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

A variant of multitask n-vehicle exploration problem: maximizing every processor's average profit