A review of planning and scheduling systems and methods for integrated steel production

European Journal of Operational Research 133 (2001) 1±20

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Invited Review

A review of planning and scheduling systems and methods for integrated steel production Lixin Tang a, Jiyin Liu b

b,*

, Aiying Rong b, Zihou Yang

a

a Department of Systems Engineering, Northeastern University, Shenyang, People's Republic of China Department of Industrial Engineering and Engineering Management, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, People's Republic of China

Received 14 December 1999; accepted 7 September 2000

Abstract Iron and steel industry is an essential and sizable sector for industrialized economies. Since it is capital and energy extensive, companies have been putting consistent emphasis on technology advances in the production process to increase productivity and to save energy. The modern integrated process of steelmaking, continuous casting and hot rolling (SM±CC±HR) directly connects the steelmaking furnace, the continuous caster and the hot rolling mill with hot metal ¯ow and makes a synchronized production. Such a process has many advantages over the traditional cold charge process. However, it also brings new challenges for production planning and scheduling. In this paper we ®rst give a comparative analysis of the production processes and production management problems for the SM±CC±HR and the traditional cold charge process. We then review planning and scheduling systems developed and methods used for SM± CC±HR production. Finally some key issues for further research in this ®eld are discussed. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Iron and steel industry; Integrated process; Production planning and scheduling

1. Introduction The two oil crises in the 1970s resulted in substantial price increases for mineral fuels and forced the iron and steel industry to develop energy-saving technology. During this period, the continuous casting (CC) technology, which was developed in

* Corresponding author. Tel.: +852-23587100; fax: +85223580062. E-mail address: [email protected] (J. Liu).

the 1950s and could save energy consumption in the production process from hot steel to slab, underwent a rapid growth. The casting ratio increased from 5.6% in 1970 to 25.2% in 1979 [1]. However, the energy-saving feature of the CC process itself is limited. In order to further reduce energy consumption, iron and steel companies in Japan proposed and implemented new techniques such as continuous casting±hot charge rolling (CC±HCR), continuous casting± direct hot charge rolling (CC±DHCR) and continuous casting±hot direct rolling (CC±HDR) in the late 1970s. By the

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early 1980s, it was commonly believed, by the US iron and steel community, that the iron and steel industry in the 1980s would mainly rely on the new CC±HR production processes to improve productivity, reduce energy consumption, and maintain competitiveness in the market. More details of the technology development in iron and steel production can be found in [2±5]. The three new processes, CC±HCR, CC±DHCR and CC±HDR, directly connect the SM, CC and HRM at high temperature and form an integrated and synchronized production. Compared with the traditional cold charge process, the new processes can reduce energy consumption, enhance product quality, increase production output, and shorten waiting times between production stages. Many international iron and steel companies (e.g., Cleveland work of LTV in the US, major iron and steel works of Nippon Steel Corporation, Sumitomo Metal Industries, Kawasaki Steel Corporation, NKK Corporation, and Kobe Steel Limited in Japan, Pohang Iron and Steel Corporation in Korea, and Finaredi works in Italy) have devoted much e€orts to developing new processes to increase hot charge ratio. Hot charge temperature, hot charge ratio and direct hot rolling ratio have become important indexes for evaluating iron and steel process equipment. In China, Shanghai Baoshan Iron and Steel Complex has achieved a hot charge ratio of 62.4% and introduced CC± HCR, CC±DHCR and CC±HDR into its third phase development project. Other iron and steel enterprises such as Wuhan Iron and Steel Company, Shanggang Iron and Steel Company, Jinan Steel Works, and Benxi Iron and Steel Company are also adopting or will soon adopt these new processes. The adoption of the new production processes has brought an urgent need to study and develop integrated production planing and scheduling approaches so that material ¯ow and information ¯ow can be synchronized as much as possible. Planning and scheduling is the key function in the production management. Only with a rational planing and scheduling system, can the potential bene®ts of the new production processes be fully realized. However, because of the di€erences between the traditional cold charge process and the

new hot processes, traditional planning and scheduling methods cannot be completely applied to the situations of CC±HCR, CC±DHCR and CC±HDR. In comparison with the cold charge process, planning and scheduling of CC±HCR, CC±DHCR and CC±HDR not only needs to consider the increased constraints, but also requires a high degree of real-time operation and dynamic adjustment capabilities. In particular, the coordination of di€erent production stages must be considered so as to achieve global optimization for the entire production process. Iron and steel industry is an important basic industry for any industrial economy providing the primary materials for construction, automobile, machinery and other industries. Despite this, planning and scheduling problems in iron and steel production have not drawn as wide attention of the production and operations management researchers as many other industries such as metal cutting and electronics industries. However, the iron and steel industry is capital as well as energy intensive. The importance of e€ective planning and scheduling in this industry on cost and energy reduction and environment protection is by no means less than that in other industries. This paper is intended to stimulate more research in this rich ®eld. In this paper we ®rst introduce the production processes and production management problems in iron and steel production (Section 2), and then review the major integrated planning and scheduling systems developed (Section 3) and the methods used for integrated planning and scheduling in iron and steel production (Section 4). Finally some key issues in the integrated SM±CC± HR planning and scheduling for further research are identi®ed (Section 5) before conclusions are drawn (Section 6). 2. Characteristics of the integrated production process and production management 2.1. Production processes Fig. 1 illustrates the integrated production process of SM±CC±HR. Linkage between the CC and HRM can take four alternative modes

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Fig. 1. Linkage modes between continuous caster and hot rolling mill.

