  We consider the tropical analogues of a particular bilevel optimization
problem studied by Dempe and Franke and suggest some methods of solving these
new tropical bilevel optimization problems. In particular, it is found that the
algorithm developed by Dempe and Franke can be formulated and its validity can
be proved in a more general setting, which includes the tropical bilevel
optimization problems in question. We also show how the feasible set can be
decomposed into a finite number of tropical polyhedra, to which the tropical
linear programming solvers can be applied.
