You could define Product A as a KIT (BOM) with PartA, PartB and PartC as its components. While receiving Product A would be split by components in the ratio you define in the kit BOM and you will be able to provide serial numbers to individual parts.

On the delivery order/ slip as well, you will be able to recreate the Kit with individual serial numbers for parts.

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Updated Answer

Based on your volumes, frequency and current practices related to similar products in the organization, the below options may also be viable.

Option 1:

Buy, Sell, Receive & Delivery individual parts - define and manage parts and not the product

Option 2:

Buy & Sell product, while Receiving & Delivering product & parts - create parts as products. Create the SO & PO for Product A, while receiving manually add parts & track serial numbers on them. Delivery orders generated from SO would have product line, manually include parts as additional with serial numbers

This would enable inventory tracking of parts, while you would be managing sales and invoicing for product A

Options 3:

Buy, Sell, Receive & Delivery product - while tracking only the product, you can include the part serial numbers in SO and Delivery Slip 'description' column. You could update the description at the time of sale or delivery.

Challenge would be to track the latest part serial numbers, maybe you could use the 'log note' on the product chatter to track while receiving the product.