Optimization of production schedules in the steel production system

archives of civil and mechanical engineering 12 (2012) 240–252

Available online at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/acme

Optimization of production schedules in the steel production system B. Karwat AGH—University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland

ar t ic l e i n f o

abs tra ct

Available online 23 March 2012

Planning and scheduling production processes in a steel mill are very difficult tasks due to

Keywords:

the nature of the technological processes realized during production. A system model

Steel mill

including technological and transport devices as well as a system for collection and

Steel production model

transmission of information about the realized production processes is necessary for

Production scheduling

conducting studies in the scope of planning and scheduling production processes. Modeling of production systems with the purpose of conducting simulations, making it possible to determine the optimal material and semi-finished product transfer routes between devices of the process line, is generally difficult. This problem is particularly complicated in the case of modeling a steel production system. This is due to the nature of the operation of most of the main process devices and the limited capability of storage of semi-finished products for a period longer than those strictly defined. Published by Elsevier Ltd. on behalf of Committee of Civil and Mechanical Engineering

1.

Introduction

Scheduling production processes has the aim of ensuring maximum production at an optimal device exploitation, which is particularly significant in hot sections of the steelworks and is subordinate in terms of the logistical conception of the production system as well as the supply and distribution systems. Fig. 1 presents the main production devices operating in the process line of the analyzed steel mill and distinguishes the main logistical systems A, B, C, D and E securing continuity of production in the observed line. Distribution of products for release onto the market D is superordinate in the entire logistical system, because information from this system (orders for final products) is the basis for planning (scheduling) production in the entire steelworks, and this information includes A supply logistics and B production logistics for the entire steelworks. Fig. 1 also shows the area of waste distribution logistics B. This system is also complex due to the bulk of post-process waste created in the steel mill. Currently, in modern steel mills, most of the created bulk technological waste is almost entirely utilized as

charge for production (iron-containing waste) or sold to outside recipients after the appropriate processing (slags). The steel mill model being constructed (HS) should include all sections of the steel mill, starting from the section for preparation of the charge for iron blast furnaces and ending with the rolling mill for final products, with special consideration of the most difficult part of the steel mill in terms of scheduling processes, that is, the so-called hot sections—C production logistics of continuous hot processes. In Fig. 1, the system of production logistics of continuous hot processes includes iron blast furnaces, desulfurization of the crude iron, oxygen converters, post-furnace processing of liquid steel, and units for continuous steel casting. This system can also include hot plastic working sections if the criterion for optimization of production will be the supply of cast strands of a specific cross-section and temperature within a set amount of time. It is in exactly this area of production where the creation of schedules may contribute to the optimal utilization of the production capability of all devices of the entire process line and simultaneously decrease the costs of production [1–10].

E-mail address: [email protected] 1644-9665/$ - see front matter Published by Elsevier Ltd. on behalf of Committee of Civil and Mechanical Engineering http://dx.doi.org/10.1016/j.acme.2012.03.014

archives of civil and mechanical engineering 12 (2012) 240–252

241

Fig. 1 – Scheme of the structure of the main technological objects in the steel mill. (a) SP ore sintering plant – producing an iron-containing sinter, being the basic ingredient for production of crude iron in blast furnaces – subsystem HS1; (b) BF blast furnaces – producing crude iron for further processing in oxygen converters, with the capability of casting foundry pig iron – HS2 subsystem; (c) HMDP stations for desulfurization of crude iron – enabling removal of excess sulfur from liquid crude iron before its processing into steel in oxygen converters – HS3 subsystem; (d) BOF oxygen converters – producing liquid steel, which is then subjected to further post-furnace processing – HS4 subsystem; (e) post-furnace processing stations – processes for improvement of liquid steel are conducted: AR—station for argon treatment of liquid steel, LHF—ladle furnaces, RH—vacuum steel degassing station – HS5 subsystem; (f) CCM continuous steel casting units – liquid steel is processed into cast strands – HS6 subsystem; (g) RM rolling mills – cast strands are processed into rolled final products – HS7 subsystem.

