Intelligent optimization method for the dynamic scheduling of hot metal ladles of one-ladle technology on ironmaking and steelmaking interface in steel plants

1.   Introduction

As a typical process industry, iron and steel production has the characteristics of multiple processes, high dynamics, strong coupling, and multiple uncertainties, which bring a huge challenge to production scheduling. The one-ladle technology uses the same hot metal ladle in blast furnace tapping, hot metal transportation, hot metal desulfurization, and converter charging. It is the interface technology of the ironmaking and steelmaking section that has arisen in recent years [1]. In this technology, the hot metal ladle functions in hot metal storage and transportation and can directly carry out hot metal pretreatment and charge to the converter. It has remarkably advantages in reducing fixed investment, improving operation efficiency, saving operating costs, and effectively utilizing the physical heat of the high-temperature hot metal. The turnover time of the hot metal ladle is one of the important indicators in measuring the use effect of the hot metal ladle under the one-ladle technology. Therefore, reducing the turnover time of hot metal ladles and improving the utilization rate of hot metal ladles are of great significance for iron and steel enterprises in low-carbon energy conservation and emission reduction, enhancement of technical and economic indicators, and reduction in production costs [2–3].

Hot metal ladle scheduling, especially dynamic scheduling, can cope with the complex situation of steel production, such as various disturbances, and has a key role in one-ladle technology. Meanwhile, the dynamic scheduling of hot metal ladles is the basis for the optimization scheduling of the whole steel plant. The hot metal ladle scheduling problem on the ironmaking and steelmaking interface can be divided into the hot metal ladle distribution and half-ladle transfer problem at the iron plant side, the transportation scheduling problem on the ironmaking and steelmaking interface, and the dynamic scheduling problem at the steel plant side. Given its relation to the prediction of iron production and tapping control of the blast furnace, the scheduling at the iron plant side is generally discussed separately. Research on the ironmaking and steelmaking interface usually focuses on hot metal ladles that need to be transported. In recent years, increasing attention has been paid to the operation optimization of hot metal ladles. Simulation optimization has been widely used, such as the mathematical model of the hot metal ladle turnover under the one-ladle technology on the ironmaking and steelmaking interface based on queuing theory [4]. The ladle turnover under the one-ladle technology was abstracted as a queuing system with system capacity constraints, and a theoretical calculation model of ladle turnover number based on the queuing theory of limited system capacity was adopted [5]. The module was decomposed according to the mechanism and function, and a hot metal scheduling simulation model for a torpedo car based on a hybrid system was established [6]. A mathematical model of transportation scheduling was also generated for the supply and demand balance of hot metal supply management and locomotive transportation with transshipment, locomotive task, and route configuration [7]. In view of the disturbance in the molten iron logistics, a molten iron scheduling simulation system based on a visual graphical editor platform was developed [8]. A model was also established for the hot metal distribution in blast furnaces. In this model, the quantity of hot metal ladles was replaced by the allocated hot metal weight. First, the integer solution of a hot metal ladle was obtained by the enumeration method, and the exact quantity solution was then obtained based on the two-step binary search algorithm [9]. Some works were also performed on the modeling and simulation of the dynamic operation of the ironmaking and steelmaking interface. Li et al. [10] applied the queuing theory to analyze the hot metal ladle turnover mode of the blast furnace (BF)–basic oxygen furnace (BOF) section. Lu and Luo [11] realized a simulation system of the molten iron transportation logistics on the basis of the plant simulation platform. Wang et al. [12] used the plant simulation software in a logistics simulation model of ironmaking plants under the blast furnace–converter mode. However, most of the above studies focused on the simulation modeling of torpedo cars and locomotive transport models on the ironmaking and steelmaking interface. The goal is the simulation analysis of the overall operation mode and the number of hot metal ladles on the ironmaking and steelmaking interface; however, the scheduling optimization of molten ladles in the steel plant cannot be achieved.

In dynamic scheduling in steel plants, the scheduling model relying on human experience cannot meet the dynamic scheduling needs of enterprises because of the increasingly prominent contradiction between the organization processes of various specifications orders with small batch and large scale of production [13–17]. Most of the existing research focused on the dynamic scheduling problem in the steelmaking–continuous casting stage and studied the dynamic scheduling strategy in steel plants [18–25]. The above methods can solve the dynamic scheduling problem of steel plants to a certain extent. However, they do not consider the hot metal ladle entering the steel plant, the hot metal pretreatment stage, and the empty ladle leaving the plant. In actual steel production, the dynamic scheduling of hot metal ladles is the premise of the whole steel plant scheduling. The arrival of heavy ladles and the pretreatment schedule of hot metal ladles provide a guarantee of hot metal resources for the implementation of the converter plan. The timely delivery of empty ladles creates a resource condition for carrying hot metal for the one-ladle technology on the ironmaking and steelmaking interface, ensuring the stable and efficient operation of the interface. Therefore, the dynamic scheduling of hot metal ladles in the steel plant has a great effect on the production rhythm, energy consumption, cost of the entire steel process, and efficiency of one-ladle technology. In addition, the above research focused on the dynamic scheduling of specific disturbances. Studies on disturbance identification and classification processing are lacking.

