That sounds like the Latisha Frazier case out of D.C..
I know that landfills are horrendous. Finding a body there, even when LE knows the general grid area of the landfill where the bodies may be is almost impossible. I'm thinking of Lori hacking's case and the case of Abby and Jennifer Blagg. In the Blagg case, it took them 16 days of searching a specific grid. They found the mom but never little Abby and they gave up trying to find her. (However the search was 7 months after they went missing so it's miraculous that either was found at all).
In Lori's case, they searched a specific grid for 33 days before finding her and were surprised that they did. A law officer stated that landfill searches are historically unsuccessful:
http://www.foxnews.com/story/0,2933,134233,00.html And I would think that the more time that passes, the harder it will be as more trash gets added.
But I think they need a reason to think a body might be there. In missing child cases, a male suspect is probably more likely to place a child in a landfill than a female suspect. Women tend to pick watery areas instead. In any event, LE could start by finding all dumpsters along Lena's route the day Aliayah went missing and tracing those dumpsters to specific grids in the landfill. I don't know.