Table 4 presents the 64 combinations of bounds considered to
optimize the economic objective in the augmented ε-constraint
method. All the CPLEX computational runs are limited to 1 h. Nine
Procedure 3
211
210
208
209
Sites assigned to pair [209-211]
x
Sites assigned to pair [208-209]
Sites assigned to pair [208-211]
Sites assigned to pair [208-210]
Sites assigned to pair [210-211]
Inter-depot routes
Fig. 11. Collection sites assigned to each pair of depots and the inter-depot routes for pair [208–211] provided by procedure 3.
70 T.R.P. Ramos et al. / Omega 48 (2014) 60–74
different solutions are obtained (S1–S9 in Table 4). Such solutions
can be visualized in Fig. 15, where it is shown that with improving
social objective (reducing the number of maximum working
hours), the economic and environmental objectives deteriorate.
For instance, to improve the social objective by 17.5%, the economic
and the environmental objectives deteriorate 10% and 9.5%,
respectively (S1 versus S8). However, the economic objective only
deteriorates 1.2% and the environmental 2.4% with an improvement
of 12.5% in the social objective (S3 versus S8). Regarding the
economic and environmental objectives, the trade-off only exists
between S8 and S9. To improve 0.7% in the environmental
objective, the economic objective deteriorates 0.3%. In the remaining
solutions, these objectives are directly proportional and in an
inverse proportion to the social objective.