This paper proposes a multiplicative approach to solve defective issues in lexicographic goal programming of the analytic hierarchy process (LGPAHP). Although the LGPAHP can handle inconsistent interval comparison matrices, it generates different weights in the upper and lower triangular interval judgments. Instead of adopting additive constraints, the proposed method uses multiplicative constraints to cope with deficiencies inherent in the LGPAHP. Moreover, since two deviation variables are used to cope with inconsistent cases, weights can be flexibly derived, without specifying any advance tolerance parameters. Four examples are presented to illustrate the proposed method in more detail.