The last mile delivery volume has been gradually increasing worldwide, and in particular, the volume trend is expected to accelerate dramatically due to COVID-19. Furthermore, the expansion of the last mile delivery market negatively impacts social and environmental issues (urban traffic congestion, greenhouse gas emissions, etc.) owing to the delivery system employing internal combustion engine delivery trucks in metropolitan areas. Therefore, mobile centers for the last mile delivery have been studied to solve the previously stated issues. That is because mobile centers can enable the active use of eco-friendly transportation, be easily relocated, and be installed in empty spaces in the city. In this study, we consider this problem as the multi-period multi-depot location-routing problem to operate a mobile center efficiently. We present a 2-phase method for the addressed problem and develop a heuristic algorithm. The first phase of the proposed method is formulated as a stochastic dynamic programming model for the multi-period locating problem, and the second phase is constructed as a mixed-integer programming model for the multi-depot routing problem.