![](bg3.png)
Table 1: The rules for opening/closing service centers.
Open Service Center Reallocated Pick-up Amount
Cases SC1 SC2 SC3 SC4 SC 1 SC 2 SC 3 SC 4
1 ○ SC2+SC3+SC4
2 ○ SC1+SC3+SC4
3 ○ SC1+SC2+SC4
4 ○ SC1+SC2+SC3
3 ALGORITHM DEVELOPMENT
The proposed solution algorithm in this study is
designed based on the work by Ferdinand et al.
(2012), in which they used integer based genetic
algorithm so that the parameters used in this study
are similar. In detail, this study develops six steps to
solve the proposed model based on the genetic
algorithm where it firstly chooses which service
centers (only single service center is opened) will be
opened/closed in each merging area, and then, in the
second step, assigns all the daily pick-up amounts to
the opened Type I service centers. The third step
decides which consolidation terminals are opened or
closed for the allocation of shipments from service
centers, and then reallocates all of service centers to
the available consolidation terminals. Finally, it
calculates the profits of each company based on
maxmin criterion. In the proposed genetic algorithm,
four genetic operators are used such as cloning,
parent selection, crossover, and mutation operators.
The parameter values for genetic algorithm are: the
population size equals to 500; the maximum number
of generations is 150; the cloning rate is set at 2%;
the crossover rate and mutation rate are 60-70% and
4-7%, respectively.
3.1 Chromosome Design
In this study, we consider four companies for
strategic alliance for which the chromosome consists
of four parts dealing with decision variables shown
in Figure 1. The first through third parts are
designed for Type I where five regions of each
company are considered, and the last part is for Type
II where ten regions are considered in each company.
In addition, each company are currently running two
consolidation terminals. In the first part, the first to
the fifth genes describe which service center will be
opened in each merging region where one service
center is allowed to be opened according on the rule
in Table 1.
The values of five genes, considering that single
service center is opened in each merging region, can
be selected from 1 to 4 based on the available cases
shown in Table 1 since there four companies. For
example, Figure 1 shows that the first five genes
have integer values such as 1, 3, 2, 4 and 1 which
means, in region 1 through region 5, company 1’s
service center is opened (SC1), while in region 2, 3,
and 4, the opened service centers are company 3’s,
company 2’s, and company’s 4 (SC3, SC2, and SC4)
respectively.
Figure 1: Chromosome representation.
The second part in Figure 1 describes which
consolidation terminals will be opened in each
region where single or two terminals are allowed to
be opened according to the rule in Table 2. The
value of five genes can be selected from 1 to 3 based
on the available cases. Case 1 and Case 2 show only
single terminal is opened, while, in Case 3, two
consolidation terminals are opened.
In Figure 1, the values of sixth through ninth
gens are randomly generated, in which the genes
have values such as 3, 1, 2, and 1. This means that
two terminals (Terminal 1 and 2) are opened in
Company 1, while in Company 2, 3, and 4 only one
terminal (Terminal 3, 6, and 7) are opened
respectively based on Table 2. The third and fourth
parts in Figure 1 show that the allocations of service
centers to consolidation terminals for the merging
and non-merging regions.
3.2 Crossover and Mutation Operators
This study applied a three-point crossover where the
first point is used to assign which service centers can
be opened; the second point is used to assign which
consolidation terminals will be available; the last
point is used for reassigning the Type I and Type II
service centers to the opened consolidation
terminals. The crossover process can be seen in
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