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seaside
terminal
vehicle
depot
container
depot
8
15
16
24
7
r 6
(?)
23
r 6
(?)
6
22
r 6
(?)
12
5
14
21
r 4
r 5
(?)
4
20
r 5
(?)
11
r 6
(?)
r 3
3
19
10
9
r 2
2
18
r 1
1
13
17
Fig. 2. Example scenario with 6 requests, 8 containers, and 5 vehicles. Request r 5 and
r 6
are a priori incomplete.
dark gray while nodes with a need for a container are shaded light gray. The
remaining white nodes neither require nor need a container.
The trucking company has to fulfill six requests ( r 1 to r 6 ). Export requests
r 1 ,r 2 ,r 3 and import request r 4 are complete requests. Request r 5 is an incom-
plete storage request , i.e., customer node 13 offers an empty container and we
have to decide whether this empty container shall be delivered to the container
depot or to another customer that requires an empty container. Request r 6 is an
incomplete provide request , i.e., customer node 14 requires an empty container
and we have to decide whether it is provided from the container depot or from
another customer. The maximal length T max of a vehicle route is set to 600 time
units.
The model of this small scenario comprises already 29000 constraints, 6545
binary decision variables, 96 integer decision variables, and 241 continuous deci-
sion variables. Fig. 3 shows the resulting feasible vehicles routes. The first route
(black line) consists of the node sequence 15 , 11 , 3 , 9 , 1 , 16 and the second route
(dotted line) consists of the node sequence 15 , 22 , 10 , 14 , 2 , 4 , 13 , 21 , 12 , 16. First ,
a container has been selected for each request. Here, request r i has been assigned
to container i ( i =1 ,..., 6). The storage request r 5 has been completed by de-
termining node 21 as sink of the flow of container 5. The provide request r 6 has
been completed by choosing node 22 as source, i.e., container 6 is selected as
start node of request r 6 . Second , the flow through the network has been deter-
mined for each container. Third , feasible routes are setup for the two trucks by
assigning containers to vehicles.
 
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