What is the counterpart of mining when using blockchain for traceability?
The Bitcoin blockchain achieves immutability through proof of work mining. It is considered immutable because many economic actors commit their computing power to finding new blocks. If not "enough" people are mining, the blockchain is not immutable. Recently both the Bitcoin Gold and the Ethereum Classic blockchain have been manipulated through a 51 % attack so these weak (i.e. low hash rate) blockchains are not immutable.

If you do not want to worry about having enough miners, you could consider building a token on top of either the Bitcoin blockchain or on top of the Ethereum blockchain (e.g. an ERC20 token). On Bitcoin, the Omni protocol allows for you to build your own token which is transferred on the Bitcoin blockchain. This means that you have to pay transaction fees (to the Bitcoin miners) to transfer the tokens but the benefit is that you will not have to worry about a 51 % attack (other people are trying to prevent that).

If you want non-fungible assets (each with their own ID attached), the Ethereum protocol standard ERC721 is made for this purpose. I am not aware of a similar solution on top of the Bitcoin blockchain.

If you want something else, like a more general, immutable log system that you can define yourself, you may have to write your own contract in Solidity (for the Ethereum blockchain) and only allow specific addresses (one for each member of the production chain) to write to this log.