Two concepts for large-scale, complex, robotic missions to search for frozen water at the lunar south pole are systematically analyzed to determine their relative productivity and investment requirements. A concurrent design team, a technology-assessment tool, and a sensitivity model are integrated to search a large, complex trade space. Performance goals for a broad portfolio of missions comprising NASA's lunar exploration program are optimized subject to budget, workforce, and other nontechnical constraints. Explicit distinction is made between enabling and enhancing technologies. Uncertainties and dependencies are included within the optimization framework. Given the constraints used in this analysis, the study determines that the longer mission [using a radioisotope thermoelectric generator (RTG)] would return 14 times the value of the shorter mission (using a methanol-oxygen fuel cell) for roughly a 17% increase in cost, and would be enabled with the recommended temporal technology portfolio. To assess the robustness of the investment recommendations, other potential fuel-cell chemistries are evaluated along with potential improvements in rover speed and autonomy, and a reduced activity profile. Results indicate that a lithium-oxygen fuel cell would enable the highest level of productivity among the three fuel cells studied, though not as high as that permitted by an RTG. For the shorter duration mission concepts, it was found that productivity could be enhanced by reducing the number of activities from the baseline 15 to 4, thereby permitting time for each activity to be more fully accomplished.