Owing to the lack of support for the hot metal ladle scheduling model, the actual operation is usually manually scheduled based on experience. In general, heavy ladles have priority to enter the steel plant to ensure the supply of hot metal. Empty ladles are placed on hold until the transport capacity is idle. The number and turnover efficiency of hot metal ladles put into operation are difficult to optimize. Therefore, this study takes the hot metal ladle turnover of a steel plant as a research object and proposes a data-driven dynamic scheduling method. A dynamic scheduling model of hot metal ladles for the batch converter plan is established. Prescheduling is carried out according to the production demand, and scheduling is adjusted adaptively according to the supply and demand relationship of molten iron. The dynamic scheduling strategy under the disturbance scenario and the data-driven adaptive matching method of the scheduling strategy are designed to realize the autonomous identification of industrial scene disturbances and real-time scheduling and form the real-time optimization and adjustment of the schedule for the main dynamic events.

2.   Problem description

The operation of the hot metal ladle in a steel plant using the one-ladle technology on the ironmaking and steelmaking interface is mainly employed at the stage of hot metal pretreatment and converter process. Fig. 1 shows the operation process of the hot metal ladle in the steel plant. After the heavy ladle enters the steel plant, it is directly desulfurized at the Kambara Reactor (KR) stage and then passes through the dephosphorization or decarburization converter for steelmaking through the transportation stage. When the hot metal is charged into the converter, the empty ladle is transported out of the steel plant. The one-ladle technology has advantages in reducing the temperature drop of hot metal, which depends on the efficient turnover of hot metal ladles.

Fig. 1.  Operation process of the hot metal ladle in a steel plant.

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The dynamic scheduling of hot metal ladles aims to control the operation and turnover behavior of heavy ladles and empty ladles in each stage of the stage based on the converter plan. It can be described as follows: P hot metal ladles operate on J stages to ensure the processing of I charges in the converter plan. The premise is to meet the constraints of resources and production process, determine the operation time and machines of hot metal ladles, and make adaptive adjustments to the schedule according to the dynamic changes in the production environment to realize the optimal scientific allocation and reasonable dynamic adjustment of hot metal ladles.

Here, an intelligent method for the dynamic scheduling of hot metal ladles in steel plants is established. An optimization model for the dynamic scheduling of hot metal ladles is developed. With the minimum average turnover time of hot metal ladles as the optimization objective, prescheduling is first carried out according to the accepted batch converter plan in the upper layer. The schedule is then adjusted adaptively based on the supply and demand relationship of hot metal ladles in the middle layer to improve the enforceability of the scheme. Finally, hot metal ladle arrival and operation, intelligent perception, and autonomous industrial scene disturbance recognition of the industrial scene are realized according to the tracking of key data such as the converter plan. Through the adaptive configuration of the dynamic scheduling strategy and the adjustment of the schedule, the optimal scientific allocation of hot metal ladle resources and the dynamic and reasonable adjustment under different scenarios are realized in the lower layer to effectively control the operation and turnover behavior of hot metal ladles in various stages of heavy and empty ladles. The logical structure of the data-driven three-layer intelligent dynamic scheduling method is shown in Fig. 2.

Fig. 2.  Logic structure of the dynamic scheduling of hot metal ladles in steel plants.

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3.   Mathematical model

3.1   Symbol definition

The definition of the symbols used in establishing static scheduling models is shown in Table 1. In the dynamic scheduling model under disturbances, the following parameters are added according to the symbol definition of the scheduling model, as shown in Table 2.

