Abstract
In this paper we study structural properties and properties of maximal paths of the hot rolling batches precedence graph. The hot rolling batches precedence graph arises in the problem of planning and scheduling of a hot strip mill load. Slab batches are selected and sequenced in turns. Basic technological restrictions on batch sequencing in turns are represented by the rolling batches precedence graph. Some fundamental structural properties of this graphs are stated such as the local block structure and the maximal paths structure. Motivation and overview of the result application potential are also provided.
Highlights
Current state of global steel market forces iron-steel plants to investment in product quality improving, operational cost reduction, improvement of customer service
In operations research hot rolling production planning problems are known as hot rolling unit planning problems (HRUPPs) when slabs are not batched and inserted in a turn and hot rolling batch planning problems (HRBPPs) [10] where slabs are to be batched and form one or several turns
In this paper we study the structure of geometrical sequencing constraints that are common for HRUPPs and HRBPPs
Summary
Current state of global steel market forces iron-steel plants to investment in product quality improving, operational cost reduction, improvement of customer service. HRBPPs are considered as modifications of VRP, where one or several turns must be scheduled and every turn is the node sequence of a correspondent vehicle In this case sequencing constraints are again defined by penalties for transitions between batches represented by nodes (by geometry and hardness of slabs in batches). We introduce the HRUPPs setting where sequencing is formalized as a constraint coming from practical tasks at one of the biggest steel productions in Russia (JSC MMK) and study the structure of corresponding precedence graphs. The results as it is shown here can be used to drastically reduce the amount of 0-1 variables in integer programming formulation of considered sequencing problem in comparison with classical approach. For every block B of graph G0w either H contains all nodes from B, or only one, or H and B have no common nodes
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