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Studies were conducted for an actual steel mill, for which the structure and relationships between the main sections of the process lines have been presented in Fig. 1, where the following designations have been accepted.

2.

Isolated steel production system model

In the first section, the actual model of the steel production system has been presented, in which all the main process line devices taking part in the production process have been accounted for. In order to conduct further studies for such a complex production system, analysis of what part of this system has a decisive influence on the production capabilities of the entire process line must be carried out. Using the results of such an analysis, a decomposition of the entire system must be carried out and further studies must be conducted on an isolated subsystem upon which the production capabilities of the entire steel production system are dependent. Table 1 presents an analysis of the production capabilities of the main subsystems of the steel mill. The analysis shows that certain subsystems in the analyzed steel mill are redundant in relation to the demand for their products by further subsystems. This applies to the SP subsystem for production of the ironcontaining sinter designated in Fig. 2 as HS1 and the BF subsystem for production of blast furnace crude iron designated in the same figure as HS2. In both cases, the systems for technological transport are also redundant. The system of conveyor belts between HS1 and HS2, as well as the buffer container, safeguards the continuity of supply of the ironcontaining sinter to the HS2 subsystem. Transport of the crude iron from subsystem HS2 to HS3 is realized in mixing cigars with a capacity of 420 Mg of liquid blast furnace crude iron. The two-station subsystem for desulfurization of crude iron has a processing capacity of 4.5 million Mg/year with a maximum demand for desulfurized crude iron of 4.3 million Mg/year, which is also redundant in relation to the HS4 subsystem for steel production.

The HS7 hot rolling mill subsystem is independent of the HS6 subsystem producing cast strands, because it can use ingots obtained directly from production or storage. One of the parameters lowering the costs of production is the supply of cast strands of the appropriate temperature, that is, the socalled ‘‘hot strands’’ of a minimum temperature of 400 1C. This shortens the time of their annealing in pusher furnaces and also decreases production costs. The following designations have been accepted in Fig. 2: Ti,j—time necessary for realization of the required technological process for the melt (charge) ‘‘i’’ in device ‘‘j’’; tj,(jþd)—time of transition of the charge between individual devices of the process line; i ¼1,2,y,I—designates the number of the melt (charge); j ¼1,2,y,J designates the number of the device in the process line; d ¼1,y,D—the number of the transition route in the process line. From the point of view of scheduling production in the steel production system, the HS4, HS5, and HS6 subsystems, from the production of liquid steel to its casting into cast strands in CCM devices, are crucial. That is why the isolated model of the HSS ¼/HS4, HS5, HS6S system was accepted for further study, with its scheme shown in Fig. 2. The LHF2 ladle furnace in the analyzed steel mill is a twostation device; however, in practice, in the steelworks section, the station in which the melt is processed is not distinguished. That is why, in the model scheme, this was marked with a broken line, and process devices 12 and 13 become one device with number 12 in the model. The designations accepted for the integrated steel production system shown in Fig. 1 were kept for the isolated steel mill model.

3. Mathematical model of steel production schedule optimization The following designations were accepted for the construction of the steel production system mathematical model in order to define the devices participating in the realized

Table 1 – A comparison of production parameters of the main technological devices. Name of subsystem

Device name

Device production capability (Mg/year)

Total subsystem production capability (Mg/year)

SP

DL 1 sinter belt DL 2 sinter belt DL 3 sinter belt

2.5 2.5 2.5

7.5

BF

BF1 blast furnace BF2 blast furnace BF3 blast furnace

2.4 2.8 2.4

7.6

BOF

BOF1—TBM oxygen converter BOF2—LD oxygen converter BOF3—TBM oxygen converter CCM1 continuous steel casting unit CCM2 continuous steel casting unit CCM3 continuous steel casting unit

1.5 1.5 1.5 1.6 1.4 3.0

4.5

RM I hot rolling mill for large sections RM II hot rolling mill for medium sections

1.2 0.815

RM

6.0

2.015

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243

Fig. 2 – Scheme of the isolated steel production model.

technological processes and parameters determining the times for the realized melts:

device; Wi u —set of all ‘‘i’’ melt numbers processed on ‘‘u’’ devices of the same type, uA{1,2,y,5}.