Table  1.  Symbol definition of the scheduling model

Indexes and sets
$i$	Index of charges, $i=1, 2, \cdots ,I$.
$j$	Index of stages, $j=1, 2, \cdots ,J$.
$p$	Index of hot metal ladles, $p=1, 2, \cdots ,P$.
${M}_{j}$	${M}_{j}$ is the machine set of stage j. ${|M}_{j}|$ is the total number of machines at stage j.
${M}_{j,m}$	The $m$th machine at stage j.
Ω	Set of all charges.
Parameters
${T}_{i,j}$	Processing time of charge $i$ at stage $j$.
${T}_{j,m}^{\mathrm{a}}$	The earliest available time of the $m$th machine at stage $j$.
Decision variables
${t}_{i,j}^{\mathrm{s}}$	The starting time of charge $i$ at stage $j$.
${x}_{i,j,m}$	0/1 variable that is equal to one only if charge $i$ is processed on $m$th machine at stage $j$.
${y}_{{i}_{1},{i}_{2},j,m}$	0/1 variable that is equal to one only if charge ${i}_{1}$ is processed on $m$th machine at stage $j$ before charge ${i}_{2}$.
${t}_{p}^{\mathrm{s}}$	The time of entering steel plant of hot metal ladle $p$.
${t}_{p,j}^{\mathrm{s}}$	The time of entering stage $j$ of hot metal ladle $p$.
${t}_{p,j}^{\mathrm{e}}$	The time of leaving stage $j$ of hot metal ladle $p$.
${t}_{p}^{\mathrm{e}}$	The time of leaving steel plant of hot metal ladle $p$.
${z}_{i,p}$	0/1 variable that is equal to one only if charge $i$ matches hot metal ladle $p$.

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Table  2.  Symbols added to the dynamic scheduling model

Parameters
${t}_{i,j}^{\mathrm{s}'}$	The starting time of charge $i$ at stage $j$ in the schedule being executed.
${x}_{i,j,m}'$	0/1 variable that is equal to one only if charge $i$ is processed on $m$th machine at stage $j$ in the schedule being executed.
${y}_{ {i}_{1},{i}_{2},j,m}'$	0/1 variable that is equal to one only if charge ${i}_{1}$ is processed on machine $m$ in stage $j$ before charge ${i}_{2}$ in the schedule being executed.
${t}_{p}^{\mathrm{s}'}$	The time of entering steel plant of hot metal ladle $p$ in the schedule being executed.
${t}_{p,j}^{\mathrm{s}' }$	The time of entering stage $j$ of hot metal ladle $p$ in the schedule being executed.
${t}_{p,j}^{\mathrm{e}'}$	The time of leaving stage $j$ of hot metal ladle $p$ in the schedule being executed.
${t}_{p}^{\mathrm{e}'}$	The time of leaving steel plant of hot metal ladle $p$ in the schedule being executed.
${z}_{i,p}'$	0/1 variable that is equal to one only if charge $i$ matches hot metal ladle $p$ in the schedule being executed.
$\;{\beta }_{p}$	The operation status of hot metal ladle $p$ in the schedule being executed. If hot metal ladle $p$ does not enter the steel plant, then ${\beta }_{p}=0$. If hot metal ladle $p$ is in the steel plant, then $\; {\beta }_{p}=1$. If hot metal ladle $p$ has left the steel plant, then $\; {\beta }_{p}=2$.
$\; {\beta }_{p,j}$	The operation status of hot metal ladle $p$ in stage $j$ in the schedule being executed. If the hot metal ladle $p$ does not enter stage $j$, then $\; {\beta }_{p,j}=0$. If hot metal ladle $p$ is at stage $j$, then $\;{\beta }_{p,j}=1$. If hot metal ladle $p$ has been out of stage $j$, then $\; {\beta }_{p,j}=2$.
${\gamma }_{i,j}$	The operation state of charge $i$ in stage $j$ in the schedule being executed. If charge $i$ does not enter stage $j$, then ${\gamma }_{i,j}=0$. If the charge $i$ is in stage $j$, then ${\gamma }_{i,j}=1$. If charge $i$ has been out of stage $j$, then ${\gamma }_{i,j}=2$.

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3.2   Dynamic scheduling model

In consideration of constraints such as the production organization of hot metal ladle operation, the scheduling models are established with the minimum average turnover time of hot metal ladles in the steel plant as the optimization objective, including the prescheduling model for demand-oriented executable schedule formulation and dynamic scheduling model for dynamic adjustment.

(1) Prescheduling model.

The optimization objective of the model is to minimize the average turnover time of the hot metal ladle, as shown in constraint (1):

The constraints of the production organization type are as follows.

The charge can only be processed once in the stage, as shown in constraint (2):

A sequential processing relationship occurs between two charges processed on the same machine, as shown in constraint (3):

Each machine can only process one charge at the same time, as shown in constraint (4):

To ensure the reasonable connection and matching of the operation time, the starting time of the next operation should not be earlier than the ending time of the previous operation plus the transportation time, as shown in constraint (5):

The machine has the earliest available time, and the starting time of the charge on the machine must not be earlier than its earliest available time, as shown in constraint (6):

The time of entering the stage of the hot metal ladle must not be later than the starting time of the corresponding charge at the stage, and the time of leaving the stage of the hot metal ladle must not be earlier than the ending time of the charge at the stage, as shown in constraints (7) and (8):

Decision variable constraints are shown in constraints (9)–(16):

(2) Dynamic scheduling model.

