  Pulsar Timing Arrays (PTAs) are a collection of precisely timed millisecond
pulsars (MSPs) that can search for gravitational waves (GWs) in the nanohertz
frequency range by observing characteristic signatures in the timing residuals.
The sensitivity of a PTA depends on the direction of the propagating
gravitational wave source, the timing accuracy of the pulsars, and the
allocation of the available observing time. The goal of this paper is to
determine the optimal time allocation strategy among the MSPs in the North
American Nanohertz Observatory for Gravitational Waves (NANOGrav) for a single
source of GW under a particular set of assumptions. We consider both an
isotropic distribution of sources across the sky and a specific source in the
Virgo cluster. This work improves on previous efforts by modeling the effect of
intrinsic spin noise for each pulsar. We find that, in general, the array is
optimized by maximizing time spent on the best-timed pulsars, with sensitivity
improvements typically ranging from a factor of 1.5 to 4.