Wi—set of all melt numbers realized in the time for which the schedule is elaborated, i ¼{1,2,y,I}, where I is the amount of melts; Wck—set of all melt numbers in the kth series of melts (series—number of melts of the same grade of steel, cast on the same CCM devices, successively, one after the other), kA{1,2,y,K}, where K is the total number of series of melts for which the schedule is elaborated, c¼ {1,2,3} designates the number of the continuous steel casting

For every process station, only one melt can be processed at a given time:

Wi \ Wkc ¼ 0;

8i; k 2 f1; . . .; Kg; iak

Wi1 [ Wi2 [    [ Wi5 ¼ Wi Wi1 ¼ f6; 7; 8g; Wi4

¼ f15g;

Wi2 ¼ f9; 10; 11g;

Wi5

¼ f19; 20; 21g

Wi3 ¼ f12; 13; 14g;

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P Ik—number of melts in the kth series of melts— Kk ¼ 1 Ik ¼ I; Uj —set of all process device numbers entering into the steel production process line, excluding rolling mills RMI and RMII, where j ¼ {6,7,y,21}; Uij —set of all process device numbers used for processing of the ith melt, Uij 2 Uj ; Uc ¼ {19,20,21}—set of CCM continuous steel casting device numbers, ðUc  Uj Þ; 9Uc 9 ¼ 3; tmini;j —auxiliary time related to setting (starting) melt i on device j (time required for restart of the device after processing of the previous melt) in minutes; tmaxj;ðj7dÞ —maximum time of transition of the charge between individual devices of the process line in minutes; tj,un(i,j)—time of transport of melt i from the previous device to the next device in minutes; xi,j—the instant of commencement of the technological operation (processing) for melt i on device j [h:min]; wn(i,j)—the closest, next melt after melt i processed on device j; un(i,j)—the closest, next device, after device j, on which melt i is processed; tm—the period of time from melt to melt in the case where CCM devices are not excluded from operation between series of melts and a so-called ‘‘connector’’ is used, in which two melts with differing chemical compositions are cast one after the other, in minutes.

As a result of the technological requirements for the realized steel production processes, only one melt may be present on one production station, and for two neighboring technological operations for the same melt, the next operation can be commenced only when the previous operation (on the previous device) has been concluded. The condition of one melt per technological station for the melt sequences can be presented in a graphic form as in Fig. 3 and dependency: xwnði;jÞ;j 2xi;j ZTi;j

ð3:1Þ

The condition for the minimum waiting time for the processing of melt ‘‘I’’ on station ‘‘jþ1’’ can be written in the form of dependency (3.2) (condition ensuring that for two neighboring operations for the same melt, the next operation can be commenced only when the previous operation has been concluded). For the melt sequence, the graphical form of condition (3.2) can be presented as in Fig. 4 xi;unðjþ1Þ 2xi;j ZTi;j þ tj;unði;jÞ for i 2 Wi ; j 2 Uij ; unði;jÞ 2 Uij

Fig. 4 – Graphical form of condition (3.2).

Fig. 5 – Graphical form of dependency (3.3) or (3.4).

Most process devices, especially those in which liquid steel is processed, may require time for preparation of the device for processing of the next melt after conclusion of processing of one melt. Such a condition can be written in the form of dependency (3.3), or in the case of using a so-called ‘‘connector’’ and casting of two different grades of steel one after another, in the form of dependency (3.4). The graphical form of these limitations has been presented in Fig. 5 xwnði;jÞ;j 2xi;j ZTi;j þ tmini;j

ð3:3Þ

xwnði;jÞ;j xi;j ZTi;j þ tm for

i 2 Wkc ;

j 2 Uij ;

wnði;jÞ 2 Wkc

ð3:4Þ

In order to obtain the optimal utilization of the production capabilities of process devices, the breaks in the operation of individual devices should be minimized, which means that in dependencies (3.2) and (3.3) or (3.4), a sign of equality should be accepted, and then the function to be minimized takes on the following form: 8 > > > > > > > > I > i¼1 > > > > > > :

