Optimization of process times and product sequences in a hot-rolling mill with batch-type reheating furnaces

Project focus

Focus of TU Wien – ACIN within the SemI40 project:

  • Mathematical modeling of batch-type reheating furnaces
  • Time-optimal control of batch-type reheating furnaces
  • Optimal timetabling of reheating, rolling, and handling tasks
  • Optimization of the product sequence for a finite production horizon


In semiconductor manufacturing, sputtering processes require pure metals or special alloys for sputtering targets. These targets must fulfill rigorous quality requirements in terms of shape, chemical purity, and microstructure to guarantee high-end semicondutor production. Sputtering targets with high melting points (e.g., molybdenum) are usually produced by sintering and subsequent hot-forming. Metal powders are pressed and sintered in the shape of blocks. Subsequently, these blocks are reheated in furnaces and rolled into plates (targets) by a hot-rolling mill.

plant overview

Outline of the production plant.

Figure 1 shows an outline of the considered plant. It consists of several furnaces which may be operated at different temperatures, a roller table with a reversing mill stand, and a product manipulator. The manipulator is used for all product transportation tasks between the furnaces and the roller table. The reheating process of the products in the furnaces is much more time consuming than the rolling passes at the reversing mill stand. Moreover, intermediate reheating steps are necessary between some rolling passes. Due to the fact that hot products cannot be stored, the availability of the required machines at the respective times has to be guaranteed. Hence, the productivity of the plant depends strongly on the required reheating times and the temporal shuffling of the process tasks. The goals of this project are to minimize the reheating times and to optimize the product sequence and the starting times of the process tasks to achieve the maximum product throughput.

A thermal simulation model for the product and furnace temperatures is developed as a basis for the minimization of the reheating times. Figure 2 shows its general components. Based on the simulation model, minimal reheating times can be determined in advance and the temperature evolution of the products can be estimated during the reheating processes. Moreover, the model can be used as a design model for a time-optimal control strategy of the reheating furnaces.

Thermal modeling of the furnaces.

Furthermore, a software tool is developed which optimizes the product sequence and the process times of all process tasks. The algorithm utilizes the minimal reheating times and known rolling and handling times of all products for an upfront planning horizon. The underlying combinatorial optimization problem (flexible job shop scheduling problem) is known to be NP-hard. The problem is split into the determination of the process times for a known product sequence (timetabling problem) and a superordinate optimization of the product sequence. The optimal process times are determined by a tailored recursive algorithm, and the product sequence is optimized using heuristic methods.

Selected publications

  • A. Aschauer, F. Roetzer, A. Steinboeck, and A. Kugi, An Efficient Algorithm for Scheduling a Flexible Job Shop with Blocking and No-Wait Constraints, in Proceedings of the 20th IFAC World Congress, Toulouse, France, 2017, pp. 12490-12495.
    author = {Aschauer, A. and Roetzer, F. and Steinboeck, A. and Kugi, A.},
    title = {An Efficient Algorithm for Scheduling a Flexible Job Shop with Blocking and No-Wait Constraints},
    booktitle = {Proceedings of the 20th IFAC World Congress},
    year = {2017},
    volume = {50},
    number = {1},
    month = {7},
    pages = {12490-12495},
    doi = {doi.org/10.1016/j.ifacol.2017.08.2056},
    address = {Toulouse, France},
    issn = {2405-8963},


  • Automation of hot-rolling mills
  • Industrial furnaces
  • Time- and sequence optimization of production processes

Funding organisations

This research work is part of the EU project SemI40, which is funded by the programme ECSEL Joint Undertaking (Grant Agreement No. 692466) and the programme “IKT der Zukunft” (project number: 853343) of the Austrian Ministry for Transport, Innovation and Technology (bmvit) between May 2016 and April 2019. More information on IKT der Zukunft can be found at https://iktderzukunft.at/en/.

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