You may use the Likert scale questions as covariates in ACBC/HB estimation, and then they will have an influence on the final utilities for each respondent (respondents will "borrow" distributional information from other respondents that rate the Likert questions similarly).
However, if you are trying to use the segmentation variables to influence the segmentation scheme for something like latent class or cluster analysis, then you could try something like the following:
1. Use the Likert Scale questions as covariates when you estimate your ACBC/HB utilities. Then, use the normalized (zero-centered diffs) utilities for the next steps.
2. Use our CCEA software for "Convergent Cluster & Ensemble Analysis". There are many different ways to do this, but one approach could be:
a) Point the CCEA software just to the part-worth utilities (the normalized zero-centered diffs) as basis variables and use the software in Ensemble Analysis mode so that it will create a .CSV file that has many different potential clustering solutions (the ensemble).
b) Point the CCEA software just to the Likert scale questions as basis variables and use the software in Ensemble Analysis mode so that it will create a .CSV file that has many different potential clustering solutions (the ensemble).
c) Combine the two .CSV ensemble files into one, by copying the additional columns from one file as new columns within the other file.
d) Run CCEA again in Ensemble mode, pointing the software to your custom-built .csv ensemble file from step c (rather than letting the software build its own ensemble file).
These steps will lead to an Ensemble solution that combines the best aspects of the cluster solutions based on the Likert scale questions with the best aspects of the cluster solutions based on the part-worth utilities. A single consensus cluster solution will be output that leverages both types of data (the Likert questions as well as the part-worths) to make the final cluster solution.