SurveyA review of planning and scheduling methods for hot rolling mills in steel production
Introduction
Steel is a widely used material in different industries (Smil, 2016). Numerous indicators relate steel production with the economic viability of countries (Dunham, 2018). Even though steel production is an old and important industry, it still has problems. According to the 2017 OECD steel market developments report (Mercier, Hotsuka, & Silva, 2017), a large number of steel companies may be operating below the sustainable profit levels.
One strategy of improving this situation is via digitalization (Uygun and Ilie, 2018, Parviainen et al., 2017, Herzog et al., 2017, Scholze, 2018). More and more steel manufacturing companies are stepping up their digitalization efforts (Kloeckner, 2017, Reifferscheid et al., 2017). Using new digitalization technologies will help steel manufacturers to achieve their most wanted goals: increase their plant efficiency and plant availability to produce more products in less time and at lower costs (Maggiolino, 2017).
Mathematical optimization of scheduling systems in steel manufacturing will help reaching these goals (Tang et al., 2001, Dios et al., 2016, Dutta et al., 2018). Better scheduling of the hot rolling mill will have a direct impact on punctuality, efficient use of raw materials and energy, the robustness of the production process against small perturbations, and a reduction of low-quality or downgraded output. As a result, the application of mathematical optimization techniques to steel manufacturing has received a substantial amount of attention, both in academia and in industry.
Unfortunately, there are not enough review articles about the mathematical optimization of scheduling in steel manufacturing. In particular, even though steel manufacturing has been reviewed in general, such as in Tang et al., 2001, Dutta and Fourer, 2001, Xiang and Tang, 2010, Isoherranen and Kess, 2016, there are no review articles targeting specific product lines such as continuous casting or hot rolling mill. This is particularly striking, as the hot rolling mill is an important part of steel manufacturing (Sharp, 1983). To fill this gap – the lack of reviews focusing on the diverse published approaches towards the mathematical optimization of hot rolling mill scheduling – this review surveys 90 articles for scheduling at hot rolling mills from 1989 to 2020 (Fig. 1).
This study is a comprehensive review about steel hot rolling mill scheduling from an operations research point of view, but some seemingly obvious articles are not included in the study for the following reasons: (1) the articles are not about steel hot rolling mill but are about aluminum or other metals (de Ladurantaye, Gendreau, & Potvin, 2007). (2) the articles are not about scheduling of hot rolling mill operations but about optimization of mechanical or metallurgical components of hot rolling mills (Hernández Carreón et al., 2007, dong QI et al., 2012). (3) the focus of the articles is more about general shop optimization (Herr & Goel, 2016) or the investigation of steel production problems (Windt & Hütt, 2011). (4) the articles are about defect detection in hot rolling mill using image processing and other techniques (He, Xu, & Zhou, 2019).
Table 1 shows the categorization of the reviewed articles. Some articles are purely theoretical (Balas, 1989, Berezin et al., 2016, Alidaee and Wang, 2012, Balas, 2007), as they formulate the problem and give some suggestions. Others are simulation studies (Xu et al., 2014, Storck and Lindberg, 2007) or give background information about proposed solutions such as, (Cowling et al., 2004, Ouelhadj et al., 2004). Nonetheless, most of the reviewed articles are structured as follows: (i) steel production, hot rolling mill problem and constraints are explained, (ii) mathematical model is defined, (iii) proposed solution method is explained, (iv) proposed method is compared with other algorithms and/or manual scheduling in numerical experiments.
Following this structure, the remainder of this paper is organized as follows: typical structure of steel factories and their product lines are introduced in Section 2. Hot rolling mill problem is defined in Section 3. Problem constraints are given in Section 3.3. Solution methods used among the reviewed articles are given in Section 4. Summary information about the experiments conducted by the reviewed articles is given in Section 5.
Our strategy for organizing the material is the following: we start from the generic step-wise representation of steel production. From each research article, we extract the specific (sub-)system of this process investigated, together with the optimization methods. Due to the diversity of the optimization methods, programming languages, choice of systemic features included in the analysis, and choice of the objective function, it is challenging to transfer and compare the findings between research articles in this field. Thus, we have organized our comparison across a range of tables, allowing the reader to immediately identify, for example, all publications using the finishing temperature as a constraint or all publications applying multi-objective solution methods.
Reviewed articles optimize different product lines (Table 2), where the most common scenario is the optimization of two product lines, namely continuous casting and hot rolling mill together. Similarly, only some articles optimize both parts of the hot rolling mill problem, warm up and coming down (see Table 3). Again, most of the articles only model for a rolling unit (1-2 days for work) instead of 2 to 4 weeks rolling campaign (Table 4). Approaches also differ via the included constraints and the optimization criteria (see Table 5). Frequently used optimization criteria are width, thickness and hardness. The type and the amount of detail in the constraints and the optimization criteria, in turn, define the aimed level of realism in the respective study. Most of the proposed solution methods are single-objective optimization methods (Table 6). The most common problem formulation and solution methods are the traveling salesman problem variants with heuristic methods (see Table 1 and Table 7). Additionally, the studies differ substantially in their use of empirical data. Most of the articles claim to use real production data and compare their approaches with the human experts (Table 9). Unfortunately, due to the metrics used and the non-availability of experimental data, the proposed approaches are not comparable. Another interesting point is that most of the articles use out-of-date computers for their numerical experiments (Table 8).
An additional role of such a review is to facilitate access to the often diverse terminology of steel manufacturing. Therefore, alternative terminologies found in the literature are pointed out in many places.
Section snippets
Steel factory product lines
For our purposes, the steel production can be categorized into five production segments (or ’product lines’), as outlined in Fig. 2: (1) primary steel making, (2) secondary steel making, (3) continuous casting, (4) hot rolling mill, and (5) further operations.
Primary steel making refers to making liquid iron from scrap metals or iron ores. The iron ores are smelted in blast furnaces while the scrap metals are smelted in electric arc furnaces. The primary advantage of an electric arc furnace is
Steel factory hot rolling mill problem definition
The function of the hot rolling mill is based upon the simple mechanism of using rolls to press steel slabs and reduce their thickness, as illustrated in Fig. 3. Before slabs can be rolled into hot rolling mills, slabs should be heated to the deformation temperature using reheating furnaces. Achieving this heating temperature is a major constraint of this problem. Immediately using the slabs from the continuous casting system instead of storing them in the slab yard will reduce the need for
Multi-objective vs. single-objective optimization
Since there are conflicting constraints in the hot rolling mill model, it is clearly a multi-objective optimization problem. There are two approaches for solving multi-objective optimization problems among the reviewed studies.
The first approach is the transformation of the multi-objective optimization problem to a single-objective optimization problem, then using algorithms designed for single-objective optimization problem, such as genetic algorithms and tabu search. Genetic algorithms and
Computer and programming language information
Computer and programming language information is summarized in Table 8. According to this table, most of the experiments are conducted on comparatively old computers. Only 7 articles used computers with more than 4 Gb of RAM and relatively modern CPUs, Intel i5 (introduced in 2009) and Intel i7 (introduced in 2008) in their experiments.
For the programming languages and tools, C++ is the first choice among the reviewed articles. Then, ILog Studio, CPLEX Solvers, Matlab and C# were the second
Conclusions
In conclusion, this study reviewed 90 hot rolling mill scheduling articles from 1989 to 2020. Reviewed articles are summarized using 10 tables and 4 figures. Based on our review of this set of publications, the following future research directions are proposed:
- (1)
Comparisons between the different scientific articles are currently near impossible. Every article uses different metrics and different datasets in the implementations. Some studies such as (Chen et al., 2008) use vehicle routing
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