Information Technology Reference
In-Depth Information
to the request weights which are also randomly generated in [0
.
7
,
1
.
3] for each
carrier in each iteration. As a result, each instance consists of three carriers and
in average 1186 requests over the entire planning horizon.
Pickup and delivery locations of requests are randomly located within a square
of size 200
150. The distance between two location nodes is the Euclidean
distance. For more than 80% of all requests, the distance between pickup and
delivery locations is in the range from 20 to 160 and the average value is about 90.
The velocity of all vehicles is assumed to be 1 so that the driving time between
two nodes equals the distance. The variable cost rate
β
k
for a distance unit is
set to 1 for all vehicles
k
×
K
. The time windows for a request
r
generated in
iteration
it
are defined in the following way. Let
r
+
and
r
−
represent the pickup
and delivery locations of request
r
. For the first iteration (
it
=1),
a
r
+
is given
a random value in [
τ/
3
,τ
]. In the following iterations,
a
r
+
is set to a random
value in range (
τ
∈
(
it
+1)].
b
r
+
is given by adding
a
r
+
with a time window
width, which is determined as
τ/
2
·
it,τ
·
30%. The time window for the delivery
location [
a
r
−
,b
r
−
] is simply defined as [
a
r
+
+
d
r
+
r
−
+
s
r
+
,b
r
+
+
d
r
+
r
−
+
s
r
+
],
while
d
r
+
r
−
is the driving time from
r
+
to
r
−
and
s
r
+
is the service time at
r
+
.
All operations are assigned the same service time of 10. Since the execution of
some requests generated in the last iteration
it
= 30 may be finished later, the
entire planning horizon of our instances is [0
,
3300].
Since requests are allowed to be transferred to common carriers, the price
for outsourcing requests must also be specified. This cost
γ
r
for a request
r
is
calculated as
γ
r
=
ϕd
r
θ
d
r
,where
ϕ
is a constant cost rate per distance unit
and set to 2, and
d
r
is the adjusted travel distance between pickup and delivery
locations and defined as
d
r
=max
±
. The motivation to use the adjusted
travel distance is that the common carriers charge a fixed minimum fee for each
request if the distance to travel lies below a specific level.
θ
is a parameter which
is set to 0.9986.
θ
d
r
can be seen as a distance-dependent discount on the cost rate
per distance unit. Through introducing
θ
, the fact that in practice freight rates
reduce with increasing transportation length can be captured in our instances.
Each carrier is assigned a vehicle fleet. The number of vehicles is determined
as the average request number per planning period with a deviation of up to
±
{
5
,d
r
+
r
−
}
30%. Vehicles are located at randomly generated start locations with empty
load at the very beginning
t
0
. The average number of vehicles per carrier in an
instance is 13.3, while the specific numbers are varying from 9 to 17.
The second step is to assign each request
r
a release time
t
rl
r
to make a static
instance to a dynamic one.
δ
1
% of all requests are given a release time of (
a
r
+
−
3
τ
),
δ
2
%of(
a
r
+
−
τ
). Negative values are set to zero since
we start our simulation at
t
0
= 0. Through changing the values of
δ
, the degree
of dynamism of a single instance can be varied. Using the ten static instances,
three sets of DCTPP instances are generated. They have different degrees of
dynamism: high dynamism (HD), middle dynamism (MD), and low dynamism
(LD). The parameter triple (
δ
1
,δ
2
,δ
3
) is fixed for set HD to (10
,
10
,
80), for MD
to (10
,
80
,
10), and for LD to (80
,
10
,
10).
2
τ
), and
δ
3
%of(
a
r
+
−
