It depends on how big the relays need to be, how many of these you want, what voltages you have and a whole load of other things.
A PIC could easily do the control but it needs programming and interfacing to the relays, and it will need a low voltage supply.
An industrial PLC (Programmable logic controller) is easier to programme, would be easier to supply and would probably drive what you need without further interfaces, but might need a more expensive programmer and would cost more.
You could also wire up 2 or three timer relays, but they are also quite expensive.