**1. Introduction**

As a key link in steel production, hot rolling refers to a process in which the steel slabs sustain heating in a furnace, rough rolling, and fine rolling before becoming steel products (Figure 1). The main task of the batch-processing planning of hot rolling is to determine an appropriate sequence for the processing of multiple slabs, to achieve low power consumption, low cost of stack transfer, high efficiency, and high product quality, while the technical requirements of rolling are met [1]. Throughout the steel production process, the batch-processing plan of hot rolling directly determines the product quality and production efficiency of the steel plant. In the past, in most studies on the batch-processing planning of hot rolling, the penalty items relating to the differences (such as width, thickness, hardness, and delivery time) were only taken into consideration among adjacent slabs, while the differences in power consumption between slabs of difference sizes were ignored [2–4]. In fact, apart from guaranteeing product quality and production efficiency, a sound processing plan of rolling also served to reduce production cost through electricity cost cut-backs, thereby maximizing the economic benefits [5].

Throughout actual hot rolling, most electricity is used to drive the motor of the rolling mill and power various auxiliary electrical devices. The power consumption in hot rolling is closely related to the sizes and conditions of the devices, process parameters, as well as the types and sizes of the steel products [6]. Under the condition of time-of-use (TOU) electricity pricing, the sequence with which the slabs are processed has a major impact on power consumption. In the research area of hot rolling, only few studies were carried out regarding the impact investigation of TOU electricity pricing on the batch-processing planning of hot rolling. Most studies were focused on methods of better connection and matching during steelmaking, of continuous casting, and hot rolling processes. A charge-rolling

plan coordination model based on the optimal furnace charge plan and optimal rolling plan models was presented [7,8], in which the tabu search algorithm was proposed for the corresponding solution. A steelmaking continuous-casting hot-rolling integrated planning model was proposed to enable an effective connection among the rolling unit plan [9], the furnace charge plan, and the casting plan. An integrated model on the production and logistics planning level was constructed [10], based on an analysis of the characteristics of steelmaking and hot rolling processes, as well as on the transition between the two processes, where the constraints of capacity and the conflicts between the two stages were taken into consideration. A mathematical model was presented for batch-processing optimization in the steelmaking and hot rolling processes [11]. This model was proposed for the model solution with the neighborhood search algorithm based on heuristic rules. The batch-processing planning problem of hot rolling was treated as a constraint compliant problem [12], while the vehicle routing problem with soft time windows (VRPSTW) constraint of uncertain plan number was constructed to satisfy the model. In certain studies, the effects of other factors on the rolling plan of hot-rolling planning were taken into consideration. As an example, the problem of slab stack transfer in the rolling plan was taken into consideration [13,14], whereas the solution was conducted with the improved genetic algorithm, resulting in reduced handling costs. The impact of TOU electricity pricing on the rolling planning was taken into consideration [6], but in the proposed model, the power consumptions of individual rolling units were only considered, instead of the influence of the rolling sequence on the electricity cost under TOU electricity pricing. Mao et al. [5] considered the influence of TOU electricity pricing when constructing a rolling unit as the production load unit, and a multi-objective optimization model for hot rolling was established and a multi-objective optimization algorithm was applied to solve this problem. However, all the goals were classified into one objective function in this paper.

In summary, in most previous studies, optimal rolling-plan models were proposed to be established, to produce products with the highest possible quality and production efficiency prior to the delivery deadline, indifferently to electricity cost reduction throughout production. Because the main characteristic of genetic algorithms is to directly operate the structural objects, only the objective function and the corresponding fitness functions that affect the search direction are needed. Therefore, the genetic algorithm provides a method for solving complex system problems. It does not depend on the specific fields and types of problems, and has strong robustness, so it has been widely used in many scientific fields. [15]. On the basis of previous studies, in this paper, a model for batch-processing planning of hot rolling under TOU electricity pricing was presented, resulting in a method of solving the model with an improved genetic algorithm.

**Figure 1.** Flow chart of the rolling process.