The objective of the dynamic scheduling model is the same as that of the scheduling model. According to the scheduling model, its constraint conditions should also meet the requirement that the completed charge operations are not allowed to be changed. The additional constraints are shown in constraints (17)–(23).

4.   Solution method

The implementation of dynamic scheduling for hot metal ladles is shown in Fig. 3. The converter plan is automatically identified to obtain a new batch plan. According to the accepted batch converter plan, the hot metal ladle turnover is prearranged based on the rules of processing sequence determination and machine selection. Using the prediction of the arrival rhythm of the hot metal ladle in the steel plant as a basis, the schedule is appropriately adjusted to form an executable schedule. Finally, the difference between the schedule and monitoring data is compared through the real-time monitoring of the dynamic data of the converter plan, the actual situation of the hot metal ladle entering the plant, and the dynamic information of the whole process of the hot metal ladle in the steel plant. Identification of disturbance and dynamic event type is performed, the dynamic perception of the disturbance driven by the data is realized, and the dynamic scheduling is triggered. Furthermore, the evaluation is carried out on the basis of the impact degree and scope of the dynamic events, and the dynamic event information is transmitted to complete the adaptive matching of the dynamic scheduling strategy and realize the dynamic adjustment.

Fig. 3.  Implementation of dynamic scheduling for hot metal ladles.

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4.1   Prescheduling algorithm for production demands

A heuristic method is used to quickly solve the hot metal ladle scheduling model to meet real-time requirements. The main problems to be solved are machine selection and reasonable optimization of the processing sequence and operation time in each stage. The heuristic method is as follows.

(1) Processing sequence and operation time calculation.

The processing sequence aims to determine the scheduling sequence of all processing tasks. To meet the requirements of the converter plan, the scheduling sequence is determined according to the decreasing order of the starting time ${t}_{i}^{\mathrm{s}}$ of the corresponding processing task of the hot metal ladle.

${t}_{i,j}^{\mathrm{e}}$ is the ending time of charge $i$ at stage $j$. Given that the starting time and processing machine of each processing task on the converter are known, the starting time ${t}_{i,J}^{\mathrm{s}}$ and ending time ${t}_{i,J}^{\mathrm{e}}$ of charging hot metal of the processing task on the converter can be calculated as follows:

Constraint (4) is used to calculate the starting time and ending time of the processing task before the converter:

Given that the time of entering the stage of the hot metal ladle must be earlier than the starting time of the corresponding charge at the stage, and the time of leaving the stage must be later than the ending time of the charge at the stage, constraint (7) is used to determine the time of entering the stage and the time of leaving the stage of the hot metal ladle:

(2) Machine selection algorithm.

Machine determination for processing tasks aims to select KR before the converter process. Constraints (2)–(3) and (5)–(6) must be met; that is, a processing machine is assigned to a processing task at the stage, and two processing tasks processed on the same machine have a processing relationship. In addition, the operation time conflict of processing tasks must be avoided to meet the earliest available time constraint of machines. Therefore, a machine allocation method based on rule priority is adopted to realize a reasonable machine allocation. The machine-matching rule, minimum time conflict rule, and random selection rule are employed. When a clear machine-matching relationship is observed, the machine-matching rule is first used to allocate the machine for the processing task. When multiple machines are available, the processing machine must be allocated according to the minimum time conflict rule. If more than one machine can be selected, then one machine is allocated randomly from the multiple machines as the processing machine for the processing task.

(i) Machine-matching rules.

If there is a corresponding relationship between KR and BOF, then the machine meeting the corresponding relationship should be selected preferentially according to the BOF determined in the converter plan.

(ii) Minimum time conflict rules.

The assumption is that the processing task $i$ is assigned to the machine ${M}_{1,m}$ of KR, and its starting time is ${t}_{i,1}^{\mathrm{s}}$ and ending time is ${t}_{i,1}^{\mathrm{e}}$. The earliest available time for the machine ${M}_{1,m}$ is ${T}_{1,m}^{\mathrm{a}}$. The conflict time of the processing task on the machine ${M}_{1,m}$ is ${C}_{i,1,m}$, which is calculated as follows:

If ${C}_{i,1,m}\le 0$, then there is no time conflict of processing task $i$ on the machine ${M}_{1,m}$ and the processing task does not need to wait between adjacent stages. If ${C}_{i,1,m} > 0$, then the processing task generates a waiting time on the adjacent stage, and the waiting time is the conflict time ${C}_{i,1,m}$. Therefore, the machine with the minimum time conflict is selected from multiple machines, i.e., the machine with the minimum waiting time between adjacent stages for the processing task is selected to minimize the turnover time of hot metal ladles.

