A case of rule-based heuristics for scheduling hot rolling seamless steel tube production

Transcription

1 Article A case of rule-based heuristics for scheduling hot rolling seamless steel tube production Jianxiang Li, 1 Ling Li, 2 Lixin Tang 3 and Huijiang Wu 3 (1) Department of Automatic Control, School of Information Science and Technology, Beijing Institute of Technology, Beijing , China (2) College of Business and Public Administration, Old Dominion University, Norfolk, USA lli@odu.edu (3) Department of Systems Engineering, School of Information Science and Engineering, Northeastern University, Shenyang , China Abstract: A production scheduling problem for hot rolling seamless steel tube at Tianjin Pipe Corporation of China is studied. Considering the complexity of the problem and the acceptable time for solving it, a rule-based heuristic approach is proposed and implemented. The proposed approach is a bottleneck scheduling method and considers simultaneously all production processes in three production units and optimizes them as a whole. Additionally, the running result shows, on average, that a 3% increase in throughput and a 5% reduction in late deliveries have been achieved since the system implementation. Keywords: scheduling, heuristics, hot rolling seamless steel tube production 1. Introduction Iron and steel are the backbone materials for the world economy because steel provides strong support for automotive, aircraft, appliances, real estate and many other industries. In the last 20 years, China has led the steel production industry in the world. In 1996, China s steel output volume reached 100 million tonnes and the country became the world s largest steelmaker. To gain competitiveness in the global economy, the iron and steel industry has to improve its production management through short delivery times coupled with growing product diversity. Therefore, effective production scheduling has become a key issue for on-time delivery and customization. This paper considers one specific aspect of the scheduling problem in producing hot rolling seamless steel tube (HRSST). HRSST is among the numerous steel products produced by the iron and steel industry. In general, HRSST accounts for 6% 18% of the total output of steel products. Tianjin Pipe Corporation (TPCO) in China is one of the largest steel pipe manufacturing companies in China. TPCO s annual output of HRSST is over 500,000 tonnes, of which oilwell casings account for 70%, making TPCO the largest supplier of oilwell casings for the oil fields in China. Currently, the company is in the process of re-engineering its production process and HRSST production scheduling represents one of the largest improvement efforts. The production of HRSST is distinct from the production of other steel products such as flatrolled steel and hot strip steel. The production processes of most steel products typically have three stages, but HRSST requires two more production procedures before the job is complete. The production process of HRSST c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd. Expert Systems, July 2006, Vol. 23, No

2 includes steelmaking, continuous casting, hot rolling, heat treating and machine finishing. In this study, a rule-based heuristic approach for scheduling HRSST production is developed and illustrated using a real example from TPCO, China. The rule-based heuristics simultaneously schedule and sequence job orders. Three heuristics are used to batch and sequence the candidate orders for the first two production units and for four different production lines in the third production unit. Then, a set of formulae are employed to determine production dates and shifts for all the batches, which are further divided into furnaces. After the implementation of the suggested heuristics, monthly averages of a 3% increase in throughput and a 5% decrease in late deliveries have been achieved. The paper is organized as follows. Section 2 provides a literature review and describes related work published previously. Section 3 describes the HRSST production process. Section 4 describes the proposed heuristic approach. Section 5 reports the case results. Finally, Section 6 gives conclusions, shortcomings of the study and future research directions. 2. Overview of literature In the past, the HRSST scheduling problem was solved manually at TPCO. In general, the HRSST scheduling problem is divided into several production stages, such as steelmaking continuous casting scheduling, rolling scheduling etc. Each production stage handles its own scheduling problem, and then the individually developed schedules are coordinated at meetings. Schedule coordination among different production stages is very time consuming. Very often, the scheduler finds it difficult to generate a feasible solution, not to mention a good or optimal solution. Due to the complexity of the scheduling problem, the attempt to optimize the overall production process of HRSST is impractical. A previous study shows that optimizing only one stage, such as the hot rolling scheduling, is an NP-complete problem (Tang et al., 1999). Therefore, to find an optimal solution of a fivestage production process is impossible. Heuristic procedures are a reasonable alternative for generating feasible scheduling solutions. Heuristic algorithms incorporate problem-specific knowledge that often leads to good solutions that can be obtained in a reasonable amount of time, which is important for scheduling manufacturing activities. There is little literature that specifically addresses the HRSST scheduling problem. Siddique (1990) presents a heuristic algorithm for the hot rolling scheduling of HRSST. Fukaya and Katagiri (1991) introduce an expert system for determining the manufacturing sequence in the hot rolling process of HRSST. Tang et al. (1999) formulate the hot rolling scheduling problem of HRSST as a travelling salesman problem model and recommend a genetic algorithm to solve the proposed model. Among those studies that focus on the HRSST scheduling problem, only the hot rolling scheduling problem, which is one part of the HRSST scheduling problem, is tackled. However, the papers on the scheduling problems of other steel products can provide good insights to the HRSST scheduling problem. For example, papers on steelmaking and continuous casting scheduling by Dorn et al. (1996), Hamada et al. (1995), Harjunkoski and Grossmann (2001) and Santos et al. (2003) can be integrated into the HRSST scheduling problem. Cowling (2003) reported an experiment on a flexible decision support system for steel hot rolling mill scheduling. Lee et al. (1996) developed an integrated scheduling prototype which considers both the continuous casting technology and process constraints. Artificialintelligence-based methods have been extensively employed for steelmaking, hot rolling casting production planning and scheduling problems in recent years. These artificial intelligence methods include expert systems, intelligent search methods and constraint satisfaction methods (Chang et al., 1993; Assaf et al., 1995; Hamada et al., 1995; Dorn et al., 1996; Lopez et al., 1998; Suh et al., 1998; Cowling, 2003; Santos et al., 2003). Additionally, a number of studies have used operations-research-based methods for planning and scheduling in steel 146 Expert Systems, July 2006, Vol. 23, No. 3 c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd.