according to the way in which the CC provides slabs for the HRM as well as the temperature of slabs. These linkage modes de®ne the following di€erent production processes. · CC±CCR: Continuous casting±cold charge rolling, also called cold charge for short. In this traditional process, CC slabs are moved to the slab yard instead of directly to the heat furnace. Later, the slab stacks are lifted up and put on the rails in front of the heat furnace and then charged to the heat furnace based on the rolling plans. In general, charge temperature is below 400°C. · CC±HCR: Continuous casting±hot charge rolling. First, tepid and immaculate slabs are sent to the heat preservation pit (or other insulation measures may be taken). Then the slabs are lifted from the pit and charged into the heat furnace in batches for heating, based on the rolling requirements. Finally, the slabs are fed into the HRM for rolling. Generally, charge temperature ranges from 400°C to 800°C. · CC±DHCR: Continuous casting±direct hot charge rolling, also called hot charge for short. Hot and immaculate slabs, which have been cut into ®xed sizes, are directly charged into the heat furnace through transfer rails or cars in the hot state and then the hot rolling process is undertaken. Charge temperature varies from 700°C to 1000°C. · CC±HDR: Continuous casting±hot direct rolling. Without being heated through the heat furnace, hot and immaculate slabs are directly sent

into the HRM after the heater heats the slab edges. In general, slabs are kept over 1100°C before rolling. More direct linkage between CC and HRM means more energy saving and shorter production lead time. The following indexes are therefore often used to indicate the technology level of a steel company. · Hot charge ratio: the percentage for which the quantity of hot charge slabs accounts in the total CC production quantity. · Direct rolling ratio: the percentage for which the quantity of direct rolling slabs accounts in the total CC production quantity. · Hot charge temperature: the temperature of the slabs when they enter the heat furnace in the process of CC±HCR and CC±DHCR. The features and the related e€ects of the above four processes are summarized in Table 1. The ®gures in the last few columns of the table imply great bene®ts of the hot charge and direct rolling processes in cost and energy savings. It can be seen that the CC±HDR technique can achieve the highest savings, followed by CC±DHCR and CC±HCR techniques. Such bene®ts have been realized in the steel works adopting these techniques. For example, after adopting CC±HCR with charge temperature of 700°C to 800°C in June 1992, Baoshan steel works' production cycle reduced from 7 days to about ten hours. The heating time reduction increased the output of the heating furnace by 20±30%. The total energy consumption reduced by 30% and the total cost reduction is 18.4

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Table 1 Summary and comparison of the characteristics and e€ects of the four di€erent processes

million Yuan (RMB) per annum with a yearly production output of 4.6 million tons [6]. More savings have been reported for the more direct processes. Sakai works of Nippon Steel Corporation reduced the total energy consumption by 90% after adopting CC±HDR in July, 1981 [1,7]. LTV's steel works in Cleveland implemented the CC± DHCR process in September 1993 with an annual output of 2 million tons. The saving in operating cost was expected to reach $100 million by the end of 1994 [8,9]. In addition to lead time, energy and cost reductions, the new techniques can also reduce the material loss caused by oxidization. The ®nished product-to-material radio can increase by 1±1.5% [1,6]. 2.2. Production management characteristics Due to the di€erences in the production processes of CC±CCR, CC±HCR, CC±DHCR and CC±HDR, the production planning and scheduling problems in these processes are also di€erent. In particular, great di€erences exist between the problem in CC±CCR and those in the three hot processes (CC±HCR, CC±DHCR and CC±HDR). The major di€erences are discussed as follows: (1) For CC±CCR, planning and scheduling decisions in di€erent production stages are made independently. In each stage, scheduling considers only the production constraints within the stage in question. Planning and scheduling of the three hot processes, on the other hand, aims at the syn-

chronization of CC and HRM and considers not only the production constraints within each stage, but also the constraints associated with the downstream stages. (2) In the CC±CCR process, there is an intermediate slab yard, which is used to reconcile and maintain the coordinated production between steelmaking works and steel rolling mills. The rolling planning and scheduling which is generally o€-line operates on the real slabs stored in the yard. By contrast, no intermediate slab yard exists in the hot processes because of continuous operation under high temperature. Slabs have not been actually produced when the integrated planning and scheduling is established. Therefore, the planning and scheduling which is generally on-line addresses virtual slabs. (3) The integrated processes require that production management should guarantee time and volume consistency of the material ¯ow in the production stages directly connected with one another under high temperature. Only in this way can the production proceed continuously and steadily. (4) In the integrated processes, since the processed objects (heats) are cast and rolled continuously under high temperature, there is a higher requirement for continuous material ¯ow, short ¯ow time, as well as real time and precise planning and scheduling. (5) Since the integrated planning and scheduling operates on virtual slabs, there often exist di€erences in time, volume and quality between

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real slabs and prescheduled virtual slabs. At the same time, in the process of production, there are a great number of uncertain factors. For example, heats arrive dynamically, machines break down randomly, jobs are delayed, and so on so forth. All these make the original plan deviate from the actual situation and thus it is necessary to make dynamic adjustment. As a result, the integrated planning and scheduling is required to have greater dynamic adjustment capability. (6) In the traditional SM±CC±HR process (cold charge process), the SM, CC and HRM belong to two di€erent plants which execute production planning management independently. In the steel rolling mill, each set of rollers rolls slabs from wide to narrow. In the CC±DHCR, the SM, CC and HRM which are integrated into a single entity conform to the uni®ed overall production plan and the steel rolling mill can no longer roll slabs simply according to the sequence from wide to narrow. Instead, it must observe the scheduling from SM to CC. A steel rolling mill operates 24 hours, which are divided into three shifts, and normally produces 5±7 heat±cast±rolls, each of which comprises 6 casts and each cast in turn consists of 4±8 heats. A heat±cast±roll, which is di€erent from a heat, a cast or a roll, is the basic unit in the integrated SM±CC±HR planning and scheduling. Planning and scheduling in the integrated process is a combined lot scheduling problem integrating multiple production stages. Unlike the problem for an independent stage, which focuses on the lot scheduling problem of only the stage considered, the integrated planning and scheduling is a€ected by two sets of constraints simultaneously. First, in the SM±CC stage, major constraints center on steel grade and speci®cation. Steel grade must be consistent and speci®cation must be similar for adjacent heats. Second, in the HRM stage, principal constraints lie in width and thickness. Width should ideally change from wide to narrow and thickness should vary smoothly. All these constraints have to be considered concurrently in arranging the heat±cast±rolls. Comparisons of the production lot planning, production scheduling and material ¯ow characteristics for the four processes are summarized in Tables 2±4, respectively, in Appendix A.