X

ðxwnði;jÞ xi;j Ti;j Þ þ

j 2 Uij i 2 Wkc

I X

X

i¼1

j 2 Uij unði; jÞ 2 Uij

wnðijÞ 2 Wkc

ð3:2Þ

ðxi;unði;jÞ xi;j Ti;j tj;unði;jÞ Þ

9 > > > > > > > > = > > > > > > > > ;

ð3:5Þ for the simultaneous fulfillment of conditions (3.2) and (3.3) or (3.4) and xwnði;jÞ 2xi;j ZTi;j for i 2 Wi ;

Fig. 3 – Graphical form of condition (3.1).

j 2 Uij ;

wnði;jÞ 2 Wi

ð3:6Þ

The set of all possible transition routes between process line devices has been shown in the form of (3.7), and the set of bounds pertaining to transition times for these technological routes has been written in the form of dependency (3.8). Bounds formulated in such a way have the purpose of securing the liquid crude iron and steel from a decrease in

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9 > > > > > t4;6 ; t4;7 ; t4;8 ; t5;6 ; t5;7 ; t5;8 rtmax48 > > > > t9;12 ; t9;13 ; t9;14 ; t10;12 ; t10;13 ; t10;14 ; t11;12 ; t11;13 ; t11;14 rtmax914 > > > > > = t9;16 ; t10;16 ; t11;16 ; t9;18 ; t10;18 ; t11;18 rtmax918 t1;4 ; t1;5 ; t2;4 ; t2;5 ; t3;4 ; t3;5 rtmax15

temperature to below the limit temperature 9 BF1; BF2; BF3-HMDP1; HMDP2 > > > > HMDP1; HMDP2-BOF1; BOF2; BOF3 > > > > > > AR1; AR2; AR3-LHF1; LHF2 > > > > = AR1; AR2; AR3-WO1; WO3

t14;16 ; t14;17 rtmax1417

LHF1; LHF2-RH LHF2-WO1; WO2; WO3 RH-WO1; WO2; WO3

t12;15 ; t13;15 ; t14;15 rtmax1215

ð3:7Þ

> > > > > > > > > > > > > > ;

LHF1-WO1; WO2

ð3:8Þ

> > > > > > > > > > > > > > ;

t12;16 ; t12;17 ; t12;18 ; t13;16 ; t13;17 ; t13;18 rtmax1218 t15;16 ; t15;17 ; t15;18 rtmax1518

Table 2 – Times of realization of technological processes for the casting sequences W21 and W61 on the CCM1 device. W21 sequence 280 mm  400 mm  5350 mm j/i

3

BOF1p BOF1k BOF2p BOF2k BOF3p BOF3k AR1p AR1k AR2p AR2k AR3p AR3k LHF1p LHF1k RHp RHk WO1p WO1k CCM1p CCM1k

