hello, I'm a beginner and I just started my thesis, I'm working on a biobjective optimization ( cost +environmental impact) for a distribution network. I managed to model the objective functions but in order to run an optimization with ILOG CPLEX I need your help. in my mathematical model I'm proposing two transport modes with two different costs, how can I process it in ILOG CPLEX ? all I find is tutorials for a network with one cost for transportation? anyone can help and thank you in advance ( excuse my english) asked 15 Mar '16, 11:59 hajardeq 
CPLEX is a single objective solver. If you want to solve biobjective problems using CPLEX you need to implement a custom solver. Two popular choices for biobjective problems are the \(\varepsilon\)constraint method and twophase methods. answered 15 Mar '16, 14:49 Sune You can take a look at this stuff: https://github.com/SuneGadegaard/TwoPhaseMethod . I do not guarantee (but I hope) that it is bugfree! It is a simple straightforward implementation of a twophase method that use CPLEX to solve the subproblems arising. It should work for minimization problems.
(16 Mar '16, 05:59)
Sune

I'm not sure I understand your question correctly, but if you are asking what I think you are asking, just create two sets of transportation variables, one for each mode, with different costs. Anywhere you would have used a single transportation variable (e.g., the volume of A moved from B to C), you now use a sum of two variables (volume of A moved B to C using mode 1 PLUS volume of A moved B to C using mode 2). answered 21 Mar '16, 15:38 Paul Rubin ♦♦ 