I want my customer to track their own inventory in their site

Users on a B2B site/customer portal can monitor inventory levels, reorder points and view the usage/replenishment history for an inventory item.  To allow a user to do this, you would first need to give the user permission via site groups.  You will notice a permission named "Ability to view inventory" that would need to be allowed for the user.  You will also need to add an inventory link to one of your navigation menus.  You will notice that inventory is one of the standard menu items.  Please note that users on a B2C/retail site cannot view inventory levels on the site. 

To be alerted to the inventory level getting low, make sure to set a re-order point in the inventory setup. By doing this, administrators will be emailed when the inventory falls below the re-order point. If you have the option of using custom email notifications, you could set up another group in the store and assign a user (one of the store customers) to also get a copy of the email notification.
For more information on Inventory please refer to the link : Ch. 057 Managing Product Inventory