3 rolling mills (Lee et al., 1996; Tamaru et al., 1998; Tang et al., 2000; Harjunkoski & Grossmann, 2001; Cowling et al., 2003). All these studies on steel mill planning and scheduling provide a useful background and valuable insight for HRSST production scheduling. 3. Background of HRSST production 3.1. Overview of the HRSST production process The overall production process of HRSST at TPCO consists of five major manufacturing processes (or five stages): steelmaking (SM), continuous casting (CC), hot rolling (HR), heat treating (HT) and pipe machining (PM), as shown in Figure 1. The five processes are further grouped into three production units: Production Unit 1 (PU1) which consists of steelmaking and continuous casting; Production Unit 2 (PU2) which includes hot rolling; and Production Unit 3 (PU3) which comprises heat treating and pipe machining. First, raw materials such as scrap steel and sponge iron are heated and melted into smelted steel in stage one and then cast into blooms (also called round billets) of different dimensions through the continuous casting process in stage two. The qualified blooms are placed in a buffer called Bloom Storage (BS). When stage three is ready, blooms are withdrawn from the Bloom Storage. Then, blooms are pierced and rolled into hollows called semi-finished tubes at the third stage. The semi-finished tubes are usually placed in either the Immediate Warehouse (IW) or the Semi-finished Goods Warehouse (SGW). The semi-finished tubes in the Semi-finished Goods Warehouse are sold to market. The ones in the Immediate Warehouse will be further processed in the next stages. Before the semifinished tubes from the Immediate Warehouse are processed in stage five, some of them are required to be heat-treated in stage four to obtain desired physical and chemical attributes. The heat-treated semi-finished tubes called heated tubes are also placed in the Immediate Warehouse. Stage five makes the semi-finished tubes or the heated tubes from the Immediate Warehouse into their final forms called finished tubes. The finished tubes as product output can be sold to market or placed in the Finished Goods Warehouse (FGW) as inventories for future sales. Stage five includes three production lines that can process different products. The HRSST production process consists of five stages. The five different physical states, smelted steel, bloom, semi-finished tubes, heated tubes and finished tubes, correspond to five stages. Within a production stage, the production process is continuous; between the Figure 1: HRSST production process at TPCO. c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd. Expert Systems, July 2006, Vol. 23, No

4 production stages, production is discontinuous and there are buffers such as Bloom Storage and the Immediate Warehouse. Set-up time is sequence dependent. The set-up time between processing two orders with similar attributes is much shorter than the set-up time between two orders with different attributes. The orders attributes depend upon the production stage. For smelted steel, steel grades and steel varieties are important. For blooms, besides steel grades and steel varieties, outer diameters and lengths are important. For semifinished tubes, steel grades, steel varieties, outer diameters, lengths, wall thicknesses and the reheating process (which will be described in Section 3.2) are important. For heated tubes, steel grades, steel varieties, outer diameters, wall thicknesses and lengths are important. For finished tubes, steel grades, steel varieties, outer diameters, wall thicknesses, lengths and buckle types (the shape of the screw thread at the end of the steel tubes, such as round or trapezoid) are important Hot rolling production process Each of the five manufacturing processes of HRSST production includes multiple opera- machine product operation bloom TC RHF PM RU RHF1 tube bloom pierced bloom ONP reheating cutting heating piercing rolling QIP tools magnetic pole, probe, tubing guide push rod, conical plug mandril, roller BPP stander product Semifinished tube bare pipe check NDI straightening cutting cooling sizing machine NDIM STM CS CB SZM TC: Torch Cutter SZM: Sizing Mill RHF: Rotary Heating Furnace CB: Cooling Bed PM: Piercing Mill CS: Crosscut Saw RU: Rolling Unit STM: Straightening Machine RHF1: Reheating Furnace NDI: Non-destructive Inspection ONP: Online Normalization Process NDIM: NDI Machine QIP: Quick in Process BPP: By-pass Process Figure 2: Hot rolling production process. 148 Expert Systems, July 2006, Vol. 23, No. 3 c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd.

