  We introduce two novel time-dependent figures of merit for both online and
offline optimizations of advanced gravitational-wave (GW) detector network
operations with respect to (i) detecting continuous signals from known source
locations and (ii) detecting GWs of neutron star binary coalescences from known
local galaxies, which thereby have the highest potential for electromagnetic
counterpart detection. For each of these scientific goals, we characterize an
$N$-detector network, and all its $(N-1)$-detector subnetworks, to identify
subnetworks and individual detectors (key contributors) that contribute the
most to achieving the scientific goal. Our results show that aLIGO-Hanford is
expected to be the key contributor in 2017 to the goal of detecting GWs from
the Crab pulsar within the network of LIGO and Virgo detectors. For the same
time period and for the same network, both LIGO detectors are key contributors
to the goal of detecting GWs from the Vela pulsar, as well as to detecting
signals from 10 high interest pulsars. Key contributors to detecting continuous
GWs from the Galactic Center can only be identified for finite time intervals
within each sidereal day with either the 3-detector network of the LIGO and
Virgo detectors in 2017, or the 4-detector network of the LIGO, Virgo, and
KAGRA detectors in 2019-2020. Characterization of the LIGO-Virgo detectors with
respect to goal (ii) identified the two LIGO detectors as key contributors.
Additionally, for all analyses, we identify time periods within a day when lock
losses or scheduled service operations could result with the least amount of
signal-to-noise or transient detection probability loss for a detector network.