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3. Review of integrated production management systems for SM±CC±HR 3.1. Development of integrated production management systems for SM±CC±HR Japan pioneered in implementing CC±HCR, CC±DHCR and CC±HDR production. In 1988, Japanese Iron and Steel Journal published a special issue on the integrated production process and management for the SM±CC±HR. This event is a signal that the new integrated process would represent the trend for future development in the Japanese iron and steel industry, and it thus received considerable attention from main iron and steel companies in Japan. Many Japanese iron and steel enterprises implemented direct production process and reformed or built the integrated production management system on the basis of this process. Iron and steel companies in other countries also established their own integrated production management systems according to their equipment conditions and operation modes while developing the integrated production process. For example, South Korea has developed an integrated production management system for their CC± HCR and CC±DHCR production. Since 1993, LTV iron and steel company in the US has been developing integrated planning and scheduling systems. Functions and characteristics of all the above systems can be summarized as follows. They can create direct on-line production lot plan for the whole process from converter to rolling mill and establish real time scheduling timetable quickly. When abnormal material ¯ow occurs, they can make rapid dynamic adjustment and execute rescheduling. A brief description of each of these systems is given below. 3.1.1. Nippon Steel Corporation (a) Oita Works of Nippon Steel Corporation [10]. The system implemented in Oita Works achieved consistent management and direct production lot design, throughout the whole process from the blast furnace (BF) to HRM. It creates 48 hours timetables using minute as the basic time unit and shows the results graphically for checking at any time if necessary. When something abnor-

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mal happens to the material ¯ow, it may reestablish the timetable to improve productivity, save energy and material, and reduce production cost to the greatest extent. (b) Sakai Works of Nippon Steel Corporation [7]. In Sakai Works, the consistent production management and quality management are important parts of the management support system for its CC±HDR production with no intermediate steps. First, the common production lot from converter to rolling mill is determined and then based on this, the optimal consistent production plan is created and adjusted dynamically. 3.1.2. Kashima Works of Sumitomo Metal Industries ‰11±13Š The production mode with mixed rolling plans was adopted. Time sequence management function in each stage and rapid plan adjustment feature for operation changes laid the foundation for improving the operation rate and establishing the consistent plan from the CC to HRM. The integrated production management system was developed and introduced in 1995. The main features of the system can be described as follows: (i) When the system was developed, the scheduling task was broken down into the human component and the computer component to alleviate the burden of the mainframe computer and reduce the diculty of the problem. The computer component was further divided into the workstation component and the host computer component. (ii) To mitigate the mismatch between the hot rolling capacity and the CC capacity (the rolling capacity is greater than the CC capacity), the hybrid charge mode was adopted. In this mode, slabs in the slab yard and slabs in the CC±HDR process are rolled alternately to ®ll the rolling gap and lessen the de®ciency of the CC capacity. (iii) The models for the HRM and CC scheduling are constructed separately and a two-stage scheduling strategy (macro-scheduling and micro-scheduling) is applied. 3.1.3. Mizushima works of Kawasaki Steel Corporation ‰14,15Š This system mainly consists of modules for weekly planning, daily planning, real time adjust-

ment and operating management for the entire process from SM to HRM and ®nished product warehouses. Synchronized operation plan and common HEAT±CAST±ROLL are created with 5 days as one unit. The weekly plan is designed to perform the production lot design and implementation. The daily plan is devoted to deciding the production sequence of pieces in the production lot. In order to enhance the system adaptability to the environment, the plan establishment process is properly divided into two parts: one involves the computer system and the other includes human decisions. The plan is created interactively to accomplish real time adjustment and to perform rescheduling. 3.1.4. NKK Corporation (a) Fukuyama Works of NKK Corporation [16± 19]. To save energy, shorten material ¯ow cycle and adapt to the market requirements for high product quality and order variety, it is necessary to develop the consistent production plan and job plan for the comprehensive optimization of the blast furnace±primary rolling automatically, simply and accurately. In this system, the CC and HRM employ a uni®ed production lot design. The system creates and monitors the on-line consistent production plan, and implements the real-time modi®cation and adjustment dynamically. It takes only two minutes to regenerate an 8 hours job plan from BF to primary rolling. The integrated production system, which comprises weekly planning, daily planning and dynamic adjustment, is established to support the CC±HCR and CC±DHCR production. (b) Keihin Works of NKK Corporation [20]. Keihin Works applied the expert system method to develop the comprehensive production control system for the integrated process from the BF to the HRM. This system includes three parts: production planning, workshop scheduling and job control. It achieves automatic scheduling using a three-stage strategy. The planning stages are micro-scheduling generation, rough scheduling generation and machine con¯ict elimination. The system reduces scheduling experience, process and management constraints as well as scheduling rules into the knowledge in the expert system and

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applies them to generate the scheduling scheme. It also adopts the visual graphics technology to display the scheduling scheme and allows revision of the scheduling scheme conveniently. 3.1.5. Kakogawa Works of Kobe Steel Limited ‰21Š In 1994, a production planning and scheduling system for the integrated process of CC and HRM was developed combining expert system and operations research methods. It considers the constraints of the production scheduling process and management in both SM±CC and HR. It also provides evaluation function for the scheduling performance. 3.1.6. Cleveland Steel Works of LTV in the US ‰22Š In November 1993, an integrated scheduling system was developed for CC±DHCR. The CC± DHCR scheduling problem is the common scheduling problem considering production constraints in both CC and HRM simultaneously. The rolling mode of the CC±DHCR also needs a scheduling plan which operates on the virtual slabs instead of the slabs in the slab yard. 3.1.7. Kwangyang Works of POSCO (Pohang Iron and Steel Company) ‰23Š CC ratio has reached 100% in Kwangyang Works. Some 70% of the steel are produced through CC±DHCR or CC±HDR. It has developed the comprehensive process adjustment and job planning system of the CC±DHCR (HIPASS) and thus achieved the goals of saving energy and reducing production cost. HIPASS is a real time production scheduling and monitoring system, which can handle production lot scheduling plan for up to 5 days. It also keeps record of the actual production dynamically through the on-line tracking system and implements the dynamic adjustment of production scheduling. Presently, when creating a convert operation plan including 100 heats, the converter±HRM scheduler requires 3 minutes and the BF±converter±HRM scheduler needs one minute. Therefore, any abnormal production situation can be adjusted in time to ensure that the plan proceeds successfully.