5 tions. Figure 2 describes the hot rolling production process, which is often the bottleneck of HRSST production at TPCO and has a significant impact on understanding the scheduling heuristics that are presented in this study. Several closely related steps transform blooms into finished or semi-finished tubes in the second production unit. After the blooms from the Bloom Storage arrive in PU2, they are torch-cut to the right length. The cut billets then move to the rotary heating furnace, because the hot rolling process must be performed at high temperature as the name implies. When the desired temperature of the billets is attained, the billets are transferred to the piercing mill where the solid billets are converted into tube blooms by the rotary piercing process. In the rotary piercing process, the formation of the tube bloom is achieved by peripherally rolling a round billet over a push rod with a conical plug by driven rolls that are set at an angle to the horizontal plane. When the plug is held against the forward motion of the billet in the weakened central region, the billet passes over it and the plug serves to ensure that the centre opens out into a round hole. In this way the hot billet passing over the piercing plug emerges as a rough thick-walled tube bloom. The hot tube blooms then move to the rolling unit. At the rolling unit, specialized sets of rolls with mandrels reduce the blooms to more exact shapes and dimensions. From the rolling unit, the blooms (called pierced blooms at this time) are moved to the reheating furnace. This step is optional according to the variety of finished goods and the reheating process that the blooms adopt. The reheating process can be classified into three types: online normalization process, quick in process and by-pass process. The blooms from the rolling unit or the reheating furnace next move to the sizing mill where they are reduced to their final sizes. The cooling bed provides a temporary place to leave the hot blooms (called bare pipes at this time) so that they cool down to the appropriate temperature. Further, the cooled blooms are cut by the crosscut saw and straightened by the straightening machine. At this point, the blooms achieve their final length. The non-destructive inspection process is also optional. All types of steel tubes except structural tubes or supporting tubes must pass through this operation. Finally the semifinished tubes are complete. 4. Production scheduling framework and the heuristic approach 4.1. Problem identification At TPCO, the whole plan decision is hierarchically divided into six levels: three-year, annual, seasonal, monthly, weekly and daily. Daily scheduling lies at the bottom level. Monthly plan is disaggregated to daily schedules. Daily scheduling is to determine which orders in the order pool are to be produced on the same day and how to sequence these orders. The overall objective is to effectively utilize the production capacity, avoid over- and under-loading the production facilities, meet inventory requirements and satisfy customer demand. In this sense, daily scheduling is very challenging and is a critical contributing factor in implementing the overall production plan. Therefore, the focus of the study is on daily scheduling. In a nutshell, the scheduling problem of HRSST is to determine the accurate time when a candidate order is to be produced in every stage in order to ensure one stage can promptly feed into the next stage, and thus all orders can be delivered on time with correct quantity. The goal is to specify a good (hopefully optimal ) sequence in which the orders are to be produced in every stage so that the production capacity of every production facility is efficiently utilized. The overall objective of TPCO is to satisfy customer needs through maximizing throughput. Therefore, the objective function is to maximize throughput under the production constraints. The schedule generated must be feasible. The main constraints include limited production capacity, lead time and the production process (i.e. to ensure one stage can promptly feed the next stage). The capacity of buffers and stores must be sufficient. The due c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd. Expert Systems, July 2006, Vol. 23, No