5

7

11

00:50 01:46 21:44 22:30

W61 sequence 280 mm  400 mm  5350 mm

14

19

21

25

29

07:49 08:30

08:51 10:01

11:23 12:06

13:32 14:28

03:04 04:03

36

17:37 18:18 08:35 08:41

00:05 00:20 00:23 01:20 01:20 01:42 02:26 02:36 02:37 04:35

10:05 10:30

12:10 12:30

14:34 14:55

04:05 04:14

02:21 03:11 03:17 03:36 04:25 04:36 04:37 06:27

40

17:55 19:02

04:40 05:32

01:53 02:10

37

16:00 16:46

23:21 00:05

22:30 22:45 22:50 00:10 23:31 00:10 00:25 00:43 00:45 02:35

33

19:54 20:39 19:07 19:36

16:54 17:04 05:35 06:15 06:41 07:20 07:26 07:44 08:08 08:15 08:16 10:27

04:47 05:21 05:26 05:48 06:16 06:28 06:29 08:14

08:53 09:39 09:44 10:00 10:22 10:28 10:29 12:20

10:52 11:25 11:30 11:50 12:15 12:21 12:22 14:19

12:48 13:27 13:32 13:52 14:13 14:20 14:21 16:05

15:05 15:50

17:10 17:40

18:19 18:36 18:47 19:20

16:04 16:13 16:15 17:58

17:56 17:59 18:00 19:47

19:33 19:48 19:49 21:31

19:45 21:12

20:40 21:15 21:21 22:55

21:27 21:32 21:33 23:20

23:10 23:21 23:22 01:02

Table 3 – Times of realization of technological processes for the casting sequences W12 and W72 on the CCM2 device. W12 sequence 160 mm  160 mm  12,000 mm j/i

1

2

4

BOF1p BOF1k BOF2p

18:47 19:31

21:25 22:05

23:03 23:43

BOF2k BOF3p BOF3k AR1p AR1k AR2p AR2k AR3p AR3k LHF1p LHF1k LHF2p LHF2k RHp RHk WO2p WO2k CCM2p CCM2k

10

W72 sequence 160 mm  160 mm  5950 mm 13

16

20

23

04:12 05:01

27

31

35

12:37 13:18

14:59 15:39

17:08 17:48

38

41

01:50

05:50

07:50

10:35

20:45

03:00

06:40

08:47

11:05

21:24 18:53 19:41

19:35 19:47

21:31 22:40 20:10 20:52

22:50 22:57 22:59 00:53

22:10 22:30

23:47 23:59

05:04 05:22 03:05

06:40

08:50

11:32

03:20

07:20

09:34

11:47

03:23 04:40 22:48 00:35

00:40 00:54 00:55 03:02

13:20 13:30

05:43 06:32

07:30 08:27

09:44 10:31

15:45 16:03

44

22:03 22:46

17:54 17:59 21:32 21:55

11:55 12:35

13:45 15:00

16:15 17:00

18:15 18:45

19:42 20:07 20:16 20:45

12:48 12:56 12:57 14:47

15:05 15:28 16:14 16:27 16:28 18:15

17:04 17:25 17:59 18:16 18:17 20:09

18:49 19:12 19:50 20:10 20:11 22:08

20:59 21:23 22:06 22:09 22:10 00:07

22:05 22:37

22:52 23:29 23:34 00:36

22:41 23:05 23:55 00:08 00:09 02:01

00:53 01:16 01:53 02:02 02:03 03:52

00:17 02:40

02:47 03:03 03:04 05:02

04:55 05:03 05:04 07:00

06:48 07:01 07:02 08:54

08:43 08:55 08:56 10:53

10:46 10:54 10:55 12:55

246

02:15 03:05 03:15 03:30 03:30 04:25 23:47 01:10 01:20 01:30 01:30 02:28 22:55 00:10 00:20 00:37 00:37 01:29 22:20 23:15 23:30 23:40 23:40 00:36 14:50 15:35 15:43 15:55 15:55 16:42 11:20 12:50 13:00 13:10 13:10 14:11 08:35 10:05 10:13 10:32 10:32 11:27 08:00 09:10 09:19 09:40 09:40 10:30

01:17 01:30

01:47 03:45 03:55 04:00 04:00 04:44 LHF2p LHF2k WO3p WO3k CCM3p CCM3k

03:15 03:22 00:21 01:17

02:35

BOF1k BOF3p BOF3k AR1p AR1k AR3p AR3k

03:45 04:30 04:40 04:45 04:45 05:28

04:05 05:10 05:20 05:30 05:30 06:14

04:21 04:30 03:28 03:50

04:45 05:50 05:58 06:16 06:16 07:02

07:05 08:20 08:29 08:42 08:42 09:38

07:23 07:39 06:15 06:35 03:38 04:21 01:24 03:28

12:07 13:45 13:55 14:13 14:13 15:02

13:30 14:50 15:00 15:04 15:04 15:53

15:50 16:25 16:35 16:44 16:44 17:34

16:53 17:22 17:30 17:36 17:36 18:28

17:45 18:10 18:18 18:30 18:30 19:20

21:23 22:25 22:35 22:43 22:43 23:38

21:38 21:58 17:14 17:28 16:25 16:38 14:11 14:25 12:56 13:11 10:25 10:49 07:43 08:14

