Table 1.
Optimal traffic volume.
Table 2.
Traffic volume allocation based on priority encoding rules.
Fig 1.
Closed-loop supply chain network structure.
Table 3.
Definition of mathematical symbols.
Fig 2.
Solution flowchart of the migrating birds optimization algorithms based on product source coding.
Table 4.
Characteristics of numerical examples considered in this study.
Table 5.
Range of parameters in this study.
Table 6.
Objective function values and CPU times of the considered solution approaches.
Table 7.
Objective function values and CPU times of the considered solution approaches.
Table 8.
Optimal transportation volumes from factories to distribution centers in example 1.
Fig 3.
Convergence patterns of PSMBO and GA for example 4.
Table 9.
Related data for the considered facilities in example 1.
Table 10.
Relevant data for the considered consumer areas.
Table 11.
Location schemes and objective function values for different values of the confidence level.
Fig 4.
Changes in the target objective function for different confidence levels.