6 date of orders relative to the product throughput is not required to be considered in the time horizon of the schedule. Above all, to respond quickly to the frequent change of production conditions and order information, rapid re-scheduling is needed to increase production flexibility. The generating time for schedules is critical and must be short. At TPCO, it is requested that a re-scheduling be achieved within 3 minutes. Consequently running a good solver for a couple of hours to produce a better solution is not an appropriate choice Manual scheduling procedure The monthly plan provides the order pool for daily scheduling. Based on their order pools, the three production units generate their respective rough schedules by sequencing the candidate orders. Once a week, the schedulers from the three production units reconcile scheduling conflicts among the production units. Based on the resulting weekly plan, the three production units then make their respective daily schedules. In order to obtain a feasible daily schedule, intensive coordination may be needed. The coordination is so time consuming that it is impossible to provide adequate alternative solutions in a reasonable time from which the schedulers may choose. Therefore, the quality of these ad hoc solutions cannot be guaranteed. Besides, the quality of schedules varies depending on the schedulers experience Heuristic approach From the surveys conducted at TPCO, the managers have found that over 90% of the delay is due to PU2. In other words, PU2 s capacity is often the bottleneck of the whole production process. Improving the efficiency of the bottleneck workstation can improve the overall efficiency of the production system. Thus, PU2 is considered as the core production unit which should be scheduled first. To obtain a good scheduling for PU2, some implicit shopfloor experiences are used as explicit rules to form heuristics for job scheduling. Based on the heuristics for PU2, two more heuristics are developed to generate good schedules for PU1 and PU3. Thus the production scheduling of HRSST is conducted effectively and the complexity is greatly decreased. The objective function of the rule-based heuristics is to minimize the total set-up times at every stage. In this way every production facility is efficiently utilized and the throughput is maximized. Figure 3 provides the workflow of the heuristic approach in which all the important steps are included. The rule-based heuristics are chosen mainly because good feasible scheduling solutions can be generated in a reasonable amount of time. In fact, the hot rolling scheduling problem can be formulated with mathematical programming models and solved by artificial-intelligencebased methods, such as the modified genetic algorithm proposed by Tang et al. (2000) and the technique of constraint satisfaction developed by Chang et al. (1993). They can produce better scheduling than the heuristic approach but the time involved is longer than acceptable. Nevertheless, existing schedule techniques, e.g. branch and bound or various local search techniques, can further improve the quality of scheduling by exploring more alternatives Proposed rule-based heuristics The rule-based heuristic approach proposed in this study for the production scheduling of HRSST mainly consists of three heuristics and a set of formulae. First, the three heuristics are used to batch and sequence the candidate orders for PU1, PU2 and four different production lines of PU3, respectively. The production date and shift of every batch, which are further divided into furnaces, are then determined by a set of formulae. In this section, the heuristics for PU1 and PU2 are discussed in detail. The heuristics for PU2 are introduced first because they are the basis of those for PU1. The set of formulae will also be proposed. The heuristics for PU3 are not described here because they are similar to those used for PU Expert Systems, July 2006, Vol. 23, No. 3 c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd.

7 HEURISTIC APPROACH PU1 Monthly Plan PU2 Monthly Plan PU3 Monthly Plan sequence and group orders synchronously Process A determine the order pool for different production lines sequence orders PU2 schedule sequence orders for every production line group orders group orders for every production line Process A Maintenance schedule Process A for every production line PU1 schedule HT schedule PM1 schedule PM2 schedule PM3 schedule Note: Process A = divide lots into furnace, determine the date and shift for every furnace HT = the production line of heat treating PM1/2/3 = the production line nos.1/2/3 of pipe machining Figure 3: Workflow of the heuristic approach Rule-based heuristics for batching and sequencing the candidate orders at PU2 A good strategy for batching and sequencing the candidate orders can help to minimize set-up time and lead to a good schedule. On the shopfloor, there are many rules (also called knowledge or experience) directing the schedulers to batch and sequence the candidate orders. These rules are often incomplete and implicit, yet very valuable. Seven scheduling rules were developed after interviewing many schedulers at TPCO and Shanghai Baoshan Iron and Steel Complex (China). Rule 1: The orders belonging to the same class of pass must be processed together. Pass is used to denote a range of outer diameter. For example, pass 235 denotes the range from 168 mm to 291 mm. All machines in PU2 need to be reset when the pass of the blooms to be processed changes from one type to another. It is time consuming (approximately 4 hours) and hence such changes should be avoided. Rule 2: Orders with the same outer diameter and similar wall thickness should be processed together. This decreases the frequency of replacing mandrels and resetting the sizing mill, and hence reduces set-up times. It takes approximately 10 minutes to replace a mandrel or reset the sizing mill. c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd. Expert Systems, July 2006, Vol. 23, No