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3.2. The e€ects of the integrated production management for SM±CC±HR The development of the integrated production management systems for SM±CC±HR production has greatly realized the potentials of the integrated SM±CC±HR production process, and therefore generated signi®cant economic pro®ts. 1. Improvement of the direct ratio. At Mizushima Works of Kawasaki Steel Corporation, the direct ratio has gone up from 70% to 99% [14]. 2. Energy-saving. At Mizushima Works of Kawasaki Steel Corporation, the input temperature increases from the initial 300°C to 720°C at present and energy consumption has been reduced to 118 Kcal/t [14]. 3. Increase of the eciency and e€ectiveness regarding the job plan creation. Now it takes NKK only 2 minutes to do rescheduling (while previously, it took nearly 30 minutes to make planning and scheduling in various stages). In the meanwhile, the ®nished product rate has been improved considerably. They adopt the consistent production management system which integrates the heat design and roll plan by the V-lot design system. The system can design multiple cast and roll units at a time [16]. 4. Reduction of the slab inventory and scrap heats. At Kakogawa Works of Kobe Steel, the slab inventory has been decreased by 10,000 tons and the scrap heat ratio has become nearly zero [21]. 5. Increase of the on-time delivery rate. At Kwangyang Works of POSCO, the on-time delivery rate reached 97% after the HIPASS system was put into operation [23]. 6. Improvement of the production pro®t. At Sumitomo Metal Industries, the implementation of the integrated job planning and scheduling system produces the annual pro®t of 1700 million Yen [11]. As mentioned above, the integrated SM±CC±HR production has realized the uni®ed, automatic and multifunctional production management, universally enhanced the scheduling function and strengthened the on-line material ¯ow management function. However, there has not been many published research results on the integrated iron

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and steel production planning and scheduling problems. In addition, all the published papers have the following two limitations in potential applications. (1) They focus mainly on the introduction of the functions and features of the system and lack the description of the key kernel of the system. Therefore, it is dicult for the readers to apply the principles and experiences of these systems in developing integrated planning and scheduling systems for their own companies. (2) They concentrate on arti®cial intelligence (AI) and human±machine interaction methods and pay little attention to optimization methods. As a result, there has not been systematic research on the integrated iron and steel planning and scheduling problems by combining AI and optimization techniques based on integrated SM±CC±HR planning and scheduling models. 4. Review of integrated production planning and scheduling methods for SM±CC±HR processes Up to now, research on the iron and steel production planning and scheduling mainly uses the following four types of methods. (1) Operations research methods: this type of methods establishes the optimization models of the production planning and scheduling problems in SM±CC±HR production processes and obtains optimal or near-optimal solutions by means of accurate or heuristic algorithms. (2) AI methods: this type can be further divided into the following categories. (a) Expert systems: they solve the production planning and scheduling problems through extracting and using schedulers' expertise and experiences and actual process constraints. (b) Intelligent search methods: these are random heuristic search methods including genetic algorithms (GA), simulated annealing (SA) and tabu search (TS) algorithms. (c) Constraint satisfaction methods: many practical production scheduling problems can be reduced to constraint satisfaction problems (CSPs) because they involve complex constraints. In this manner, a satisfactory feasible solution can be achieved with the priority being to meet the constraints. (3) Human±machine coordination methods: these methods create production

schedules through interactive dialogues between the human scheduler and the computer scheduling system. (4) A-teams methods (multi-agents methods): they work through cooperation of multiple models and multiple algorithms to suit the requirements for the complex process constraints and to produce the ideal feasible solutions. Distributed agents can be designed to handle the requirements for multi-stage iron and steel process planning and scheduling. This section reviews research work using these methods in production planning and scheduling problems in iron and steel production processes. 4.1. Operations research (OR)-based methods 4.1.1. OR-based production planning and scheduling in steel rolling mills Solving o€-line iron and steel production planning and scheduling problems through the mathematical programming formulations was proposed by Redwine and Wismer [24] and solutions to the problems were found through dynamic programming algorithms. Wright et al. [25] formulated a multi-objective mathematical model for the scheduling problems determining the hot rolling sequence. For the hot strip scheduling problems in the given rolling plans, Jacobs and Wright [26] presented an objective programming model and related algorithms. Balas and Martin [27] reduced hot rolling production scheduling problems to knapsack constraint problems and prize collecting TSP models and designed a Roll-A-Round program for single roll scheduling. For the material ¯ow scheduling problem and timing coordination from the heat furnace to the HRM, Peterson et al. [28] built a multi-objective mathematical programming model and constructed effective heuristic algorithms. Kosibia and Wright [29] investigated the hot strip sequencing problem and established a TSP model. However, this model only solved the single roll scheduling problem. Tang [30] did systematic research on the production lot planning problem and established general models applicable to various types of steel rolling mills such as strip mills, section steel mills and steel pipe plants. Two solution strategies were also

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proposed to ®nd the solutions to the models: one was a serial approach to the asymmetrical single TSP model and the other was a parallel approach to the multi-TSP model. The single TSP model was employed to arrange a single roll plan while the multi-TSP model was used to establish the lot plan with multiple rolls in a round. By introducing virtual nodes, the multi-TSP was converted into a single TSP which was then solved using GAs [31]. Lopez et al. [32] formulated the hot strip mill production scheduling as a mathematical program model. This model combines traditional TSP problem with a knapsack-type constraint. It considers the limitation of rolling capacity in a turn. This means that there may be orders unscheduled in the result. The selection of the orders to be scheduled was treated as a knapsack problem and the sequencing of selected orders was formulated as TSP. The model was solved using tabu search. 4.1.2. The SM±CC production planning and scheduling Lally et al. [33] developed a mixed integer programming model to solve the CC scheduling problem. However, the model was a simpli®ed one which did not consider the actual complex process and management constraints in the CC process. Tong et al. [34] constructed a sophisticated mixed integer programming model for the two-strand CC scheduling problem which was solved by heuristic GAs. A cast scheduling model was implemented at LTV steel works in 1983 [35,36]. Meil and Lee [37] described production scheduling procedures for the two-strand CC. Lee et al. [22] developed the scheduling system for the two-strand CC and adopted GAs to solve the problem and obtained satisfactory solutions meeting all the constraints. Takahashi [38] addressed the SM±CC scheduling problem using a three-stage strategy: (1) microscheduling, (2) rough scheduling, and (3) machine con¯ict elimination. At the same time, a linear programming model was built through which the optimal scheduling timetable could be obtained. Neuwirth [39] described the key modeling factors concerning the SM±CC scheduling at Gmbh steel works in Austria and established a scheduling model regarding the heat allocation on the machines. However, the optimal mathematical model

