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6 CONCLUSIONS
In this paper, we introduced a novel kind of
sustainable supply chain network design problem
with a GHG emission constraint. The problem
addressed the design of supply network arising
mainly in the public sector, where we need to satisfy
the demand for services like education and health
care locating a number of facilities. We limit the
GHG emissions generated by the facilities and the
transportation involved in servicing the customers.
The problem was formulated as a mixed integer 0-1
linear programming problem (MIP) and solved using
a genetic algorithm coded in Scilab. We conducted
an experimental study on instances of small sizes
taken from the ORLIB. In order to validate our GA
solutions we used GAMS to obtain optimal objective
values on the MIP. The genetic algorithm performs
very good considering we set a few number of
iterations. We observed that when you reduce the
total amount of GHG emissions permitted, and the
number of facilities remain free, the number of
facilities to open increase, also increasing the cost of
the solution but reducing the amount of GHG
emitted by the transportation component.
Table 1: Computational Results. First column indicates
number of problem instance; Fixed Costs in thousands; z*
is the optimal solution; z(GA) is the solution value
provided by GA.
#
Pr
Fixed
Costs
(th.)
Total
GHG
(mil.)
z* z(GA) GAP
(%)
1 25,0 10,0 1,746,347 1,775,425 1.7
2 17,5 10,0 1,727,848 1,731,842 0.2
3 12,5 10,0 1,700,236 1,700,841 <0.1
4 25,0 5,0 1,746,348 1,775,425 1.7
5 25,0 3,2 1,953,224 1,953,224 0.0
6 17,5 3,2 1,840,724 1,840,724 0.0
7 12,5 3,2 1,765,724 1,765,724 0.0
8 7,5 3,2 1,690,724 1,690,724 0.0
9 7,5 3,3 1,663,018 1,684,578 1.3
10 12,5 3,3 1,700.236 1,765,723 3.9
11 17,5 3,3 1,730,236 1,773,011 2,5
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A GENETIC ALGORITHM FOR SOLVING A PUBLIC SECTOR SUSTAINABLE SUPPLY CHAIN DESIGN
PROBLEM
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