8 Rule 3: Orders that adopt the online normalization reheating process should be processed together. In this way we can avoid emptying the reheating furnace. It takes about 40 minutes to empty the furnace. Rule 4: Orders with the same steel grade should be processed together and the steel grade transitions between adjacent orders should occur gradually. PU2 accepts billets from PU1. The orders processed in PU1 are usually batched in groups and sequenced subsequently based on the steel grade, so batching and sequencing the orders of PU2 based on the steel grades contributes to cooperation between the schedules of PU1 and PU2. Rule 5: Orders that adopt the online normalization reheating process should be processed at the end of each pass. In other words, it is desired to first process the orders that adopt the other reheating processes instead of the online normalization process. In this way the reheating furnace can be emptied while resetting all machines, consequently saving time and enhancing productivity. Moreover, it is well known that the orders that adopt the online normalization reheating process usually need not be heat treated after they arrive at PU3. Thus the idle time of the production line of heat treating can be reduced, its capacity is fully utilized, and the cooperation between the schedules of PU2 and PU3 is improved. Rule 6: The outer diameter transitions between adjacent orders should be gradual. When the outer diameter of the inspected blooms changes slightly, a part or the whole of the nondestructive inspection machine must be re-set and some operational parameters must be adjusted as well, thus wasting time. For example, it takes about 10 minutes to adjust the probe when the outer diameter changes slightly. If the outer diameter changes so much that it is necessary to replace whole components, the wasted time will be up to half an hour. Rule 7: The candidate orders should be sequenced from thinnest to thickest in terms of wall thickness. The extracting mill, which is used to extract the tubes from the mandrels, easily swells after processing thick tubes. If it is then used to process thin tubes, it will damage them. To avoid damage, the extracting mill needs to be replaced, which takes time. Therefore, within the rated capacity of the extracting mill, it is desirable to roll the tubes in a sequence from thinnest to thickest in terms of wall thickness. In summary, there are five factors impacting on batching and sequencing the candidate orders: pass, outer diameter, wall thickness, reheating process and steel grade. However, these factors have different impacts and hence there are different priorities in determining how to batch and sequence the orders. In terms of the time consumed, the highest priority is given to pass because it costs more time than for the other factors when the pass of the blooms to be processed changes from one type to another. Based on the same consideration, the reheating process (online normalization process or not) has the second highest priority. Outer diameter and wall thickness have the third and fourth highest priorities, respectively. The former dominates the latter because replacing mandrels is easier and quicker than resetting the sizing mill. Steel grade has the lowest priority. Once the rules are determined, rule-based heuristics for batching and sequencing the candidate orders at PU2 are constructed. The major difference between the existing methods, e.g. Tang et al. (1999) and Siddique (1990), and the proposed heuristics is that the existing methods batch the candidate orders into groups first and then sequence the orders subsequently. The proposed heuristics batch and sequence the candidate orders simultaneously. The proposed heuristics are as follows. (1) Sequence the candidate orders according to the same sequence of pass as in the last planning period. If the latest pass in the last planning period still has much capacity left, it is arranged as the first one in the current planning period and the others follow it according to the determined sequence. Pass is the first key of sorting the orders. 152 Expert Systems, July 2006, Vol. 23, No. 3 c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd.

9 (2) Sequence the orders in ascending order of online normalization process. In this study, the online normalization process is considered as a value of 0 or 1. The online normalization process is 1 if the order s reheating process is the online normalization process, otherwise 0. The online normalization process is the second key of sorting the orders. (3) Sequence the orders in ascending order of outer diameter. Outer diameter is the third key of sorting the orders. (4) Sequence the orders in ascending order of wall thickness. Wall thickness is the fourth key of sorting the orders. (5) Sequence the orders in lexicographical order of steel grade. Steel grade is the last key of sorting the orders. (6) Show the final sequence using charts and tables. If the scheduler is not satisfied with the sequence, he=she can modify it manually. The default is to accept it. (7) Batch the adjacent orders with identical parameters mentioned in (1) to (5) into lots (groups) Dividing lots into furnaces When the lot size is too large, it often cannot be completed within one day. In practice, the scrape steel is first batched into furnaces and then melted in the electric arc furnace at PU1; therefore using the quantity of each furnace as the basic scheduling unit for PU1 is a better and more practical choice. In addition, to track the source of the raw materials, the product lots of PU2 should also be divided into the quantities of the relative furnaces of PU1. The strategy of dividing a lot into furnaces is as follows. (1) Determine the batch quantity of a furnace. The batch quantity (about 150 tonnes) of every furnace at PU1 is the capacity volume of the electric arc furnace. The batch quantity (about 140 tonnes) of every furnace at PU2 is the capacity volume of the electric arc furnace multiplied by the yield percentage. (2) Determine the number of furnaces needed to process lot j (j ¼ 1, 2,..., J) and the quantity of every furnace according to N j ¼ intðw j =wþ Q jk ¼ w k¼ 1; 2; :::; N j if modðw j =wþ¼0 and N j ¼ intðw j =wþ Q jk ¼ w k¼ 1; 2; :::; N j 1 Q jk ¼ modðw j =wþ k ¼ N j ð1þ if modðw j =wþ 6¼ 0; where w is the batch quantity of a furnace, W j is the lot size j, N j is the number of furnaces divided by lot j, Q jk is the quantity of the kth furnace of lot j, and both int and mod are operators Determine the production date and shift of every furnace First compute the processing time of every furnace by T jk ¼ a j Q jk j ¼ 1; 2; :::; J; k ¼ 1; 2; :::; N j ð2þ where T jk is the processing time of furnace k of lot j and a j is the capacity (time) consumption per unit of the product lot j. Suppose the starting time of furnace 1 of lot 1 (S 11 ) is 0; then the starting time of furnace k of lot j (S jk ) and the ending time of furnace k of lot j (E jk ) can be calculated by the recursion formula E jk ¼ S jk þ T jk S jk ¼ E j;k 1 þ T jk þ U j S j1 ¼ E j 1;Nj 1 þ V j 1; j j ¼ 1; 2; :::; J; k ¼ 1; 2; :::; N j ð3þ where U j is the set-up time when the production changes from one furnace to the next of product lot j and V j 1,j is the set-up time when the production changes from lot j 1 to lot j. Once S jk is known, the production date of furnace k of lot j (D jk ) can be computed by formula (4), where D 0 is the initial date over the planning horizon. Here assume that c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd. Expert Systems, July 2006, Vol. 23, No