(iii) Random selection rules.

When the machine-matching rule is met and multiple processing machines with a minimum time conflict are available, the random selection rule is adopted, i.e., a machine is randomly selected for the processing task from multiple selectable machines.

(3) Heuristic algorithm for batch converter plan.

Step 1: The earliest available time ${T}_{j,m}^{\mathrm{a}}$ of the machine, the processing time ${T}_{i,j}$ in each stage, and the transportation time ${t}_{p,j}$ between stages are initialized.

Step 2: The processing sequence $\beta$ of processing tasks is obtained according to the descending sequence of the starting time of the processing tasks at the converter stage.

Step 3: Set $\beta$ is traversed, and the starting time ${t}_{i,j}^{\mathrm{s}}$ and ending time ${t}_{i,j}^{\mathrm{e}}$ of the processing task are calculated according to formulas (24)–(27). The time of entering the stage $\;\;{t}_{p,j}^{\mathrm{s}}$ and the time of leaving the stage ${t}_{p,j}^{\mathrm{e}}$ of the hot metal ladle are calculated according to formulas (28)–(29).

Step 4: Processing task $i$ to be scheduled is selected according to the processing sequence.

Step 5: If the processing task $i$ is processed in the converter process, then its processing machine is ${M}_{2,m}$ determined in the converter plan, i.e., ${x}_{i,2,{M}_{2,m}}$ = 1. Otherwise, the machine should be allocated according to the machine selection method. Conflict time ${C}_{i,1,m}$ is calculated according to formula (30). If ${C}_{i,1,m} > 0$, then the time conflict occurs, and the conflict is resolved. The starting time ${t}_{i,1}^{\mathrm{s}}$ and ending time ${t}_{i,1}^{\mathrm{e}}$ of the processing task are updated, and the time of entering the stage ${t}_{p,1}^{\mathrm{s}}$ and the time of leaving the stage ${t}_{p,1}^{\mathrm{e}}$ of the hot metal ladle are also updated according to formulas (26)–(29): ${t}_{i,1}^{\mathrm{e}}={T}_{1,m}^{\mathrm{a}}$, ${t}_{i,1}^{\mathrm{s}}={t}_{i,1}^{\mathrm{e}}-{T}_{i,1}$, ${t}_{p,1}^{\mathrm{s}}={t}_{i,1}^{\mathrm{s}}$, and ${t}_{p,1}^{\mathrm{e}}={t}_{i,1}^{\mathrm{e}}$. The earliest available time of machine ${T}_{1,m}^{\mathrm{a}}$ is updated as ${T}_{1,m}^{\mathrm{a}}$ = ${t}_{i,1}^{\mathrm{s}}$.

Step 6: If all the processing tasks in the processing sequence have been scheduled, then Step 7 is performed; otherwise, Step 4 is repeated.

Step 7: According to the decreasing sequence of the starting time of the processing task at the KR stage, the sequence $\gamma$ of the hot metal ladle entering the steel plant is obtained. Set $\gamma$ is traversed, and the time of entering steel plant ${t}_{p}^{\mathrm{s}}$ of the hot metal ladle $p$ corresponding to the processing task is determined according to constraint (4), ${t}_{p}^{\mathrm{s}}={t}_{i,1}^{\mathrm{s}}-{t}_{p,1}$, where ${t}_{p,1}$ is the transportation time of the hot metal ladle $p$ from entering the steel plant to the KR stage.

Step 8: The sequence $\vartheta$ of hot metal ladles leaving the steel plant is obtained by increasing the ending time of charging hot metal. Set $\vartheta$ is traversed, and the time of leaving steel plant ${t}_{p}^{\mathrm{e}}$ of hot metal ladle $p$ corresponding to the processing task is determined according to constraint (4), ${t}_{p}^{\mathrm{e}}={t}_{i,2}^{\mathrm{e}}+{t}_{p,3}$, where ${t}_{p,3}$ is the transportation time of empty ladle $p$ in the steel plant.

Step 9: The schedule of hot metal ladles is obtained as output.

4.2   Schedule adjustment algorithm considering the hot metal supply rhythm

The scheduling of hot metal ladles based on the converter plan may lead to inconsistency between the production rhythm of the steel plant and the actual hot metal supply rhythm. Therefore, the schedule is positively optimized on the basis of the predicted hot metal supply rhythm to improve its enforceability.

