Block structure of hot rolling batch precedence graph and construction of hot iron rolling plans balanced by product types

The authors continue study of operative hot iron rolling planning settings. The report will present the results on hot rolling batch precedence graph study. In particular, blocks (in the sense of general graph theory) of subgraphs on batches of one after roll width are characterized. It will be shown that any maximal path (by node inclusion) contains such block, has only one common node with it or has no common nodes. The authors plan to discuss possible variants of how to use these results to construct an algorithm that can build hot iron rolling plans balanced by product types.