10 D jk is the date when furnace k of lot j starts to produce. D jk ¼ D 0 þ intðs jk =24Þ j ¼ 1; 2; :::; J; k ¼ 1; 2; :::; N j ð4þ The maintenance schedule has usually been developed before the production schedule is generated. It determines that on the date appointed some time (about 4 hours for every maintenance) is used on maintenance and inspection activities; during that time, production is stopped and hence the maintenance time is subtracted from the available time of that date. The maintenance generally starts when the production transfers from one lot to the next; in this way the set-up can be done during the maintenance time period to reduce non-productive time. With D jk as the date for maintenance, the following strategy is adopted. (1) If k ¼ 1, this means that a new lot starts its production; re-calculate S jk by S jk ¼ S jk V j 1; j þ RðD jk Þ ð5þ where R(D jk ) is the maintenance time appointed on the date D jk ; in particular ¼ is the operator of value assignment. (2) If k 6¼ 1, maintenance should start when the whole lot j has finished its production; so we calculate the starting time and ending time of each furnace of lot j still using the recursion formula (3). The production of lot j þ 1 starts after the maintenance activities; S j þ 1,1 should be calculated using S jþ1;1 ¼ E jnj þ RðD jk Þ ð6þ (3) The recursion formula (3) is the default formula to calculate the starting time and ending time of any furnace of any lot. Once D jk is known, the production shift of furnace k of lot j (B jk ) can be computed by formula (7). The morning shift is 10 hours long. Both afternoon and night shifts are 7 hours long. B jk ¼ 8 >< morning shift if modðs jk =24Þr10 noon shift if 10 < modðs jk =24Þr17 >: night shift if 17 < modðs jk =24Þ < 24 j ¼ 1; 2; :::; J; k ¼ 1; 2; :::; N j ð7þ Heuristics for batching and sequencing the candidate orders of PU1 The candidate orders of PU1 can be grouped into three categories. The first provides raw materials for PU2 and will be sent to PU2 via the Bloom Storage. The second is made to market and the last is made to stock. The primary task of PU1 is to feed PU2; therefore, the first option must be given the highest priority so that PU2 can obtain the raw materials in time and hence reduce non-productive waiting time. Based on this idea, heuristics for the production scheduling of PU1 are developed. The general idea of the heuristics is as follows. First, divide the three categories of orders into two parts, where the first part includes category 1 and the second part consists of categories 2 and 3. The first part is put before the second part. Sequence the orders from the first part according to the sequence in which their corresponding orders at PU2 are ordered. The corresponding order at PU2 of one order at PU1 means that the order at PU1 provides the raw materials for the order at PU2. In this way, similar orders can be arranged together so that the set-up times can be minimized and thus the orders from the first part are sequenced optimally, simultaneously complying with the restriction that the orders at PU2 can obtain the raw materials from PU1 promptly. Next the orders from the second part are ordered by steel variety, steel grade, diameter and length as the first, second, third and fourth key of sorting, respectively. Further, take the orders in the second part one by one in order to find the orders that can be inserted just after the orders in the first part with the same steel variety and steel grade (the process of matching). The 154 Expert Systems, July 2006, Vol. 23, No. 3 c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd.

