# Simulation-Based Multi-Criteria Optimization of Parallel Heat Treatment Furnaces at a Casting Manufacturer

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions and is responsible for 31% of the corresponding primary energy consumption [2] and digital planning methods are a major potential contributor toward increasing energy efficiency for production companies [3]. A higher level of energy-efficiency can be achieved by either thermal process (parameter) improvements [4,5,6], optimized demand-side management [7], or production planning [8,9,10,11,12] improvements, e.g., efficient production scheduling. The casting manufacturing system comprises of casting, heat treatment including cooling, and subsequent grinding. According to Wang [1], significant variables and uncertainties exist in the operation of heat treatment equipment, which have to be considered within scheduling, such as gas heating values, processing times, due dates, and setup-times. Since the availability of ready-to-use digital planning methods for optimized energy efficiency are both crucial for industrial implementations of this planning objective and unavailable for most applications, this paper aims at contributing a case study of a successful development and evaluation of an optimized integrated industrial planning including a presentation of the underlying method and its development.

## 2. Background and Related Work

#### 2.1. Literature on Optimized Planning Approaches

#### 2.2. Literature Concerning Simulation

## 3. Case Study Introduction

- Combining jobs to batches, which are sequenced and scheduled for processing on the heat treatment furnaces;
- Transfer of batches to the furnaces via crane;
- Processing in the furnaces;
- Release and transfer to cooling stations via crane.

## 4. Basic Planning Method

#### 4.1. Hybrid Simulation

#### 4.2. Metaheuristic Optimization

- A guided search by adapted operators in the GA (this prevents the GA from mixing parts of the chromosome that determine different variables and for some variables focusses the mutations in a certain direction, thus reducing the number of practically infeasible solutions);
- A memory function from the Tabu Search algorithm (this prevents the algorithm from evaluating solutions that have already been evaluated before);
- A mixed integer optimization (setting an optimal step size for the optimization significantly reduces the search space without compromising accuracy in practical terms);
- Hybridization by combining the GA with Pattern Search and determining the optimal population size.

## 5. Hybrid Simulation for the Case Study

## 6. Optimization Method for the Case Study

- A rule-based deterministic batching heuristic;
- A deterministic exchange-based heuristic optimization;
- A GA optimization.

#### 6.1. Model Formalization

#### 6.2. Batching Heuristic

#### 6.3. Hybrid Optimization Approach

#### 6.4. Genetic Algorithm Customization

^{®}(R2018b) and adapts a GA from the Global Optimization Toolbox. The GA, as the second optimization phase, receives the best solution from the previous deterministic heuristic as the starting point. The implemented stochastic uniform selection operator, ensuring that every individual within a line corresponds to a section of this line length proportional to its scaled value, remains untouched. The algorithm, moving along the line of individuals in steps of equal size, selects the individuals for the next generation stochastically. Because of its stochastic character, this selection operator is suitable for small GA populations. The diversity and exploratory character of the algorithm in this case is preferable to e.g., ranking based or tournament selection operators.

#### 6.5. Constraint Handling and Validation

## 7. Experimental Results for the Case Study

- A Global Search GA with different population sizes (small populations with 3, 6 and 9 individuals);
- A Divide and Conquer based, two-phase hierarchical GA, using the optimal population size from the Global Search GA and utilizing only one modification operator in the global and local search phase respectively.

#### 7.1. Discussion of the Case Study Results

_{2}emission potential is derived from the reductions in energy consumption. According to a national electricity-supplier [47] the environmental impact of electricity during the production of the electricity mix is about 170 g/kWh, while natural gas accounts for about 198 g/kWh (combustion calorific value). This value is calculated from the stoichiometric combustion equation for CH

_{4}using the molar mass for CO

_{2}. The total direct CO

_{2}emission reduction potential is about 6 tons for the given dataset. This is equivalent to around 200 tons emission reduction per year, depending on the actual furnace utilization.