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was not formulated for this problem. Tang et al. did a series of studies on SM±CC scheduling problems: First, the mixed integer programming models were established for heat design [40] and cast design [41,42] in the SM±CC lot planning, respectively, and GAs were constructed to ®nd the near-optimal solutions to the models. Second, for the machine con¯ict problems in SM±CC scheduling, a nonlinear mathematical model was created based on the Just-In-Time (JIT) idea [43]. This model could be converted into a linear programming model which may be solved through standard linear programming methods. These three models and the associated algorithms quanti®ed the SM±CC scheduling factors and could be combined fully with the actual production practice. 4.1.3. The integrated production planning and scheduling Kobe Steel Works accomplished integrated management of the material ¯ow concerning both molten iron and molten steel, developed computer programs which could automatically generate appropriate SM material ¯ow plans, and formed the optimal plan through linear programming methods [44]. Lee et al. [22] developed an experimental integrated scheduling prototype called customizable application program (CAP) under the CC± DHCR condition. While building the integrated planning and scheduling model, the group considered both the SM±CC and HRM process constraints concurrently. The objective function consisted of multiple criteria: (1) maximization of direct ratio, (2) minimization of operation costs including intermediate ladle cost, rolling cost, heat furnace cost, inventory cost and other costs related to the scheduling, and (3) minimization of order tardiness cost. Tamura et al. [13] did initial research on integrated planning and scheduling problems, established the uni®ed model and proposed the two-stage algorithms. 4.2. AI-based methods AI-based methods for SM±CC±HRM production planning and scheduling can be divided into

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the following three types: (1) expert system methods, (2) intelligent search methods, and (3) constraint satisfaction methods. 4.2.1. Expert system-based methods In recent years, expert systems have found a wide range of applications in iron and steel production scheduling. Sato et al. [45] made the ®rst attempt to solve the iron and steel production scheduling problem using expert systems. Numao and Morishita [46±48] and Morishita et al. [49] described the applications of expert systems in coordinated SM±CC production scheduling, independent micro-schedule generation, and rough schedule synthesis through heuristic methods. Machine con¯icts in the resulted rough schedule are then removed by an inference engine to generate the ®nal schedule which can be revised by the scheduler through GUI. Remarkable economic pro®t was reported after the system was put into use. At Gmbh, Stohl and Spopek [50] established a hybrid model based on coordination techniques and expert systems to solve the SM±CC scheduling problems. In the Inland Iron and Steel Company, Epp et al. [51] developed an iterative improvement scheduling system for the SM equipment and CC by means of AI. Hamada et al. [52] developed an SM±CC scheduling system combining knowledgebased expert systems and GAs and this system produced more e€ective production schedules. In order to match the slabs and customer orders, Jimich et al. [53] developed an expert system to determine the parameters and operation conditions. Arizono et al. [54] solved the production sequencing problem concerning the slab rolling through an expert system which was used to improve the production schedules created by traditional methods. Dorn and Kerr [55] investigated the SM±CC scheduling problems by combining fuzzy sets and AI. Lassila et al. [56] described a knowledge-based production scheduling system for slab rolling in large ®nishing manufacturing industry. In 1991, Kawasaki Steel Corporation reported AI methods for making the steel pipe hot rolling plan [57]. In the IPSCON steel rolling mill, Assaf et al. [58] developed optimization and implicit enumeration algorithms for steel production scheduling including the heat furnace.

4.2.2. Intelligent search methods Most of the established production planning and scheduling models belong to the class of NPhard problems because of the complexity of the actual production planning and scheduling problems in the industry. Exploring optimal solution to the problems cannot avoid the problem of combinatorial explosion and therefore are impractical for real applications. Many researchers have then turned to intelligent approximate algorithms for the problems. The intelligent algorithms are global search methods which can obtain near-optimal solutions to the problems with relatively short time and little cost in comparison with the accurate algorithms. For many real applications, it is enough to ®nd a good feasible solution instead of the optimal solution. Intelligent algorithms applied to scheduling problems mainly include GA [59], simulated annealing [60] and tabu search [61]. For hot strip mill production scheduling, Lopez et al. [32] constructed tabu search-based heuristic. Comparison with actual production schedules indicates that the proposed method could produce signi®cantly better schedules. Tang et al. [40,41] constructed a new two-stage coding GA to ®nd solutions to the heat design and cast design models for the SM±CC production and guaranteed that the iteration process proceeds in the feasible domain. For the production scheduling problem in the steel rolling mill, Tang [30] and Tang et al. [31] developed improved GAs after TSP models were built. Dorn [62] proposed iterative improvement algorithms for SM±CC scheduling. Hamada et al. [52] formulated hybrid GAs and expert experience rule-based GAs to solve the SM±CC scheduling problem. Lee et al. [22] developed the scheduling system applicable to the two-strand CC at LVT and employed fast GAs to obtain satisfactory solutions which meet all the constraints. 4.2.3. Constraint satisfaction methods Constraint satisfaction problem (CSP) is an important branch of AI. It focuses on ®nding feasible solutions satisfying the constraints rather than the optimal solution. In view of the fact that the iron and steel planning and scheduling problems comprise complex constraints, it is hard to

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®nd the optimal solution to the problem. Most practical production scheduling problems can be addressed by considering the constraints with the following priority: ®rst, the rigid constraints in the production process, then the related ¯exible constraints, and ®nally the optimality of the solution. The constraint satisfaction method was ®rst introduced by Fox [63] to solve the production scheduling problems in job shops. For the dynamic scheduling problems in the SM±CC, Epp et al. [51] established a model based on the constraint satisfaction concept and then found the solution using constraint propagation algorithms. Bisdor€ and Gabriel [64] regarded the production scheduling problem in the steel rolling mill as a CSP. Chang et al. [65] studied the production sequencing problems in the CC±DHCR, simpli®ed the problems to a great extent, formed the Hamiltonian Loops, established the CSP model, and constructed a ``Look-head'' heuristic algorithm. Nevertheless, this method neglected a lot of actual production constraints. Therefore, it was mainly a methodology research and was dicult to be put into practical use. Suh et al. [66] have proposed a reactive scheduling procedure based on the constraint satisfaction problem (CSP) to eciently deal with the hot-rolling reactive scheduling problem in a hot strip mill. 4.3. Human±machine coordination techniques and the related applications Although lacking optimization, the human± machine coordination method displays strong adaptability and ¯exibility for the practical complex production scheduling problems because of its easy operation and direct visualization. In recent years, the advances of graphics and visualization techniques have provided more convenient interfaces for the development of human±machine coordination systems. Numao and Morishita [46±48] and Morishita et al. [49] adopted expert systems and human±machine coordination techniques to develop the SM±CC production scheduling system. With the system, a feasible initial solution can be ®rst produced interactively, the expert system can then generate a better feasible

