  This paper is a follow-up to a previous work where we defined and generated
the set of all possible compromises of multilevel multiobjective linear
programming problems (ML-MOLPP). In this paper, we introduce a new algorithm to
solve ML-MOLPP in which the adaptive method of linear programming is nested.
First, we start by generating the set of all possible compromises (set of all
non-dominated solutions). After that, an algorithm based on the adaptive method
of linear programming is developed to select the best compromise among all the
possible compromises achieved. This method will allow us to transform the
initial multilevel problem into an ML-MOLPP with bounded variables. Then, apply
the adaptive method which is the most efficient to solve all the multiobjective
linear programming problems involved in the resolution process instead of the
simplex method (It should be noted that the adaptive method is more efficient
than the simplex method). Finally, all the construction stages are carefully
checked and illustrated with a numerical example.