09:36 10:19 06:52 07:39 06:33

07:19 06:12

05:16 01:35 BOF1p

8 9 6 j/i

11:27 11:48

13:17 14:11 10:35 11:23

12:03 12:51

15:11 15:32

15:25 16:24 14:24 15:11

01:13 02:10 02:20 02:30 02:30 03:28

01:40 02:00 00:40 00:55 23:10 23:25 20:33 21:12

16:25 17:12

20:31

19:32

32 30 28 26 24 22 18 17 15 12

2030 mm  220 mm  6750 mm

22:16 22:40

23:06 22:13 20:58 21:37

22:21 21:29

46 45 43 34

39

42

W83 sequence 1600 mm  220 mm  9000 mm W53 sequence 13001575 mm  220 mm  10,500 mm W43 sequence W33 sequence

2030 mm  220 mm  8500 mm

Table 4 – Times of realization of technological processes for the casting sequences W33 , W43 , W53 , and W83 on the CCM3 device.

23:50 00:32

47

00:53 01:30

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For the analyzed steel mill, the times tmaxj;ðj7dÞ accept the following numerical values in minutes: tmax15 ¼ 60; tmax48 ¼ 20; tmax914 ¼ 30; tmax918 ¼ 20; tmax1417 ¼ 30; tmax1215 ¼ 15; tmax1218 ¼ 30; tmax1518 ¼ 30: In order to shorten the heating time of cast strands in furnaces before the plastic working process in rolling mills RM I and RM II, the time from their casting on CCM devices to loading into furnaces should not be longer than tmax1923 . For fulfillment of bound (3.9), the rolling mills receive a so-called ‘‘hot charge’’, that is, cast strands of a temperature above 400 1C. This bound does not apply to cast strands for outside recipients t19;22 ; t19;23 ; t20;22 ; t20;23 ; t21;22 ; rtmax1923

ð3:9Þ

For the analyzed steel mill, the time tmax1923 ¼ 60min. Furthermore, for processing times of the ith melt in LHF ladle furnaces and the RH vacuum device for degassing of steel, a time of tmini;j ¼ 15min is to be added for every process for preparation of these devices for processing of the next melt, according to dependencies: 9 Tni;12 ¼ Ti;12 þ tmini;j > > = Tni;14 ¼ Ti;14 þ tmini;j ð3:10Þ > ; Tni;15 ¼ Ti;15 þ tmini;j >

4.

Analysis of the actual production schedule

According to the accepted designations, a set of numbers of process devices participating in the processing of the ith melt in the isolated steel production system can be recorded as follows: U ¼{6,7,8,9,10,11,12,14,15,16,17,18,19,20,21}. For the BOF1 oxygen converter, the sets of all process device numbers for possible transit routes will be as follows: U1 ¼{6,9,12,15,16,19}, U2 ¼{6,9,12,15,17,20}, U3 ¼{6,9,12,15,18,21}, U4 ¼{6,9,14,15,16,19}, U5 ¼{6,9,14,15,17,20}, U6 ¼{6,9,14,15,18,21}, U7 ¼ {6,9,12,16,19}, U8 ¼ {6,9,12,17,20}, U9 ¼ {6,9,12,18,21}, U10 ¼ {6,9,14,16,19}, U11 ¼ {6,9,14,17,20}, U12 ¼ {6,9,16,19}, U13 ¼{6,9,18,21}. For such determined transit routes of melts from the BOF1 converter, it was accepted that the argon treatment process will always take place at the AR1 station. In the analyzed steel mill, melts from converters are subjected to argon treatment at a different station than that assigned to a given converter only in emergency situations. Analysis of production scheduling in the studied steel mill was carried out for a selected period of time, during which production was very high, three oxygen converters, BOF1, BOF2, and BOF3 were operating simultaneously, and constant steel casting processes were realized on all three CCM devices: CCM1, CCM2, and CCM3. Table 1 shows the production capabilities of all of the main process devices of the analyzed steel mill. As shown in the data in the table, the lowest production capabilities in the system are exhibited by oxygen converters BOF1, BOF2, and BOF3, with a joint production of 4.5 million Mg of liquid steel. Such a mode of operation of the steelworks occurs very rarely, because oxygen converters operate alternately, with two

