  We consider a decision-making problem to evaluate absolute ratings of
alternatives that are compared in pairs according to two criteria, subject to
box constraints on the ratings. The problem is formulated as the log-Chebyshev
approximation of two pairwise comparison matrices by a common consistent matrix
(a symmetrically reciprocal matrix of unit rank), to minimize the approximation
errors for both matrices simultaneously. We rearrange the approximation problem
as a constrained bi-objective optimization problem of finding a vector that
determines the approximating consistent matrix, and then represent the problem
in terms of tropical algebra. We apply methods and results of tropical
optimization to derive an analytical solution of the constrained problem. The
solution consists in introducing two new variables that describe the values of
the objective functions and allow reducing the problem to the solution of a
system of parameterized inequalities constructed for the unknown vector, where
the new variables play the role of parameters. We exploit the existence
condition for solutions of the system to derive those values of the parameters
that belong to the Pareto front inherent to the problem. Then, we solve the
system for the unknown vector and take all solutions that correspond to the
Pareto front, as a complete solution of the bi-objective problem. We apply the
result obtained to the bi-criteria decision problem under consideration and
present illustrative examples.
