Question regarding fuel dumping

I just saw the NOVA program about how two fully loaded 747 jumbo jets
collided on a fog-blanketed runway on the island of Tenerife, claiming
the lives of 583 people in 1977. The pilot of the KLM plane ordered
his plane to be refueled, so he rolled down the runway with 55 tons of
fuel for a flight to Las Palmas, which would take at most a half hour.
The program said it was enough fuel to get the plane back to Amsterdam,
let alone Las Palmas. It was obvious that the extra fuel fed the blaze
that killed everyone on board and prevented the plane from making a
slightly faster takeoff, which could have averted the disaster.

My question is this: When should the pilot of a commercial jet dump his
fuel in flight? He obviously wasn't going to do that and was going
to land very heavy. Under what conditions is fuel dumping necessary.

Thanks.

AJ