archives of civil and mechanical engineering 12 (2012) 240–252

operating and one being in a maintenance cycle based on replacement of the refractory furnace lining. From the recorded statistical data of 6295 melts, a period of time was selected, including the realization of 47 melts on all three converters, from which 18 melts were realized on BOF1, 8 melts were realized on BOF2, and 21 melts were realized on BOF3. All melts with post-furnace processing and constant steel casting were made during a time of 33 h and 38 min and were cast using three CCM devices in the following way: – 13 melts cast in two sequences on the CCM1 device, with sequences of 8 and 5 melts, with a different grade of steel cast in each sequence; – 14 melts cast in two sequences on the CCM2 device, with sequences of 8 and 6 melts, with a different grade of steel cast in each sequence; – 20 melts cast in four sequences on the CCM3 device, with sequences of 4, 3, 7, and 6 melts, with a different grade of steel cast in every successive sequence. According to the designations accepted in Fig. 2, the following can be written for the analyzed series of melts: Ti,j—time necessary for realization of the required technological process for the melt (charge) ‘‘i’’ in device ‘‘j’’, where i¼ 1,y,47 designates the melt number, and j ¼6,y,21 designates the number of the process device; Wi ¼ {1,y,47} set of all melt numbers realized during the time for which the schedule was elaborated; Wkc —set of all melt numbers realized in the kth series of melts realized on the same constant steel casting CCM device, where k¼ {1,y,8}, c¼{1,2,3};

247

W12 ¼{1,2,4,10,13,16,20,23} casting sequence of 8 melts on the CCM2 device; W21 ¼{3,5,7,11,14,19,21,25} casting sequence of 8 melts on the CCM1 device; W33 ¼{6,8,9,12} casting sequence of 4 melts on the CCM3 device; W43 ¼{15,17,18} casting sequence of 3 melts on the CCM3 device; W53 ¼{22,24,26,28,30,32,34} casting sequence of 7 melts on the CCM3 device; W61 ¼{29,33,36,37,40} casting sequence of 5 melts on the CCM1 device; W72 ¼{27,31,35,38,41,44} casting sequence of 6 melts on the CCM2 device; W83 ¼{39,42,43,45,46,47} casting sequence of 6 melts on the CCM3 device; Uj ¼{6,y,21}—set of all process device numbers of the steel production system; Uij —set of all process device numbers used for processing of the ith melt; U2j ¼ {6,9,12,20}; U3j ¼{8,11,14,15,19};y U1j ¼ {6,9,12,14,20}; 7 24 Uj ¼ {7,10,14,15,19};y yUj ¼ {7,10,12,21};y U47 j ¼ {8,11,12,21}.

Data on 47 successively realized melts has been presented in Tables 2–4 along with specification of the technological route for individual grades of produced steel. Tables 2, 3, and 4 present data on the times of realization of individual technological processes for the casting sequence on devices CCM1, CCM2, and CCM3, respectively. Below the sequence numbers, the cross-sections and lengths of the cast strands have been given. The letter ‘‘p’’ next to the designations of devices used for realization of technological processes

Fig. 6 – Schedule 47 for melts made in real time.