11

solution, and ®nally the production schedule can be conveniently modi®ed through GIU. The Kwangyang Works of POSCO in Korea applied the human±machine coordination method to solve the rescheduling problems concerning the order changes [23]. Li et al. [67] introduced the visualization technique and combined it with the optimization model in the integrated SM±CC scheduling system. Using the system, an initial solution is ®rst obtained interactively. The optimization model is then used to generate a new solution. Based on this, modi®cations are made using the visualization technique. Finally, the scheduling result is given in the form of a userfriendly two-dimensional graph on which the model and the schedule can also be directly revised. In this manner, the optimization function of the model can be brought into full play. The introduction of the visualization technique into SM±CC scheduling provides the following characteristics: (1) real-time feedback, (2) adaptability to production environment, and (3) visualized operations. In Baoshan Iron and Steel Company of China, the hot rolling scheduling system is a typical interactive system developed by the German supplier [68]. This system possesses the following two basic features: (1) on-line and o€-line data for the production planning can be managed accurately, timely and comprehensively; (2) based on the experience and data, the scheduler can make the production plan. Afterwards, a detection link, equivalent to a tundish, is used to determine automatically whether the rigid constraints of the production process and management can be satis®ed. If the plan is feasible, the scheduling passes successfully. Otherwise, the plan fails. Once the plan fails, the information violating the constraints will be pointed out and the plan will be recreated until the constraints are met. 4.4. A-teams methods A-teams, the short term for asynchronous teams, was originally developed by Taludar et al. [69]. It is a framework which conveniently integrates multiple problem-solving programs (called agents) into a team so that the resultant e€ects are

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better than those produced by any single agent. These multiple agents work together, but independently, to generate a group of high-quality solutions on a common problem. Because the iron and steel production planning and scheduling problem requires various solution methods, the Ateams architecture is suitable for producing better results in this ®eld. Lee et al. [22] have applied Ateams to LTV cluster sequencing problems where the agents include evaluation agents, construction agents, improvement agents and destruction agents. Due to the complexity of the actual iron and steel production scheduling problems, multiple models and algorithms are integrated to ®nd solutions eciently. When solving a scheduling problem, these models and algorithms perform computation simultaneously or at di€erent times so that a satisfactory solution is found after their results are compared. Therefore, multiple agents are required for cooperation and coordination. In the mean time, the distributed multiple agents are especially suitable because the iron and steel production planning and scheduling is closely associated with the production process and the iron and steel production includes multiple stages. The focuses of the production scheduling problems for these stages are di€erent and need di€erent models and methods. In summary, di€erent methods have been attempted to solve iron and steel production planning and scheduling problems. The primary advantages of optimization models lie in their capability of abstracting the problem features, re¯ecting the problem relationships and quantitatively describing the problems. However, the optimization models are weak in environment adaptability due to the in¯exible model expressions. Therefore they are generally suitable for static scheduling environments. There exists a variety of unstructured factors in production scheduling practice, such as the decision-maker's experience and wisdom, which can only be described qualitatively instead of quantitatively. These factors may be better handled through the expert systems. However, an expert system itself lacks the abilities to acquire information and learn new knowledge. This disadvantage makes it hard

for the system to adapt to the environment well and to process eciently the creative intelligence of the decision-makers. On the other hand, although the human±machine coordination method facilitates interactive operations and provides strong adaptability, it does not provide optimization assistance and the resulting schedule needs to be adjusted repeatedly. Hence its eciency for schedule generation is low. Considering the advantages and disadvantages of di€erent methods, the combination of operations research, expert systems and visualization techniques provides great potential for e€ectively solving integrated production scheduling problems [70,71]. 5. Key issues for further research in integrated SM± CC±HR production planning and scheduling In comparison with the traditional cold charge process, the new CC±HCR, CC±DHCR and CC± DHR processes are complex in that they consider not only the increased constraints, but also have high real time requirements and dynamic adjustment demands. Further research needs to be done in modeling the problems, designing e€ective and ecient solution algorithms, as well as developing software systems. In this section, we describe and discuss the key issues for further research concerning the integrated production planning and scheduling, based on the characteristics of the production processes presented in Section 2. 5.1. The integrated multi-stage lot planning for the SM±CC±HR production In the conventional steel making and steel rolling production (cold charge process), the production plans for the steelmaking and steel rolling are made independently based on the design units called heat, cast and roll. In the SM±CC stage, the lot plans (heats and casts) are mainly limited by the steel grade and speci®cation of the slabs. The steel grade must be consistent and the slab speci®cations within a lot must be close to each other. On the other hand, the rolling plans are mainly constrained by the strip width and

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thickness: the width must vary from wide to narrow and thickness should change smoothly. Therefore, the lot planning problems for the cold charge process are essentially single production stage problems. In the CC±HDR process, SM, CC and HRM are integrated and the production plans for steelmaking and steel rolling, which cannot be created individually, have to follow the uni®ed planning arrangement. In the SM±CC±HR process, the lot plan is made according to the design unit known as heat±cast±roll which is di€erent from either heat, cast or roll. It integrates multiple production stages to form the combined plan. In the heat± cast±roll, the lot planning must consider the process constraints of both SM±CC and HRM stages simultaneously. For this reason, it is called a multi-stage lot planning problem. The key issues of the design and research on the integrated multistage lot planning include the following aspects: extracting the characteristic factors of the heat± cast±roll problem, exploring the fuzzy expression of the complex constraints, establishing the optimized multi-objective optimization models and seeking the approximate or optimal algorithms. The research problems can be decomposed into the following categories: 1. Research on fuzzy clustering analysis models and algorithms for order classi®cation. 2. Establishing models for the integrated multistage lot planning. (a) Constructing the optimal mathematical model for integrated cast-to-roll planning. (b) Building the optimal mathematical model for integrated heat±cast±roll planning. 3. Investigating e€ective heuristic algorithms suitable for the constrained optimization regarding the integrated lot planning. 5.2. The integrated multi-stage time scheduling problems for the SM±CC±HR production When the SM, CC and HRM have to be connected directly with hot metal ¯ow, the upstream production stage is required to provide raw materials for the downstream procedure at given times and a speci®ed temperature and quality. The

