A constant speed is assumed, making each vehicle to
traverse 1 block of the city every time unit, while con-
suming 1 unit of its battery capacity (w.l.o.g., 60km/h
constant speed and 60kWh constant consumption).
Both EVs have a battery capacity of 10kWh and room
for 5 passengers. Whereas EV
1
is released at the start
of the simulation (time unit 0), EV
2
is released when
its battery capacity is generated by SEC
1
(i.e., given
the constant energy generation of 2kWh per time unit,
the vehicle is generated at time unit 5). If SE C
1
had
had more vehicles in S
E
, they would have been re-
leased (in order) at time units 10, 15, and so on.
E ≡ {(SEC
1
, EV
1
, 0, 10, 5), (SEC
1
, EV
2
, 5, 10, 5)}
The city receives 3 TPs, with ids T P
1
, T P
2
and TV
3
.
T P
1
is announced at time unit 0, to pick-up the pas-
senger at location (2,3) between time units 0 and 4,
and to drop-off at location (0,0) between time units 5
and 7. T P
2
is announced at time unit 2, to pick-up the
passenger at location (2,2) between time units 3 and
4, and to drop-off at location (1,1) between time units
5 and 6. T P
3
is announced at time unit 6, to pick-up
the passenger at location (2,3) between time units 6
and 7, and to drop-off at location (1,3) between time
units 7 and 9.
T ≡ {(T P
1
, (0, 2, 3, 0, 0, 0, 4, 5, 7)),
(T P
2
, (2, 2, 1, 1, 1, 3, 4, 5, 6)),
(T P
3
, (6, 2, 3, 1, 3, 6, 7, 7, 9))}
A feasible solution to this instance allocates T P
1
and
T P
2
to EV
1
, while T P
3
is not allocated.
Alloc ≡ {(T P
1
, EV
1
), (T P
2
, EV
1
), (T P
3
, −1)}
In the allocation above, the vehicles have the fol-
lowing schedules:
Sched ≡ {(EV
1
, [(0, 2, 1, 2, 2, 3, 0, 1, 10, 8, +T P
1
, 2, 2),
(2, 4, 2, 3, 2, 1, 1, 2, 8, 6, +T P
2
, 0, 2),
(4, 5, 2, 1, 1, 1, 2, 1, 6, 5, −T P
2
, 1, 1),
(5, 7, 1, 1, 0, 0, 1, 0, 5, 3, −T P
1
, 0, 2),
(7, 10, 0, 0, 1, 2, 0, 0, 3, 0, ret, 0, 3)]),
(EV
2
, [(5, 10, 1, 2, 1, 2, 0, 0, 10, 10, idle, 5, 0)]}
Figure 1 displays the route of EV
1
and EV
2
in
Sched. W.l.o.g., the coverage of the Manhattan dis-
tance between two points is assumed to be traversed
always by covering first the distance of the x-axis fol-
lowed up by the distance in the y-axis. The release of
an EV is highlighted in blue, an idle movement in grey
and an active movement by its starting point (green)
and destination one (red).
The route of EV
1
is composed of 5 movements:
1. From time unit 0 to time unit 2, it leaves the SEC
1
to serve the pick-up of T P
1
. On doing so, it goes
from (1,2) to (2,3), increases its number of pas-
sengers from 0 to 1, and reduces its battery capac-
ity from 10 to 8. As the pick-up of T P
1
must be
within time units 0 and 4 and EV
1
arrives at time
unit 2, a leeway of 2 time units is associated to the
movement, as it could have been re-scheduled by
delaying it up to 2 time units in case the vehicle
had needed any re-routing.
2. From time unit 2 to time unit 4, the vehicle serves
the pick-up of T P
2
. On doing so, it goes from
(2,3) to (2,1), increases its number of passengers
from 1 to 2, and reduces its battery capacity from
8 to 6. As the pick-up of T P
2
must be within time
units 3 and 4 and EV
1
arrives at time unit 4, a lee-
way of 0 time units is associated to the movement,
as it cannot be further delayed by any re-routing.
3. From time unit 4 to time unit 5, the vehicle serves
the drop-off of T P
2
. On doing so, it goes from
(2,1) to (1,1), decreases its number of passengers
from 2 to 1, and reduces its battery capacity from
6 to 5. As the drop-off of T P
2
must be within time
units 5 and 6 and EV
1
arrives at time unit 5, a lee-
way of 1 time unit is associated to the movement.
4. From time unit 5 to time unit 7, the vehicle serves
the drop-off of T P
1
. On doing so, it goes from
(1,1) to (0,0), decreases its number of passengers
from 1 to 0, and reduces its battery capacity from
5 to 3. As the drop-off of T P
1
must be within
time units 5 and 7 and EV
1
arrives at time unit
7, a leeway of 0 time units is associated to the
movement.
5. From time unit 7 to time unit 10, the vehicle re-
turns to SEC
1
before the end of the simulation.
On doing so, it goes from (0,0) to (1,2), stays at 0
passengers, and reduces its battery capacity from
3 to 0. As the end of the time horizon is at time
unit 10, and the vehicle arrives to SEC
1
at time
unit 10, a leeway of 0 time units is associated to
the movement.
Figure 1: S ched Outputted as Solution.
A Carbon-Neutral, Community-Based, Reactive and Scalable Ride-Sharing Service
31