# need help for bi-objective optimization with ILOG CPLEX for a distribution network

 0 hello, I'm a beginner and I just started my thesis, I'm working on a bi-objective 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 11●1 accept rate: 0%

 0 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 ♦♦ 14.6k●5●13 accept rate: 19%
 1 CPLEX is a single objective solver. If you want to solve bi-objective problems using CPLEX you need to implement a custom solver. Two popular choices for bi-objective problems are the $$\varepsilon$$-constraint method and two-phase methods. answered 15 Mar '16, 14:49 Sune 958●4●14 accept rate: 20% You can take a look at this stuff: https://github.com/SuneGadegaard/TwoPhaseMethod . I do not guarantee (but I hope) that it is bug-free! It is a simple straightforward implementation of a two-phase method that use CPLEX to solve the sub-problems arising. It should work for minimization problems. (16 Mar '16, 05:59) Sune
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