In order for all your objects in Fallout Shelter to work without interruption, you need to attract more people to the Shelter, and here's how to do it.
The fastest and easiest way to get more residents is by having babies naturally. If you put a man and a woman in a dwelling, the latter will become pregnant. The higher their charisma, the less time they need. Once a woman becomes pregnant, she will give birth to her baby in a few hours. The child does nothing and will just explore the Vault, but in a few hours he will grow up to be an adult.
Another way is with a radio tower. To open it, you need 20 villagers and someone with high charisma to be able to operate the tower. However, be aware that attracting people through the radio is much slower than just being born.
Finally, you can find new settlers when you send people to the wasteland. Sometimes they run into refugees at Red Rocket Truckstop or Super Duper Market who want to join your Vault.