Step 1: If the arrival rhythm of the hot metal iron in the schedule meets the actual supply rhythm, then Step 4 is performed; otherwise, Step 2 is conducted.

Step 2: The time of entering steel plant ${t}_{p}^{\mathrm{s}}$ of hot metal ladle is adjusted according to the actual supply rhythm.

Step 3: The schedule at the KR stage is adjusted through the forward optimization method.

Step 3.1: The processing sequence of processing tasks $\delta$ is obtained according to the increasing time of entering steel plant of processing tasks.

Step 3.2: Set $\delta$ is traversed. On the basis of constraints (2)–(7), machine ${M}_{1,m}$ at the KR stage is allocated for the processing task according to the machine selection method, and the starting time ${t}_{i,1}^{\mathrm{s}}$ of the processing task at the KR stage and the time of entering KR stage ${t}_{p,1}^{\mathrm{s}}$ of its corresponding hot metal ladle $p$ are determined, ${t}_{i,1}^{\mathrm{s}}{=t}_{p,1}^{\mathrm{s}}=\mathrm{m}\mathrm{a}\mathrm{x}\left\{{t}_{p}^{\mathrm{s}}-{t}_{p,1},{T}_{1,m}^{\mathrm{a}}\right\}$, where ${t}_{p,1}$ is the transportation time of the hot metal ladle $p$ from entering the steel plant to the KR stage.

Step 3.3: The ending time ${t}_{i,1}^{\mathrm{e}}$ and the time of leaving the steel plant ${t}_{p,1}^{\mathrm{e}}$ of the hot metal ladle are determined. The earliest available time ${T}_{1,m}^{\mathrm{a}}$ of the machine is updated, ${t}_{i,1}^{\mathrm{e}}={t}_{i,1}^{\mathrm{s}}+{T}_{i,1}$, ${t}_{p,1}^{\mathrm{e}}={t}_{i,1}^{\mathrm{e}}$, and ${T}_{1,m}^{\mathrm{a}}$ = ${t}_{i,1}^{\mathrm{e}}$.

Step 4: The hot metal ladle schedule meeting the actual iron supply rhythm is obtained as output.

4.3   Dynamic scheduling algorithm with different scheduling strategies

During the execution of the schedule, the dynamic scheduling model and algorithm are enabled according to the real-time perception and identification of disturbance events. Given that different dynamic events have different degrees of the operation of the hot metal ladle in the dynamic scheduling algorithm, three scheduling strategies for different dynamic events, namely, time flexibility fine-tuning, machine exchange, and rescheduling, are designed according to the influence degree and scope of the disturbance.

(1) Solution method based on time flexibility strategy.

The time flexibility before converters can be used to respond to dynamic events with small time changes in the converter plan, namely, small disturbance events. When the change in the converter plan is mainly advanced or delayed by 5 min, the flexibility of the hot metal ladle operation time is used to respond. The matching relationship between the hot metal ladle and KR is not changed, and the disturbance is absorbed only by adjusting the transportation time of the hot metal ladle in each stage. The main solution steps of this strategy are as follows.

Step 1: Processing task set $\; \beta$ with the starting time change in the converter plan is obtained according to the disturbance identification.

Step 2: The matching relationship between the processing task and machine, starting time and ending time before the converter stage remain unchanged. On the basis of meeting constraint (4), the starting time ${t}_{i,2}^{\mathrm{s}}$ and ending time ${t}_{i,2}^{\mathrm{e}}$ of the processing task are updated according to the new converter plan.

Step 3: Constraint (4) is used to update the time of leaving steel plant ${t}_{p}^{\mathrm{e}}$ of the hot metal ladle $p$ corresponding to the processing task with the converter time change, ${t}_{p}^{\mathrm{e}}={t}_{i,2}^{\mathrm{e}}+{t}_{p,3}$, where ${t}_{p,3}$ is the transportation time of empty ladle $p$ in the steel plant.

(2) Solution method based on machine exchange strategy.

For dynamic events that only affect the processing machine of the hot metal ladle but do not influence its starting time on the converter, i.e., the medium disturbance with the converter time change >5 min but no change in the machine, a solution method based on the machine exchange strategy is used for dynamic scheduling optimization. Local machine adjustment is applied at the KR stage to ensure the stability of the schedule. The main solution steps of this strategy are as follows.

Step 1: If the starting time of the processing task $i$ has not changed at the converter stage, then its processing machine is consistent with the processing machine in the initial schedule, i.e., ${{x}_{i,j,m}=x}_{i,j,m}'$; otherwise, the machine will be allocated according to the machine selection method.

