Anton A. Berezin     (Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russian Federation)
Svetlana I. Leonova     (Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russian Federation)
Igor A. Vakula     (Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russian Federation)


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.


Hot rolling planning, Precedence graf, Graph structure, Local block structure, Maximal paths

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Balas E. The prize collecting travelling salesman problem // Networks, October 1989. Vol. 19. P. 621–636.

Balas E., Clarence H.M. Combinatorial optimization in steel rolling // Workshop on Combinatorial Optimization in Science and Technology, April, 1991.

Cowling P., Rezig W. Integration of continuous caster and hot strip mill planning for steel production // Journal of Scheduling, July--August, 2000. Vol. 3, no. 4. P. 185–208.

Harary F. Graph Theory. MA: Addison-Wesley, Reading, 1969. 274 p.

Chen X., Wan, W.-S. and Xu, X.-H.} Modeling rolling batch planning as vehicle routing problem with time windows // Computers & Operations Research, 1998. Vol. 25, no. 12. P. 1127–1136.

Vakula I.A., Leonova S.I. On building hot rolling turns // Contemporary problems in mathematics and its applications: 45-th International Youth School-Conference: Proceedings. Ekaterinburg: IMM UrB RAS, USU. 2014. P. 164–166. [In Russian]

Vakula I.A., Leonova S.I. Hot rolling planning problem // Mathematical programming and applications: XV-th All-Russian Conference: Abstracts. Ekaterinburg: IMM UrB RAS, USU. 2015. P. 77–78. [In Russian]

Lixin Tang, Jiyin Liu, Aiying Rong, Zihou Yang. A review of planning and scheduling systems and methods for integrated steel production // European Journal of Operational Research. August 16, 2001. Vol. 133, no. 1. P. 1–20.

Xianpeng Wang, Lixin Tang. Integration of batching and scheduling for hot rolling production in the steel industry // The International Journal of Advanced Manufacturing Technology. 2008. Vol. 36. P. 431-441.

Shixin Liu. Model and Algorithm for Hot Rolling Batch Planning in Steel Plants // International Journal of Information and Management Sciences. 2010. Vol. 21, no. 3. P. 247–263.


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