13

SM furnace needs to timely pour the molten steel into the CC and the CC must rhythmically furnish slabs for the HRM. Only when the operation pace of each job is scienti®cally arranged, the scheduling of the principal equipment is reasonably determined, and the time and pattern of material supply and demand between production stages are accurate and well matched, can we make the material ¯ow proceed in a streaming manner. In this way, we can reduce intermediate waiting time, avoid unnecessary machine idleness. Obviously, determining the schedule of the job and the principal equipment is an integrated multi-stage scheduling problem with constraints. The speci®c aspects may be described as follows: (1) In the process of SM±CC±HR, the set-up time of the equipment and preparation time of the tools are generally associated with the preceding (or preceding batch of) processed objects and the corresponding scheduling problem is a problem with sequence dependent set-up times. Therefore, it is necessary to study the models and algorithms concerning single machine and no-wait ¯owshop scheduling problems with sequence dependent setup times. (2) The heat furnace can be viewed as a batch processor because it heats multiple slabs concurrently. The slab sequence determination problem is classi®ed under the scheduling problem of the batch processor. Therefore, it is necessary to investigate the models and algorithms regarding the earliness/tardiness scheduling problem for a single batch processor. (3) The integrated scheduling problem is a kind of hybrid multi-stage scheduling problem with parallel machines and batch processors in some stages. So it is essential to study the models and algorithms for the streaming scheduling problems which satisfy the hybrid constraints. (4) It is imperative to do research on the models and algorithms determined by the integrated multi-stage timetable. The core of the integrated multi-stage scheduling involves analyzing the characteristics of the problems, constructing the appropriate mathematical model concerning the scheduling problem and exploring the e€ective solution algorithms for the model.

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5.3. Dynamic scheduling for the SM±CC±HR production In the integrated SM±CC±HR production process for the iron and steel industry, the material ¯ow linkage and pattern match among production stages are required to be consistent and the whole process proceeds continuously under high temperature. Since the scheduling done prior to production operates on the virtual slabs, in the course of execution, the actual production is often a€ected by some random factors, leading to deviations from the integrated schedule at some production stages. At the SM stage, the following problems frequently occur: (1) the orders change, (2) the machines fail, and (3) the smelting time exceeds the prescribed limit. At the CC stage, the following phenomena often occur: (1) the heats arrive randomly and dynamically, (2) steel leak appears in the CC, and (3) the intermediate ladle is replaced. In the HRM stage, the following situations may appear: (1) the job (slab) quality is not up to standard, (2) the jobs are delayed and (3) the slabs are backed up in the HRM. All these abnormal situations not only disrupt the scheduling within the procedure, but also in¯uence the normal job scheduling in the downstream procedure and thereby require that the system should do automatic rescheduling rapidly. This class of problems are known as production scheduling problems in dynamic environment. Scienti®c and quick dynamic scheduling plays a vital role in the reduction of the steel cost, improvement of the production quality, and timely delivery of the products. Dynamic scheduling is an important issue in the integrated iron and steel production scheduling. For the SM±CC dynamic scheduling problems, Numao and Morishita [48] undertook the coordinated scheduling by combining AI and interactive technology. Stohl and Spopek [50] solved the scheduling problems concerning order changes by means of human±machine coordination. Dorn and Kerr [55] from the Intelligent Laboratory of Vienna University of Technology, Austria studied the dynamic iron and steel production scheduling problems based on the integration of fuzzy sets and AI. The general dynamic scheduling problem

is a new challenging research area. Nof and Grant [72], Surech and Chaudhuri [73] and Szelke and Kerr [74] gave research reviews on the dynamic scheduling problems, which marked dynamic scheduling as an important branch of scheduling research. For the dynamic scheduling problems, the simulation method based on dynamic dispatching rules is usually employed. This approach is easy to implement but considers only local information in making decisions. Szelke and Kerr [74] and Pierreval [75] proposed dynamic methods based on AI. However, the knowledge base for practical problems is often very large and the knowledge reasoning and search speed is rather low. Consequently, it is hard to satisfy the real time requirement for the dynamic scheduling. Based on the rolling horizon method, Ovacik and Uzsoy did research on the dynamic single machine scheduling [76] and dynamic parallel machine scheduling [77] with time windows, assuming future events can be predicted. Nevertheless, it is generally dicult to foresee what will happen in the future for practical problems, and this limits the application of the method. Further research may be done on the following aspects of dynamic scheduling: (1) fast pattern recognition of the random events which cause rescheduling, (2) theory and methodology concerning real-time on-line scheduling, (3) theory and methodology for combining di€erent methods and strategies, and (4) the applications of dynamic scheduling methods in the integrated SM±CC±HR scheduling environment. 6. Conclusions The steel industry is an essential and sizable sector for industrialized economies. While the integrated process of steelmaking, continuous casting and hot rolling (SM±CC±HR) has many advantages over the traditional cold charge process, it also brings new challenges for production planning and scheduling. In this paper, we ®rst compared the characteristics of di€erent SM±CC± HR production processes and the constraints and requirements in their production management. The integrated planning and scheduling for the

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Table 2 Comparison of production lot planning characteristics for di€erent types of processes Planning index

Process type

Characteristics

Planning object

CC±CCR CC±HCR CC±DHCR CC±HDR

Real slabs Virtual slabs Virtual slabs Virtual slabs

Planning unit

CC±CCR

Three separate plans are made using HEAT, CAST and ROLL as planning units, respectively An integrated plan is made based on HEAT±CAST±ROLL An integrated plan is made based on HEAT±CAST±ROLL An integrated plan is made based on HEAT±CAST±ROLL

CC±HCR CC±DHCR CC±HDR Constraint characteristics

CC±CCR CC±HCR CC±DHCR CC±HDR

SM constraint (HEAT)

CC±CCR CC±HCR CC±DHCR CC±HDR

CC constraint (CAST)

CC±CCR CC±HCR CC±DHCR CC±HDR

HRM constraint (ROLL)