Step 2: According to the descending sequence of the starting time of the KR stage for processing tasks that have not entered the stage, the sequence $\gamma$ of hot metal ladles entering the steel plant is obtained. Set $\gamma$ is traversed, and the time of entering steel plant ${t}_{p}^{\mathrm{s}}$ of hot metal ladle $p$ corresponding to the processing tasks is determined according to constraint (4), ${t}_{p}^{\mathrm{s}}={t}_{i,1}^{\mathrm{s}}-{t}_{p,1}$, where ${t}_{p,1}$ is the transportation time of the hot metal ladle $p$ from entering the steel plant to the KR stage.

Step 3: The sequence $\vartheta$ of hot metal ladles leaving the steel plant is obtained according to the increasing sequence of the ending time of charging hot metal. Sequence $\vartheta$ is traversed. The time of leaving steel plant ${t}_{p}^{\rm e}$ of hot metal ladle $p$ corresponding to the process processing task that has not entered the process is determined according to constraint (4), ${t}_{p}^{\mathrm{e}}={t}_{i,2}^{\mathrm{e}}+{t}_{p,3}$, where ${t}_{p,3}$ is the transportation time of empty ladle $p$ in the steel plant.

(3) Solution method based on a rescheduling strategy.

For the large disturbance events of converter time and machine change, a rescheduling strategy is adopted. The new hot metal ladle schedule is formulated based on the original schedule according to the real-time scheduling information to achieve the global optimization of hot metal ladle turnover. The main solution steps of this strategy are as follows.

Step 1: Processing task $i$ to be scheduled is selected according to the processing sequence.

Step 2: The machine is allocated according to the machine selection method.

Step 3: According to the descending sequence of the starting time of the KR stage for processing tasks that have not entered the process, the sequence $\gamma$ of hot metal ladles entering the steel plant is obtained. Set $\gamma$ is traversed, and the time of enterting steel plant ${t}_{p}^{\mathrm{s}}$ of hot metal ladle $p$ corresponding to the processing task is determined according to constraint (4), ${t}_{p}^{\mathrm{s}}={t}_{i,1}^{\mathrm{s}}-{t}_{p,1}$.

Step 4: The sequence $\vartheta$ of hot metal ladles leaving the steel plant is obtained according to the increasing ending time of charging hot metal. Set $\vartheta$ is traversed. The time of leaving steel plant of hot metal ladle $p$ corresponding to the process processing task that has not entered the process is determined according to constraint (4), ${t}_{p}^{\mathrm{e}}={t}_{i,2}^{\mathrm{e}}+{t}_{p,3}$.

The matching calculation of each scheduling strategy is performed for various disturbance types, and the adaptive matching and real-time adjustment of the dynamic scheduling strategy are realized for the disturbances such as converter plan change, hot metal supply rhythm, and hot metal ladle operation time deviation to ensure the rationality of the hot metal ladle schedule and improve the optimization effect of the operation.

5.   Case analysis and discussion

The above dynamic scheduling method is applied to an actual steel plant to verify the feasibility and effectiveness of the dynamic scheduling model and adjustment strategy. The facility layout is shown in Fig. 4. The steel plant comprises four KR desulfurization stations and five converters. Among them, two converters are dephosphorization furnaces, and three conventional decarburization converters are decarburization furnaces. The one-ladle technology is adopted on the ironmaking and steelmaking interfaces to organize hot metal transportation and pretreatment. The hot metal ladle enters the steel plant from Steel Line 1 or Steel Line 2 for hot metal pretreatment and converter steelmaking. During the duplex process, KR A and KR B enter the dephosphorization furnace D/E. In the case of the nonduplex process, KR C and KR D enter the decarburization furnace A/B/C. After the completion of charging hot metal, the hot metal ladle leaves the steel plant from steel line 1, steel line 2, or steel line 3.

Fig. 4.  Schematic of the operation stage of hot metal ladles in the steel plant.

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For the analysis of the effectiveness of the operation of the model system, the 24 h real-time data of the on-site operation of the system are collected. The operation performance of the hot metal ladle is compared and analyzed based on the model scheduling and dynamic scheduling simulation results. In this period, the batch converter plan has been accepted twice, 90 charges are planned to be produced on the converters, 90 hot metal ladles are planned to be fed, 88 hot metal ladles are actually fed, the converter plan is changed 18 times, and the time of entering steel plant of 90 hot metal ladles deviates from the schedule. The disturbance distribution of all charges is shown in Fig. 5. Only the converter time change is the main disturbance in real industrial production, followed by the machine change. The simultaneous change in the converter time and machine has the lowest probability. In particular, the dynamic scheduling of a certain charge is shown in Table 3. Owing to the formulation of the converter plan, the charge experiences only 13 disturbances of all three types of changes in total. The disturbance model can match the reasonable dynamic scheduling strategy according to the type of disturbance. The adjustment results show the effectiveness of the model and dynamic adjustment strategy in responding to the on-site disturbance. The comparison of scheduling and dynamic adjustment results with production performance in this period shows the optimization of the model, proving that the model can effectively achieve dynamic scheduling according to dynamic disturbance.

