  We discuss a variant of multitask n-vehicle exploration problem. Instead of
requiring an optimal permutation of vehicles in every group, the new problem
asks all vehicles in a group to arrive at a same destination. It can also be
viewed as to maximize every processor's average profit, given n tasks, and each
task's consume-time and profit. Meanwhile, we propose a new kind of partition
problem in fractional form, and analyze its computational complexity. Moreover,
by regarding fractional partition as a special case, we prove that the
maximizing average profit problem is NP-hard when the number of processors is
fixed and it is strongly NP-hard in general. At last, a pseudo-polynomial time
algorithm for the maximizing average profit problem and the fractional
partition problem is presented, thanks to the idea of the pseudo-polynomial
time algorithm for the classical partition problem.