CC±CCR CC±HCR CC±DHCR CC±HDR

Optimality

CC±CCR CC±HCR CC±DHCR CC±HDR

Each independent production plan is subject to only the constraints within the stage in question The integrated plan is subject to the constraints of SM, CC and HRM simultaneously The integrated plan is subject to the constraints of SM, CC and HRM simultaneously The integrated plan is subject to the constraints of SM, CC and HRM simultaneously Steel grade is identical two CC strands Steel grade is identical adjustable range Steel grade is identical adjustable range Steel grade is identical adjustable range Steel grade range Steel grade range Steel grade range Steel grade range

from slab to slab and width lies between the limits of from slab to slab and width falls within the CC from slab to slab and width falls within the CC from slab to slab and width falls within the CC

is close form slab to slab and width falls within the CC adjustable is close form slab to slab and width falls within the CC adjustable is close form slab to slab and width falls within the CC adjustable is close form slab to slab and width falls within the CC adjustable

Slab width pro®le takes the form of tortoise shell and hardness changes smoothly Slab width takes the form of tortoise shell form and hardness changes smoothly Slab width takes the form of tortoise shell form and hardness changes smoothly Free rolling. Rolling length with the same width increases, but there still exist some limitations on the total rolling length Local optimization Global optimization Global optimization Global optimization

SM±CC±HR production needs to consider the constraints concerning the material ¯ow and time linkage between the upstream and downstream

production stages besides the model constraints which already exist in the heat design, cast design and roll design of the cold charge process. We

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Table 3 Comparison of production scheduling characteristics for di€erent types of processes Scheduling index

Process type

Characteristics

Real time requirements

CC±CCR CC±HCR

Most scheduling is o€-line and real time requirement is not high Scheduling is on-line, but there exists a bu€er. Real time requirements are higher Scheduling is on-line and real time requirements are extremely high Scheduling is on-line and real time requirements are extremely high

CC±DHCR CC±HDR Rescheduling requirements

CC±CCR CC±HCR CC±DHCR CC±HDR

Scheduling type

CC±CCR

Rescheduling frequency is low and rescheduling primarily focuses on the static scheduling Rescheduling frequency is higher and new scheduling has to be created quickly Rescheduling frequency is higher and new scheduling has to be created quickly Rescheduling frequency is higher and new scheduling has to be created quickly

CC±DHCR CC±HDR

There exists a slab yard servingas an intermediate storage bu€er with in®nite capacity There exists an insulated chamber serving as intermediate storage bu€er with de®nite capacity There is no intermediate storage bu€er There is no intermediate storage bu€er

Scheduling model

CC±CCR CC±HCR CC±DHCR CC±HDR

Single-stage, single-machine or hybrid ¯owshop scheduling problem Multi-stage hybrid ¯owshop streamlining scheduling problem Multi-stage hybrid ¯owshop scheduling problem Multi-stage hybrid ¯owshop scheduling problem

Final objective

CC±CCR CC±HCR CC±DHCR CC±HDR

On-time delivery and On-time delivery, the waiting time On-time delivery, the On-time delivery, the

Timing consistency

CC±CCR CC±HCR CC±DHCR CC±HDR

No requirement Timing consistency between the SM and HR is required Timing consistency between the SM and HR is required Timing consistency between the SM and HR is required

Scheduling result

CC±CCR CC±HCR CC±DHCR CC±HDR

Single-stage timetable Multi-stage timetable Multi-stage timetable Multi-stage timetable

CC±HCR

then reviewed the planning and scheduling systems developed for steel production and the methods used in modeling and solving the planning and scheduling problems. The methods fall into a few main categories. It is believed that the architecture involving multiple models, algorithms, and distributed agents can provide an e€ective way to manipulate multi-stage problems for the integrated planning and scheduling. Owing to the practical complexity of the integrated planning

the least intermediate waiting time least makespan and the shortest intermediate least makespan and no intermediate waiting time least makespan and no intermediate waiting time

and scheduling models, searching for more ecient and e€ective approximate algorithms will be continued. In developing practical integrated planning and scheduling systems, it is necessary to combine di€erent techniques such as operations research, AI and coordinated visualization together so that the advantages of each technique can be brought into full play and that the system can be endowed with adaptability, ¯exibility and optimality. Based on the analysis and review, we

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Table 4 Comparison of material ¯ow linkages among production stages for di€erent types of processes Planning index

Process type

Characteristics

Constraint

CC±CCR

Rolling plan is made according to the tortoise shell form and slabs in the slab yard can meet this constraint The slab width in the rolling plan meets the requirement of tortoise shell form while the slab in the cast plan assumes the form of rectangular shape; therefore, there exists con¯ict if these two plans are directly connected The slab width in the rolling plan meets the requirement of tortoise shell form while the slab in the cast plan assumes the form of rectangular shape; therefore, there exists con¯ict if these two plans are directly connected Free rolling. Wide slabs and narrow slabs are mixed to form a serrated pro®le

CC±HCR Con¯ict

CC±DHCR CC±HDR

Con¯ict feature

CC±CCR CC±HCR CC±DHCR CC±HDR

A slab yard serves as a bu€er A heat preserving pit serves as a bu€er No bu€er No bu€er

Con¯ict processing

CC±CCR

The slab yard can handle slabs supplied by the SM and those needed by the HRM at di€erent times and furnish slabs based on hot rolling requirements (a) Di€erence between two CC strands; (b) adjustable CC width; (c) external width adjustment techniques such as lateral pressure machine and width adjustment machine; (d) hybrid rolling (a) Di€erence between two CC strands; (b) adjustable CC width; (c) external width adjustment techniques such as lateral pressure machine and width adjustment machine; (d) hybrid rolling Free rolling. There is no con¯ict about the shape

CC±HCR Strategy

CC±DHCR CC±HDR

®nally pointed out some key issues for further research on the integrated planning and scheduling for the SM±CC±HR production. It is hoped that this paper will stimulate the interests of more researchers in the operations research and operations management ®eld to work on the planning and scheduling problems in this important industry.

Acknowledgements This research is supported by National Natural Science Foundation of China through Approval No.79700006 and by National 863/CIMS Scheme of China Through Approval No. 863-511-708-009.

Appendix A Comparison of di€erent types of steel production processes (see Tables 2±4).

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