11 goal is to make the orders with the same parameters be together as much as possible to minimize the set-up times, simultaneously satisfying the restriction that the orders at PU2 can obtain the raw materials from PU1 promptly. The orders of the second part that have no match with an order in the first part stay after the first part. The steps are presented as follows. Step 1: Divide the three categories of orders into two parts, where the first part includes category 1 and the second part consists of categories 2 and 3. The first part is put before the second part. Order the orders from the second part by steel variety, steel grade, diameter and length as the first, second, third and fourth key of sorting, respectively. Suppose the first part includes M orders, the second part includes N orders, order i (i ¼ 1, 2,..., M) is the order from the first part and order j ( j ¼ 1, 2,..., N) is the order from the second part. Step 2: Sequence order i (i ¼ 1, 2,..., M) according to the sequence in which O(i)is ordered in the PU2 schedule. Step 3: Calculate the processing time (T i ), start time (S i ) and ending time (E i ) of order i using formulae (2) (6), and calculate the processing time (T j ) of order j ( j ¼ 1, 2,..., N). Note that formulae (2) (6) are presented to determine the time for each furnace; however, they can also be used here to estimate the time for each order. Step 4: Let i ¼ 1. Step 5: Take order i from the first part. Step 6: Let j ¼ 1. Step 7: Step 8: Take order j from the second part. Determine whether order j matches order i, i.e. the parameters steel variety and steel grade of order i must be identical to those of order j and the parameters diameter and length of order i may also be the same as those of order j. If true, then go to step 9; otherwise to step 11. Step 9: Let temps k ¼ S k þ T j þ U i and temp- E k ¼ E k þ T j þ U i (k ¼ i þ 1,..., M); then determine whether temps k þ LEADTIMErS O(k) for all k ¼ i þ 1,..., M. If yes, then go to step 10; otherwise go to step 11. Note that U i is the set-up time for the production of order i, LEADTIME is the lead time between PU1 and PU2 and S O(k) is the starting time of order O(k) at PU2. Step 10: Insert order j just after order i, which means that order j from the second part becomes order i þ 1 of the first part. Let S k ¼ temps k, E k ¼ tempe k (k ¼ i þ 1,..., M), and then let M ¼ M þ 1 and N ¼ N 1; go to step 12. Step 11: Determine whether j ¼ N or not. If yes, go to step 12; otherwise let j ¼ j þ 1 and then go to step 7. Step 12: Determine whether i ¼ M or not. If yes, go to step 13; otherwise let i ¼ i þ 1 and then go to step 5. Step 13: Batch the adjacent orders with the same parameters (steel variety and steel grade) into lots. 5. Implementation and evaluation The heuristic approach presented in this paper has contributed to developing a scheduling decision support system for TPCO. The system is developed using Microsoft Visual Basic and SQL Server and includes two major subsystems: data management and production scheduling. The data management subsystem stores and manages the data used by the production scheduling subsystem, e.g. the order book containing details of customer order dimensions and qualities, the BOM, inventories information, plant specification information etc. The production scheduling subsystem is employed to develop good feasible schedules for the three production units of TPCO. Additionally, a rolling scheme is used to cope with uncertainty. Major steps for the production scheduling subsystem to generate a production schedule are as follows. c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd. Expert Systems, July 2006, Vol. 23, No

12 Step 1: Generate the initial order sequence for PU2 using the rule-based heuristics. Step 2: Show the sequence using charts and tables. The scheduler can judge the quality of the schedule. If the scheduler is not satisfied with the sequence, he=she can modify the sequence manually until the solution is satisfactory. Note that the default is to accept the sequence. Step 3: Based on a satisfactory sequence, generate the schedule for PU2 using the set of formulae. Step 4: Based on the schedule of PU2, generate the schedules for PU1 and PU3 using the other two heuristics and the set of formulae. Step 5: Show the schedules of PU1 and PU3 using charts and tables. If the scheduler is not satisfied with these two schedules, he=she can modify the schedules using a man machine interactive method. The system determines whether the modification leads to conflicts among the three units. If no conflict exists, the modification is accepted; otherwise a warning message is shown and these two schedules are recovered. Note that the default is to accept these two schedules. Step 6: Repeat steps 2 to 5 if necessary. The rule-based heuristics discussed above were integrated into decision support scheduling software using Microsoft Visual Basic and SQL Server. The scheduling system has been tested successfully at TPCO. In May 2002, we collected production, BOM, customer orders and other relevant data and used both the decision support scheduling system and manual methods to schedule production. We compared the production schedules generated by the scheduling system and the manual method. The results showed that on a monthly average a 3% increase in throughput and a 5% decrease in late deliveries have been achieved using the scheduling software. The schedulers at TPCO consider the scheduling software a good decision support system, which also greatly reduces the time needed for scheduling production. 6. Conclusions In this paper, we study the production scheduling problem of HRSST at TPCO, China. A rulebased heuristic approach is proposed and implemented. The proposed approach is a bottleneck scheduling method, and considers simultaneously all production processes in three production units and optimizes them as a whole. It is quick, which is an advantage because the time for generating the schedule is critical at TPCO. It is based on shopfloor rules and hence is easily understood and used by the schedulers. It is also a simple approach, but it is an improvement over traditional manual scheduling. The running result shows that the system can greatly reduce the schedulers burden and improve productivity. On average, a 3% increase in throughput and a 5% reduction in late deliveries have been achieved since the system implementation. There are some shortcomings of this research. First, it is a case-based study and may not be applicable to other scheduling scenarios. Future research may consider integrating more theory to tackle issues such as lot split, bottleneck scheduling and multi-production-unit scheduling. Another shortcoming of the study is that it does not offer a comparative study of the heuristics proposed in this study and methods proposed in other studies such as techniques of constraint satisfaction, genetic algorithms and other local search algorithms. Future research may consider comparing various scheduling methods using real data to provide useful managerial information. Acknowledgement The project is supported by the National Natural Science Foundation of China through No and No , and Fok Ying Tung Education Foundation through No References ASSAF, I., M. CHEN and J. KATZBERG (1995) Steel scheduling optimization for IPSCO s rolling mill and reheat furnace, WESCANEX 95 Proceedings, New York: IEEE, Expert Systems, July 2006, Vol. 23, No. 3 c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd.