#### 7.2. Consideration of Dynamic Energy Prices

_{2}efficient. Currently, there are significant hurdles for companies to access the flexible energy trade, most of which are based in the inability for smaller industrial energy consumers (“small” in this case includes industrial production plants as the casting manufacturer in the case study) to predict and plan their demand. This results in fixed energy tariffs for most production plants in Europe—sometimes with a degree of flexibility but never with direct access to long- and short-term energy markets and stock-exchanges. The presented simulation-based approach is both able to better predict and plan the energy demand for the next days and it can consider flexible energy prices as input data for the optimization.

## 8. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Wang, J.; Qiao, F.; Zhao, F.; Sutherland, J.W. Batch scheduling for minimal energy consumption and tardiness under uncertainties: A heat treatment application. CIRP Ann.
**2016**, 65, 17–20. [Google Scholar] [CrossRef][Green Version] - He, Y.; Li, Y.; Wu, T.; Sutherland, J.W. An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops. J. Clean. Prod.
**2015**, 87, 245–254. [Google Scholar] [CrossRef] - Matta, A. Automation technologies for sustainable production [TC Spotlight]. IEEE Robot. Autom. Manag.
**2019**, 26, 98–102. [Google Scholar] [CrossRef] - Zhang, S.; Xing, Y.; Wang, D.; Wang, N.; Jimenez, G. Optimal heat treatment furnace based on new robust point approximation strategy. J. Clean. Prod.
**2020**, 254, 120097. [Google Scholar] [CrossRef] - Rao, R.V.; Rai, D.P. Optimization of selected casting processes using Jaya algorithm. Mater. Today Proc.
**2017**, 4, 11056–11067. [Google Scholar] [CrossRef] - Kang, J.; Rong, Y. Modeling and simulation of load heating in heat treatment furnaces. J. Mater. Process. Technol.
**2006**, 174, 109–114. [Google Scholar] [CrossRef] - Ramin, D.; Spinelli, S.; Brusaferri, A. Demand-side management via optimal production scheduling in power-intensive industries: The case of metal casting process. Appl. Energy
**2018**, 225, 622–636. [Google Scholar] [CrossRef] - Tiwari, M.K.; Mukhopadhyay, A.; Sanyal, D. Parameter optimization through performance analysis of model based control of a batch heat treatment furnace with low NOx radiant tube burner. Energy Convers. Manag.
**2005**, 46, 2114–2133. [Google Scholar] [CrossRef] - Tang, H.; Chen, R.; Li, Y.; Peng, Z.; Guo, S.; Du, Y. Flexible job-shop scheduling with tolerated time interval and limited starting time interval based on hybrid discrete PSO-SA: An application from a casting workshop. Appl. Soft Comput.
**2019**, 78, 176–194. [Google Scholar] [CrossRef] - Rahal, S.; Li, Z.; Papageorgiou, D.J. Proactive and reactive scheduling of the steelmaking and continuous casting process through adaptive robust optimization. Comput. Chem. Eng.
**2020**, 133, 106658. [Google Scholar] [CrossRef] - Qin, H.; Fan, P.; Tang, H.; Huang, P.; Fang, B.; Pan, S. An effective hybrid discrete grey wolf optimizer for the casting production scheduling problem with multi-objective and multi-constraint. Comput. Ind. Eng.
**2019**, 128, 458–476. [Google Scholar] [CrossRef] - Jiang, S.-L.; Zheng, Z.; Liu, M. A multi-stage dynamic soft scheduling algorithm for the uncertain steelmaking-continuous casting scheduling problem. Appl. Soft Comput.
**2017**, 60, 722–736. [Google Scholar] [CrossRef] - Yu, C.; Semeraro, Q.; Matta, A. A genetic algorithm for the hybrid flow shop scheduling with unrelated machines and machine eligibility. Comput. Oper. Res.
**2018**, 100, 211–229. [Google Scholar] [CrossRef] - Cheng, B.; Li, K.; Chen, B. Scheduling a single batch-processing machine with non-identical job sizes in fuzzy environment using an improved ant colony optimization. J. Manuf. Syst.
