This paper focuses on three areas: the first is a review of current knowledge about social and service robots for elderly care. The second is an optimization conceptual model aimed at maximizing the efficiency of assigning robots to serve the elderly. The proposed multi-criteria optimization model is the first one proposed in the area of optimization for robot assignment for the elderly with robot utilization level and caregiver stress level. The third is the findings of studies on the needs, requirements, and adoption of technology in elderly care. We consider the use of robots as a part of the ENRICHME project for long-term interaction and monitoring of older persons with mild cognitive impairment, to optimize their independence. Additionally, we performed focus group discussions (FGD) to collect opinions about robot-related requirements of the elderly and their caregivers. Four FDGs of six persons were organized: two comprising older adults, and two of the other formal and informal caregivers, based on a detailed script. The statements of older participants and their caregivers were consistent in several areas. The analysis revealed user characteristics, robot-related issues, functionality, and barriers to overcome before the deployment of the robot. An introduction of the robot must be thoroughly planned, include comprehensive pre-training, and take the ethical and practical issues into account. The involvement of future users in the customization of the robot is essential.