Tracking down alumni/ae can be done any number of ways. The most important thing to realize is that this effort happens every 4-5 years when an alum or an undergrad gets enough ambition to inquire. The chapter needs to invest in a good software program so that this effort is done once, then maintained regularly.
Call your national fraternity and request a roster of all initiates (good addresses, lost alumni, inactive and deceased). There shouldn't be any issue.
At the same time, call your University and seek a list of all graduates from the chapter. There may be a number of issues. Many universities hold their information confidential. Some that are willing to give information may not have tracked students by the organizations they participated in.
Take all the information and merge it into the database. Then, find all the missing alumni/ae, using:
www.anywho.com
www.switchboard.com
You can also pay to find lost alumni/ae, using such programs as Magic and Alumni Finder.
I can provide assistance, if anyone needs it.
Pete