**2010**, 29, 29–34. [Google Scholar] [CrossRef] - Baykasoğlu, A.; Ozsoydan, F.B. Dynamic scheduling of parallel heat treatment furnaces: A case study at a manufacturing system. J. Manuf. Syst.
**2018**, 46, 152–162. [Google Scholar] [CrossRef] - Lin, Y.-K.; Hsieh, F.-Y. Unrelated parallel machine scheduling with setup times and ready times. Int. J. Prod. Res.
**2013**, 52, 1200–1214. [Google Scholar] [CrossRef] - Eroglu, D.Y.; Özmutlu, H.C.; Özmutlu, S. Genetic algorithm with local search for the unrelated parallel machine scheduling problem with sequence-dependent set-up times. Int. J. Prod. Res.
**2014**, 52, 5841–5856. [Google Scholar] [CrossRef] - Lenort, R.; Roman, K.; Andrea, S. Heuristic algorithm for planning and scheduling of forged pieces heat treatment. 2012. Available online: http://dspace.vsb.cz/handle/10084/89844 (accessed on 16 September 2020).
- Huang, R.-H.; Yu, S.-C.; Chen, P.-H. Energy-saving scheduling in a flexible flow shop using a hybrid genetic algorithm. J. Environ. Prot.
**2017**, 8, 1037–1056. [Google Scholar] [CrossRef][Green Version] - Thiede, S.; Schönemann, M.; Kurle, D.; Herrmann, C. Multi-level simulation in manufacturing companies: The water-energy nexus case. J. Clean. Prod.
**2016**, 139, 1118–1127. [Google Scholar] [CrossRef] - Rager, M. Energieorientierte produktionsplanung: Analyse, konzeption und umsetzung; Gabler Verlagg: Wiesbaden, Germany, 2008. [Google Scholar]
- Sihn, W.; Sobottka, T.; Heinzl, B.; Kamhuber, F. Interdisciplinary multi-criteria optimization using hybrid simulation to pursue energy efficiency through production planning. CIRP Ann.
**2018**, 67, 447–450. [Google Scholar] [CrossRef] - Reinhardt, H.; Bergmann, J.-P.; Münnich, M.; Rein, D.; Putz, M. A survey on modeling and forecasting the energy consumption in discrete manufacturing. Procedia CIRP
**2020**, 90, 443–448. [Google Scholar] [CrossRef] - Sobottka, T.; Kamhuber, F.; Faezirad, M.; Sihn, W. Potential for machine learning in optimized production planning with hybrid simulation. Procedia Manuf.
**2019**, 39, 1844–1853. [Google Scholar] [CrossRef] - Herrmann, C.; Thiede, S. Process chain simulation to foster energy efficiency in manufacturing. CIRP J. Manuf. Sci. Technol.
**2009**, 1, 221–229. [Google Scholar] [CrossRef] - Schönemann, M.; Schmidt, C.; Herrmann, C.; Thiede, S. Multi-level modeling and simulation of manufacturing systems for lightweight automotive components. Procedia CIRP
**2016**, 41, 1049–1054. [Google Scholar] [CrossRef][Green Version] - Garwood, T.L.; Hughes, B.R.; Oates, M.R.; O’Connor, D.; Hughes, R. A review of energy simulation tools for the manufacturing sector. Renew. Sustain. Energy Rev.
**2018**, 81, 895–911. [Google Scholar] [CrossRef] - Bunse, K.; Vodicka, M.; Schönsleben, P.; Brülhart, M.; Ernst, F.O. Integrating energy efficiency performance in production management – gap analysis between industrial needs and scientific literature. J. Clean. Prod.
**2011**, 19, 667–679. [Google Scholar] [CrossRef] - Dias, L.M.S.; Vieira, A.A.C.; Pereira, G.A.B.; Oliveira, J.A. Discrete simulation software ranking—A top list of the worldwide most popular and used tools. In Simulating Complex Service Systems; IEEE: Washington, DC, USA, 2016; pp. 1060–1071. [Google Scholar]
- Jahangirian, M.; Eldabi, T.; Naseer, A.; Stergioulas, L.K.; Young, T. Simulation in manufacturing and business: A review. Eur. J. Oper. Res.
**2010**, 203, 1–13. [Google Scholar] [CrossRef][Green Version] - Thiede, S. Energy Efficiency in Manufacturing Systems; Springer Science & Business Media: Berlin, Germany, 2012. [Google Scholar]
- Junge, M. Simulationsgestützte Entwicklung und Optimierung einer energieeffizienten Produktionssteuerung. Ph.D. Thesis, Kassel University, Kassel, Germany, 2007. [Google Scholar]