13 CHANG, S.Y., Y.S. HONG and C.Y. JUN (1993) Constraint satisfaction approach to scheduling DHCR process, CDC 93 Proceedings, New York: IEEE, COWLING, P. (2003) A flexible decision support system for steel hot rolling mill scheduling, Computers and Industrial Engineering, 45, COWLING, P., D. OUELHADJ and S. PETROVIC (2003) A multi-agent architecture for dynamic scheduling of steel hot rolling, Journal of Intelligent Manufacturing, 14, DORN, J., M. GIRSCH,G.SKELE and W. SLANY (1996) Comparison of iterative improvement techniques for schedule optimisation, European Journal of Operational Research, 94, FUKAYA, N. and T. KATAGIRI (1991) Expert system for manufacturing sequence determination in hot rolling process of seamless steel pipe, Kawasaki Steel Giho, 23 (3), HAMADA, K., T. BABA, K.SATO and M. YUFU (1995) Hybridizing a genetic algorithm with algorithm with rule-base reasoning for production planning, IEEE Expert, 10, HARJUNKOSKI, I. and I.E. GROSSMANN (2001) A decomposition approach for the scheduling of a steel plant production, Computers and Chemical Engineering, 25, LEE, H.S., S.S. MURTHY, S.W. HAIDER and D.V. MORSE (1996) Primary production scheduling at steelmaking industries, IBM Journal of Research and Development, 40, LOPEZ, L., M.W. CARTER and M. GENDREAU (1998) The hot strip mill production scheduling problem: a tabu search approach, European Journal of Operational Research, 106, SANTOS, C.A., J.A. SPIM and A. GARCIA (2003) Mathematical modeling and optimization strategies (genetic algorithm and knowledge base) applied to the continuous casting of steel, Engineering Applications of Artificial Intelligence, 16, SIDDIQUE, M. (1990) A knowledge-based system for process planning in a seamless steel tube plant, PhD thesis, Aston University, UK. SUH, M.S., A. LEE, Y.J. LEE and K.Y. KO (1998) Evaluation on ordering strategies for constraint satisfaction reactive scheduling, Decision Support Systems, 22, TAMARU, R., M. NAGAI, Y. NAKAGAWA, T. TANIZAKI and H. NAKAJIMA (1998) Synchronized scheduling method in manufacturing steel sheets, International Transactions on Operational Research, 5 (3), TANG, L.X., G.F. ZHANG, Z.H. YANG and M.G. WANG (1999) Research on hot-rolling scheduling for tube production, Chinese Journal of Iron and Steel, 34 (4), TANG, L.X., J.Y. LIU, A.Y. RONG and Z.H. YANG (2000) A multiple traveling salesman problem model for hot rolling scheduling in Shanghai Baoshan Iron & Steel Complex, European Journal of Operational Research, 124, The authors Jianxiang Li Jianxiang Li received his PhD degree in systems engineering at Northeastern University, China, in Currently he is a lecturer in the Department of Automatic Control at the Beijing Institute of Technology, China. His primary interest is in production planning and scheduling, logistics and supply chain management. Ling Li Ling Li teaches operations management and technology, electronic supply chain management and other courses at Old Dominion University. Dr Li s research interests include health service management, supply chain management, enterprise resource planning, the impact and application of information systems on operations management, e-business, knowledge-based systems, production planning and control. Lixin Tang Lixin Tang is a professor in the Department of Systems Engineering at Northeastern University, China. He obtained his PhD degree in control engineering from Northeastern University in China in His research interests include production scheduling, logistics and supply chain management and combinational optimization. He has published a monograph and more than 80 papers in international journals such as European Journal of Operational Research, Journal of the Operational Research Society, International Journal of Production Research, International Journal of Production Economics, Computers and Industrial Engineering, Journal of Intelligent Manufacturing and local journals. c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd. Expert Systems, July 2006, Vol. 23, No

14 Huijiang Wu Huijiang Wu is a lecturer in the Department of Mathematics at Shenyang College of Engineering, China. She obtained BS and MS degrees in applied mathematics from Northeastern Normal University in China in 1992 and 1995, respectively. She is also a PhD candidate at the Department of Systems Engineering in Northeastern University, China. Her primary interest includes production planning and scheduling and statistics. 158 Expert Systems, July 2006, Vol. 23, No. 3 c 2006 The Authors. Journal Compilation c 2006 Blackwell Publishing Ltd.