Fig. 5.  Stacked bar chart of the disturbance number of 88 hot metal ladles.

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Table  3.  Dynamic scheduling of a certain charge

Scheduling adjustment	Dynamic events	Adjustment strategy	Total turnover time / min
Original scheduling			107
1	7 min delay	Time flexibility	109
2	5 min delay	Time flexibility	106
3	2 min in advance	Time flexibility	103
4	Machine change	Machine exchange	117
5	22 min in advance	Time flexibility	104
6	Machine change	Machine exchange	115
7	Machine change	Rescheduling	113
8	7 min delay	Time flexibility	109
9	5 min delay	Time flexibility	117
10	5 min delay	Time flexibility	127
11	Machine changes	Time flexibility	122
12	5 min delay	Time flexibility	115
13	Machine changes	Rescheduling	118
Actual			120

 | Show Table

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The arrival rhythm of hot metal ladles obtained from the model scheduling meets the expectations, and the comparison of the arrival rhythm between the calculated value and the actual value is shown in Fig. 6. The model predicts that 2–5 ladles will enter the plant every hour, and the actual performance is 2–6 ladles.

Fig. 6.  Hot metal ladle arrival rhythm.

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Fig. 7 shows the comparison among the results of scheduling, rescheduling, and production performance with the time of entering steel plant of hot metal ladles and the ending time of charging hot metal during the converter process. Under the rescheduling, the time of entering steel plant and charging hot metal during the converter process for each charge is more evenly distributed on the time axis compared with the original schedule and actual production. This condition is conducive to stabilizing the production rhythm, reducing the probability of simultaneous processing of adjacent charges, and reducing the work intensity.

Fig. 7.  Comparison among scheduling, rescheduling, and production performance: (a) time of entering steel plant; (b) ending time of charging hot metal.

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The turnover time of model optimization and actual production in this period are shown in Fig. 8. The average turnover time of the original schedule is 115.3 min, and the standard deviation is 6.68 min. The average turnover time of the rescheduling is 119 min, and the standard deviation is 14.79 min. The average turnover time of the actual production performance is 119.4 min, and the standard deviation is 40.82 min. The results show that the model can effectively reduce the turnover time of hot metal ladles. In addition, the standard deviation of the hot metal ladle turnover time is greatly reduced, thus improving the stability of the production rhythm on the ironmaking and steelmaking interface.

Fig. 8.  Comparison between model optimization and production performance.

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6.   Conclusions

The operation efficiency of hot metal ladles in converter steel plants is not high, which restricts the efficient use of the one-ladle interface technology from blast furnace ironmaking to converter steelmaking. Hence, a data-driven dynamic scheduling method for hot metal ladles is proposed in this paper. The main conclusions are as follows.

(1) A dynamic scheduling optimization model of the hot metal ladle, in which the minimum average turnover time of the hot metal ladle is the optimization objective, and the production organization rules are the constraint, is proposed.

(2) The intelligent perception and autonomous identification of disturbances in industrial scenarios are realized by tracking the operation of hot metal ladles and analyzing the key data during operation. The adaptive strategy configuration of dynamic scheduling and the data-driven adjustment of scheduling are used to ensure that the model is adaptive to the industrial scene.

(3) Different dynamic scheduling strategies are applied according to the influence degree and scope of the disturbance. The dynamic adjustment with time flexibility is used for the small disturbance, the machine exchange at the same stage is applied for the local influence, and the adaptive adjustment of the model from the strategy of global rescheduling of hot metal ladle operation is used for the large disturbance. Real-time scheduling of the optimized operation of the hot metal ladle can be achieved by adopting the treatment.

(4) The validity and effectiveness of the dynamic scheduling model and strategy are tested with production data from a steel plant. The results show that the model can effectively reduce the turnover time of hot metal ladles. In addition, the standard deviation of the turnover time decreases significantly, indicating that the model can effectively reduce the fluctuation in the hot metal ladle turnover time and improve the stability of the production rhythm of the ironmaking and steelmaking interface. Moreover, disturbance events occur within 24 h and are handled effectively and reasonably by the model system. This result shows that the method can significantly improve the operation efficiency of hot metal ladles and effectively deal with the disturbance during the operation of hot metal ladles in industrial production.