# Model and Algorithm for Planning Hot-Rolled Batch Processing under Time-of-Use Electricity Pricing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Description

#### 2.1. Basic Principles of Hot Rolling Planning

- (1)
- The length of each principal piece had a certain limit;
- (2)
- When the thickness of the principal piece changed in the non-increase direction, the step must be lower than 25 cm;
- (3)
- When the width changed inversely, the step did not generally exceed 15 cm;
- (4)
- When slabs of the same width were continuously processed, the total length should not exceed a certain limit;
- (5)
- The width, thickness and hardness were not allowed to jump at the same time;
- (6)
- The thickness jump should be smooth and repeated jumps were not allowed. Changes in the non-decrease direction were preferred.
- (7)
- The hardness change should be smooth. Both gradual increase and gradual decrease were allowed. Repeated jumps were not allowed.

#### 2.2. Analysis of Energy Consumption in Rolling

## 3. Mathematical Model and Solution Method

#### 3.1. Mathematical Model

#### 3.1.1. Model Assumptions

- (1)
- The time required to process a single slab was roughly the same. In this paper, the processing time used was 2 min;
- (2)
- Basic properties, such as width, thickness, hardness, and length of each slab were known;
- (3)
- The change of the total attribute in the rolling unit could be determined through calculation.

#### 3.1.2. Objective Function

#### 3.1.3. Constraints

#### 3.2. Method for Model Solution

#### 3.2.1. Brief Description of Algorithm

#### 3.2.2. Chromosome Coding

_{1}, a

_{50}and a

_{100}were the serial numbers of the slabs; A

_{0}, A

_{1}and A

_{2}were the slab sequences constituting the rolling units.

#### 3.2.3. Chromosome Decoding

**Step****0:**- M = 0, ${A}_{j}$ = ${\mathrm{a}}_{i}$, l = 0;
**Step****1:**- Sequentially traversed the slab numbers ${\mathrm{a}}_{i}$ from the $i$th position of the chromosome, recording the length ${l}_{i}$ of the slab ${\mathrm{a}}_{i}$ and recording ${\mathrm{a}}_{i}$ in the arranged slab sequence ${A}_{j}$, doing l = l + ${l}_{i}$, and going to Step 2;
**Step****2:**- If l was larger than the length L of the rolling unit, the last element in the sequence ${A}_{j}$ was removed, turning the sequence ${A}_{j-1}$ into a rolling unit, and letting M = M + 1; if l was equal to the length L of the rolling unit, the sequence ${A}_{j}$ was turned into a rolling unit, and letting M = M + 1; otherwise, Step 1 was selected;
**Step****3:**- When i was equal to the length of the chromosome, the program exited.

