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 LIGOVirgo 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.