
}
11
end
12
end
13
h
0
←
g
b
i
\
h
14
if

h
0

>
0
then
15
Set
H
b
←
H
b
∪ {
h
}
,
h
←
h
0
16
end
17
end
18
end
19
H
b
←
H
b
∪ {
h
}
Algorithm 4:
Reorganizes passenger groups
ings that are adjacent on the shaded track, except for B5B6
which takes 2 minutes. The CVs are restricted to move along
the shaded region shown in Figure 1. We also assume that a
CV spends 0.5 minutes at a building where they drop passen
gers. As a result, the time that a passenger reaches the des
tination depends on copassengers in the CV that have prior
destinations. The modeling of dropoff time is important in
applications where the capacity of
CV
max
is small, typi
cally
≤
5
. Inspired by the application to corporatecampus
settings, we use a small number of destinations. This may
not be the case in all applications, where one might expect
the number of destinations for the LMT service to be in the
same order as the number of passengers, thus making the
problem harder to solve. In those cases, however, we believe
that the suggestion by Mah´eo, Kilby, and Hentenryck (2018)
to treat lastmile stops as aggregations of several passenger
destinations, such as bus stops, is a reasonable compromise.
Hence, the chosen number of destinations is of minor impor
tance.
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 Fall '14
 Rapid transit, travel time, Time of arrival