Information Technology Reference
In-Depth Information
5.2 Simulation Study
Both scenarios IP and CTP are simulated in our computational study. An impor-
tant issue in our simulation is the specification of due requests. In our simulation,
a known request is declared in the planning procedure for planning period
p
+1
at
t
=
pτ
as a due request if the service at its pickup location must be started be-
fore (
p
+1
.
25)
τ
. For the very last period, all requests are labeled as due requests.
We consider both strategies MY and FL as well as each degree of dynamism for
the planning scenarios IP and CTP. As a result, four settings are defined: (IP,
MY), (IP, FL), (CTP, MY), and (CTP, FL). While using the FL strategy, the
potential outsourcing costs are adjusted by a weight smaller than 1. Non-due
requests with (
p
+1
.
25)
τ<b
r
+
≤
(
p
+2)
τ
are multiplied with a weight factor
of 0.75, while the remaining non-due requests with
b
r
+
>
(
p
+2)
τ
are multiplied
with 0
.
75
2
0
.
56.
An adaptive large neighborhood search heuristic (ALNS) which has been de-
veloped based on the ALNS heuristic proposed for the PDP with time windows
in [22] is used to solve the routing problems in the
initial route generation
and
iterative route generation
. A more detailed description of this heuristic can be
found in [31]. Both the linear relaxation of the SPP-based and the SCP-based
WDP are solved by CPLEX. The time limit for each static CTP is set to 6.5
min. This time limit is meant to synchronize the decentralized process since in
most situations, the total computational time used is much less than this limit.
For each instance and simulation setting, we run the simulation three times
and the average costs per instance are calculated. These average costs of all ten
instances in each set are given in Table 1. For each set, the total costs
TC
,the
total route costs
TC
R
, the total costs of subcontracting requests
TC
C
,andthe
total number of outsourced requests are given.
≈
Tabl e 1.
Results of simulation
HD MD LD
TC TC
R
TC
C
n
C
TC TC
R
TC
C
n
C
TC TC
R
TC
C
n
C
IP,MY 156375 86613 69762 541 156287 86185 70102 545 156262 86532 69730 543
IP,FL 156290 86068 70222 544 155767 84613 71154 554 155767 84196 71571 558
CTP,MY 146197 94967 51230 434 146137 94806 51331 436 146120 95134 50986 433
CTP,FL 146134 94412 51722 441 145805 93193 52612 455 145791 92966 52825 456
CTP obviously outperforms IP for both MY and FL and all instances. The cost
reductions realized by CTP roughly amount to 6.5%. On the other hand, carriers
can reduce costs by planning in a forward-looking way. However, compared with
CTP, the benefits of FL are rather ignorable. It can be concluded that it is a
much more promising strategy to perform CTP than trying to improve the own
planning individually. The reason can be derived from a comparison of
TC
R
,
TC
C
,and
n
C
between IP and CTP. The costs of routes and the number of
requests planned in routes of CTP is significantly higher than for IP, while the
total costs
TC
are smaller. This indicates that the routes constructed in CTP are
obviously more ecient and the decisions on outsourcing are made in a better