#### 3.2.4. Selection of Fitness Function

#### 3.2.5. Genetic Operators

## 4. Case Study

#### 4.1. Basic Parameters

#### 4.2. Analysis of Optimization Results

## 5. Conclusions

- (1)
- A hot-rolling batch-processing plan optimization model, in which TOU electricity pricing was taken into consideration was established. An objective function was used in the model that was aimed at the jump penalties minimizations of the jumps among adjacent slabs in width, hardness, and thickness, as well as in the electricity costs. The optimization method reduced the electricity cost of hot rolling, while ensuring the product quality and production efficiency, in addition to the extra benefit of power consumption fluctuation reduction.
- (2)
- In the proposed method, the crossover and mutation operators of the improved genetic algorithm were used to solve the model for batch-processing plan production for hot rolling. The algorithm was characterized by strong search ability and good convergence. The penalty value after optimization was significantly lower than before optimization, proving the actual value of the proposed method.
- (3)
- An experimental verification was carried out to check the electricity costs of processing of 240 slabs through three hot rolling batch processing plans, formulated under “TOU electricity-pricing consideration”, “TOU electricity-pricing absence” and “man–-machine interaction” models. The results demonstrated that the TOU plan induced 8.9% lower electricity cost than the MMI plan and 5.0% lower electricity cost than the non-TOU plan.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Dong, G.J.; Li, K.T.; Wang, B.L. Adjustment model and algorithm of rolling plan based on real-time warehouse. Syst. Eng. Theory Pract.
**2015**, 35, 1246–1255. [Google Scholar] - Chakraborti, N.; Kumar, B.S.; Babu, V.S.; Moitra, S.; Mukhopadhyay, A. A new multi-objective genetic algorithm applied to hot-rolling process. Appl. Math. Model.
**2008**, 32, 781–1789. [Google Scholar] [CrossRef] - Tang, L.X.; Liu, J.Y.; Rong, A.Y.; Yang, Z.H. A review of planning and scheduling systems and methods for integrated steel production. Eur. J. Oper. Res.
**2001**, 133, 1–20. [Google Scholar] [CrossRef] - Yadollahpour, M.R.; Bijari, M.; Kavosh, S.; Mahnam, M. Guided local search algorithm for hot strip mill scheduling problem with considering hot charge rolling. Int. J. Adv. Manuf. Technol.
**2009**, 45, 1215–1231. [Google Scholar] [CrossRef] - Tan, M.; Duan, B.; Su, Y.X.; He, F. Optimizing production scheduling of steel plate hot rolling for economic load dispatch under time-of-use electricity pricing. Math. Probl. Eng.
**2017**, 145, 913–923. [Google Scholar] [CrossRef] [Green Version] - He, D.F.; Liu, P.Z.; Feng, K.; Xu, A.J. Collaborative optimization of rolling plan and enemy dispatching in steel plants. China Metall.
**2019**, 29, 75–80. [Google Scholar] - Cowling, P.; Ouelhadj, D.; Petrovic, S. A multi-agent architecture for dynamic scheduling of steel hot rolling. J. Intell. Manuf.
**2003**, 14, 457–470. [Google Scholar] [CrossRef] [Green Version] - Cowling, P.; Rezig, W. Integration of continuous caster and hot strip mill planning for steel production. J. Sched.
**2000**, 3, 185–208. [Google Scholar] [CrossRef] - Zheng, Z.; Liu, Y.; Chen, K.; Gao, X.Q. Unified modeling and intelligent algorithm of production planning for the process of steelmaking, continuous casting and hot rolling. J. Univ. Sci. Technol. Beijing
**2013**, 35, 687–693. [Google Scholar] - Luo, Z.H.; Tang, L.X. Modeling and solution to integrated production and logistics planning of steel making and hot rolling. J. Manag. Sci. China
**2011**, 14, 16–23. [Google Scholar] - Zhang, C.S.; Li, K.T. Optimization Model and Algorithm for Lot Planning Coordination between Steelmaking and Hot Rolling. Inf. Control
**2017**, 46, 122–128. [Google Scholar] - Li, K.T.; Guo, D.F. Model and algorithm for hot-rolling batch plan based on constraint satisfaction. Control Decis.
**2007**, 22, 389–393. [Google Scholar] - Tang, L.X.; Liu, J.Y.; Rong, A.Y.; Yang, Z.H. Modelling and a genetic algorithm solution for the slab stack shuffling problem when implementing steel rolling schedules. Int. J. Prod. Res.
**2002**, 40, 1583–1595. [Google Scholar] [CrossRef] - Singh, K.A.; Srinivas; Tiwari, M.K. Modelling the slab stack shuffling problem in developing steel rolling schedules and its solution using improved Parallel Genetic Algorithms. Int. J. Prod. Econ.
**2004**, 91, 135–147. [Google Scholar] [CrossRef] - Han, K.H.; Zhang, Q.; Shi, H.B.; Zhang, J.Y. An Improved Compact Genetic Algorithm for Scheduling Problems in a Flexible Flow Shop with a Multi-Queue Buffer. Processes
**2019**, 7, 302. [Google Scholar] [CrossRef] [Green Version] - Hu, K.J.; Zhu, F.X.; Chen, J.F.; Noda, N.; Han, W.Q.; Sano, Y. Simulation of Thermal Stress and Fatigue Life Prediction of High Speed Steel Work Roll during Hot Rolling Considering the Initial Residual Stress. Metals
**2019**, 9, 966. [Google Scholar] [CrossRef] [Green Version] - Yang, Y.J.; Jiang, Z.Y.; Zhang, X.X. Mathematical model and solving algorithm for the lot planning of slab hot rolling. J. Univ. Sci. Technol. Beijing
**2012**, 34, 457–463. [Google Scholar] - Lu, Y.M.; Xu, A.J.; He, D.F.; Tian, N.Y. Hot-rolling batch planning method available to improve DHCR proportion. J. Univ. Sci. Technol. Beijing
**2011**, 33, 1301–1306. [Google Scholar] - Zhao, X.C.; Bai, H.; Shi, Q.; Lu, X.; Zhang, Z.H. Optimal scheduling of a byproduct gas system in a steel plant concerning the time-of-use electricity pricing. Appl. Energy
**2017**, 195, 100–113. [Google Scholar] [CrossRef]

**Figure 11.**(

**a**) TOU electricity pricing not considered (

**b**) TOU electricity pricing considered Convergence curve resulted from genetic algorithm iterations.

Jump down/mm | 0~25 | 26~55 | 56~90 | 91~150 |
---|---|---|---|---|

Penalty | 1.0 | 3.0 | 5.0 | 7.0 |

Factor Change | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Penalty | 10 | 16 | 20 | 24 | 30 |

Jump up/mm | 0~0.06 | 0.0601~0.15 | 0.1501~0.24 | 0.2401~0.45 | 0.4501~3.00 |

Penalty | 200.00 | 300.00 | 400.00 | 800.00 | 1000.00 |

Jump down/mm | 0~25 | 26~55 | 56~90 | 91~150 | 0.4501~3.00 |

Penalty | 400.00 | 600.00 | 800.00 | 1000.00 | 2000.00 |

Electricity Price Range | Period | Electricity Price, Yuan/kWh |
---|---|---|

Peak periods | 08:00-11:00, 16:00-21:00 | 0.76 |

Flat periods | 06:00-08:00, 11:00-16:00, 21:00-22:00 | 0.53 |

Trough period | 22:00-06:00 (next day) | 0.31 |

Slab Number /Piece | Preparation Method | Number of Rolling Units /Piece | Penalty Value |
---|---|---|---|

240 | Human interaction | 5 | 31,266 |

Model-based optimization (not considering TOU electricity pricing) | 5 | 22,029 | |

Model-based optimization (considering TOU electricity pricing) | 5 | 26,238 |

© 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**

Hu, Z.; He, D.; Song, W.; Feng, K.
Model and Algorithm for Planning Hot-Rolled Batch Processing under Time-of-Use Electricity Pricing. *Processes* **2020**, *8*, 42.
https://doi.org/10.3390/pr8010042

**AMA Style**

Hu Z, He D, Song W, Feng K.
Model and Algorithm for Planning Hot-Rolled Batch Processing under Time-of-Use Electricity Pricing. *Processes*. 2020; 8(1):42.
https://doi.org/10.3390/pr8010042

**Chicago/Turabian Style**

Hu, Zhengbiao, Dongfeng He, Wei Song, and Kai Feng.
2020. "Model and Algorithm for Planning Hot-Rolled Batch Processing under Time-of-Use Electricity Pricing" *Processes* 8, no. 1: 42.
https://doi.org/10.3390/pr8010042