- Lin, H.; Sambamoorthy, S.; Shukla, S.K.; Thorp, J.; Mili, L. Power system and communication network co-simulation for smart grid applications. In Proceedings of the ISGT 2011, Anaheim, CA, USA, 17–19 January 2011; pp. 1–6. [Google Scholar] [CrossRef]
- Carloni, L.P.; Passerone, R.; Pinto, A.; Angiovanni-Vincentelli, A.L.; Sangiovanni-Vincentelli, A. Languages and tools for hybrid systems design. Found. Trends Electron. Des. Autom.
**2006**, 1, 1–193. [Google Scholar] [CrossRef][Green Version] - Chahal, K.; Eldabi, T. Applicability of hybrid simulation to different modes of governance in UK healthcare. In Proceedings of the 2008 Winter Simulation Conference, Miami, FL, USA, 7–10 December 2008; pp. 1469–1477. [Google Scholar]
- Heinzl, B.; Raich, P.; Preyser, F.; Kastner, W. Simulation-based Assessment of Energy Efficiency in Industry: Comparison of hybrid simulation approaches. IFAC PapersOnLine
**2018**, 51, 689–694. [Google Scholar] [CrossRef] - Nof, S.Y. Springer Handbook of Automation; Springer: Berlin/Heidelberg, Germany, 2009. [Google Scholar]
- Love, J. Process Automation Handbook; Springer Science and Business Media LLC: London, UK, 2007. [Google Scholar]
- Raich, P.; Heinzl, B.; Preyser, F.; Kastner, W. Modeling techniques for integrated simulation of industrial systems based on hybrid PDEVS. In Proceedings of the 2016 Workshop on Modeling and Simulation of Cyber-Physical Energy Systems (MSCPES), Vienna, Austria, 11 April 2016; pp. 1–6. [Google Scholar]
- Sobottka, T.; Kamhuber, F.; Rössler, M.; Sihn, W. Hybrid simulation-based optimization of discrete parts manufacturing to increase energy efficiency and productivity. Procedia Manuf.
**2018**, 21, 413–420. [Google Scholar] [CrossRef] - Heinzl, B.; Raich, P.; Preyser, F.; Kastner, W.; Smolek, P.; Leobner, I. Modular Hybrid Modeling based on DEVS for interdisciplinary simulation of production systems. In Proceedings of the 31st European Simulation and Modelling Conference—ESM’2017, Lisbon, Portugal, 25–27 October 2017; pp. 157–161. [Google Scholar]
- Heinzl, B. Hybrid Modeling of Production Systems: Co-Simulation and DEVS-Based Approach. Diploma Thesis, TU Wien, Vienna, Austria, 2016. [Google Scholar]
- Sobottka, T.; Kamhuber, F.; Sihn, W. Increasing energy efficiency in production environments through an optimized, hybrid simulation-based planning of production and its periphery. Procedia CIRP
**2017**, 61, 440–445. [Google Scholar] [CrossRef] - Sobottka, T. Eine anwendungsorientierte simulationsbasierte Methode, unter Berücksichtigung von Energieeffizienz, in der optimierenden Planung von Produktion und Logistik. Ph.D. Thesis, Vienna University of Technology, Vienna, Austria, 2018. [Google Scholar]
- Freitas, A.A. A critical review of multi-objective optimization in data mining. ACM SIGKDD Explor. Newsl.
**2004**, 6, 77–86. [Google Scholar] [CrossRef][Green Version] - Wang, J.S.; Li, S.X. An improved grey wolf optimizer based on differential evolution and elimination mechanism. Sci. Rep.
**2019**, 9, 7181. [Google Scholar] [CrossRef] [PubMed][Green Version] - EVN Energievertrieb GmbH & Co KG. EVN Produktionformation für Ihren Stromtarif. 2020. Available online: https://www.evn.at/Downloads/Businesskunden/Strom/Produktinformation_BUS_konventionell.aspx (accessed on 23 July 2020).
- Central European Gas Hub AG. Day Ahead Market. 2020. Available online: https://www.cegh.at/ (accessed on 23 July 2020).
- Energy Exchange Austria. Spotmarkt Strom/Österreich. 2020. Available online: https://www.exaa.at/de (accessed on 23 July 2020).

