Hi,
Couple of options, see if this helps:
If you're using vCenter server to manage your ESXi host then you can use "Scheduled Task" feature to schedule power-on/off of ESXi host along with configuring email notification for the task completion.
Using Schedule Task, you can provide the cluster not just an ESXi host and this requires DPM (Distributed Power Management feature to be enabled, DPM uses Wake-On-LAN, IPMI or ILO to power-on the system).
If you have any existing option to automatically start & shutdown the ESXi host then you can simply use "VM Startup/Shutdown" feature for automatically start and stop of VMs with the Host under ESXi host configuration/settings.