The $n$-vehicle exploration problem is NP-complete

The $n$-vehicle exploration problem (NVEP) is a combinatorial optimization problem, which tries to find an optimal permutation of a fleet to maximize the length traveled by the last vehicle. NVEP has a fractional form of objective function, and its computational complexity of general case remains open. We show that Hamiltonian Path $\leq_P$ NVEP, and prove that NVEP is NP-complete.