**Figure 1.**Schematic overview of the production layout comprising five heat treatment furnaces with associated cooling stations and first in–first out (FIFO) loading buffers as well as a crane for loading and unloading.

**Figure 7.**Comparison of genetic algorithm (GA) in combination with the heuristic and GA without the heuristic.

UA [W/K] | M_{th} [J/K] | RMS_{par} | RMS_{valid} | erel_{valid} | |
---|---|---|---|---|---|

Oven 1 | 284.27 | 1.643 × 10^{7} | 32.95 | 44.87 | −14.16% |

Oven 2 | 520.37 | 1.923 × 10^{7} | 36.76 | 55.05 | −5.14% |

Oven 3 | 45.06 | 2.487 × 10^{6} | 45.81 | 80.79 | −7.06% |

Oven 4 | 385.21 | 1.015 × 10^{7} | 18.07 | 72.91 | 5.72% |

Oven 5 | 464.00 | 3.075 × 10^{7} | 65.78 | 70.81 | −9.72% |

Heat Treatment | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

1 | 0 | 0 | 1 | 1 | 0 |

2 | 0 | 0 | 1 | 1 | 0 |

3 | 0 | 1 | 1 | 0 | 1 |

4 | 1 | 1 | 1 | 1 | 0 |

5 | 1 | 1 | 1 | 1 | 1 |

6 | 1 | 1 | 1 | 1 | 1 |

7 | 1 | 1 | 1 | 1 | 1 |

8 | 1 | 1 | 1 | 1 | 1 |

9 | 1 | 1 | 1 | 1 | 1 |

Variable Price Energy Cost | Contant Price Energy Cost | Advantage of Variable Price for Energy Cost | |
---|---|---|---|

Initial | 18.185 | 18.411 | 226 |

Optimized | 17.286 | 17.373 | 88 |

relative improvement | 4.94% | 5.64% |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sobottka, T.; Kamhuber, F.; Heinzl, B. Simulation-Based Multi-Criteria Optimization of Parallel Heat Treatment Furnaces at a Casting Manufacturer. *J. Manuf. Mater. Process.* **2020**, *4*, 94.
https://doi.org/10.3390/jmmp4030094

**AMA Style**

Sobottka T, Kamhuber F, Heinzl B. Simulation-Based Multi-Criteria Optimization of Parallel Heat Treatment Furnaces at a Casting Manufacturer. *Journal of Manufacturing and Materials Processing*. 2020; 4(3):94.
https://doi.org/10.3390/jmmp4030094

**Chicago/Turabian Style**

Sobottka, Thomas, Felix Kamhuber, and Bernhard Heinzl. 2020. "Simulation-Based Multi-Criteria Optimization of Parallel Heat Treatment Furnaces at a Casting Manufacturer" *Journal of Manufacturing and Materials Processing* 4, no. 3: 94.
https://doi.org/10.3390/jmmp4030094