Inventory is the number of units available for sale. The number is defined by the rooms set up in the system (SETTINGS->ROOMS->SETUP) and the number of bookings. Inventory can be quickly changed in the CALENDAR. To show inventory the system need valid prices. If you have not set a daily price or a rate the system will show 0 inventory for this date.
The inventory can never be changed to a value which is higher than the total number of rooms minus the bookings you have.
If "Overbooking Protcction" is set to "Property" (SETTINGS->ROOMS->SETUP) the system will calculate the inventory ont the total bookings in a room up to room quantity AND total bookings in the property up to total rooms in property. Meaning the room will be closed if the number of bookings in all rooms in the property is greater or equal to the total number of rooms in the property. This could occur because of an overbooking in a different room. Hidden rooms are not included in the calculation of property availability.