I guess that the pallets are consigned (so they are assets but not goods). So you ship them in addition with the real products.
So you should use stock lot. You have to create a stock.lot for each serial number linked to the pallet assets. On the shipment moves you set the proper lot to each move.
Also you can define on the pallet assets that the lot is required for customer location. Like that you are sure to have the serial number of each outgoing pallet.
From the lot form, you can open the location tree which will show you where is the pallet linked. If you want to know the exact customer, you will need to create a customer location for each customer.