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designates the start of the process and ‘‘k’’ is the conclusion of the process for successive melts. The schedule of realized melts in real time has been presented in Fig. 6, where the broken line marks casting sequences W21 andW61 on the CCM1 device, the continuous line marks casting sequences W12 and W72 on the CCM2 device, and the dotted line marks the casting sequences W33 , W43 , W53 , and W83 on the CCM3 device. The LHF2 ladle furnace has two stations, which provides the capability for simultaneous processing of two melts. This is shown in Fig. 7 as the overlapping of many melts on the same process device at the same time, e.g. melts No. 15, 17, 18. Table 5 presents an analysis of the realized melts, their post-furnace processing and continuous steel casting, and transitions of the processed melts between successive devices of the process line. The analysis was realized in terms of compliance of the realized operations with the bounds accepted for realization of the target function presented in Section 3. As can be observed in the presented analysis, for 20 melts realized in the BOF1, BOF2, and BOF3 converters, nonconformance with the correct scheduling process was observed. In 10 cases, this applies to early commencement of steel manufacturing processes in oxygen converters. Breaks in the processing of successive melts on the same devices were shorter than those that were determined, e.g. a break lasted 4 min for a determined break no shorter than 15 min. There were excessively lengthy processing types of melts on certain process devices, e.g. melt No. 8 was melted in the BOF3 converter for 124 min, and the average melting time is 44 min. Non-conformance also occurred in the excessively lengthy transition times of melts between successive devices, e.g. in the case of melt No. 41, the transition time from the RH vacuum degassing to the CCM1 continuous steel casting device was 64 min, and this time should not be longer than 15 min. An excessively lengthy transition time between these devices may cause an excessive decrease in the temperature of the liquid steel. In two cases, a machine conflict occurred. At the same time, at the LHF1 ladle furnace station, two successive melts were processed. After directing melt No. 38 to this device, the processing of melt No. 37 had to be interrupted and finished after the conclusion of processing of the melt that cause the machine conflict. Melt No. 38 had to be transferred early to the CCM2 continuous steel casting device in order to maintain the casting sequence.

Table 5 – Analysis of melt realization, their post-furnace processing and continuous casting. Melt No.

Converter no.

Non-conformance of melt realization with the bounds of the steel production system model

1

BOF1

2

BOF1

3

BOF3

4

BOF1

5

BOF3

6

BOF3

7

BOF2

8

BOF3

10 11

BOF2 BOF2

14 27

BOF3 BOF1

31

BOF1

35

BOF1

36

BOF3

37

BOF1

38

BOF3

40

BOF3

41

BOF2

44

BOF3

Melting was started too early—necessary processing on LHF1 and LHF2 Melting was started too early—break for LHF1 between melt Nos. 1 and 2 only 8 min Melting started too early – time of transition from RH to CCM1 – 35 min Melting was started too early—processing time on LHF2 143 min Melting started too early – time of transition from RH to CCM1 – 55 min Melting was started too early—processing time on LHF2 118 min Break until melt No. 10 was only 4 min – time of transition from RH to CCM1 – 61 min Melting was started too early—processing time 124 min Break until melt No. 11 was only 4 min Melting started too early – time of transition from RH to CCM1 – 41 min Melting started too early Time of transition from RH to CCM1—60 min Time of transition from RH to CCM1—52 min Time of transition from RH to CCM1—59 min Melting started too early—only 2 min after conclusion of melt No. 35 Machine conflict with melt No. 38 on the LHF1 device Time of transition from RH to CCM1—47 min Machine conflict with melt No. 41 on the LHF1 device Time of transition from RH to CCM1—64 min Time of transition from RH to CCM1—47 min

The conducted analysis makes it possible to state the thesis that the production scheduling method used in the analyzed steel mill does not fulfill all requirements stated for such systems.

5. Production scheduling using the integrated steel production system model

Fig. 7 – A fragment of the schedule with arising machine conflicts.

Data on the realization of individual technological operations for selected melts, for which non-conformance was observed in the scope of the time of realization of the process itself or the transition time between successive devices, as well as in cases of machine conflicts, has been presented in Tables 6 and 7. In the case of melt Nos. 1 and 2, it was stated that the moment of commencement of these melts was too early with

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Table 6 – Comparison of the times of duration of technological operations for selected melts. Melt No.

Technological devices – device no. – time of duration of the technological operation Ti,j in minutes BOF1 6

BOF2 7

BOF3 8

AR1 9

AR2 10

AR3 11

LHF2 12

LHF1 14

RH 15

CCM1 19

CCM2 20

CCM3 21

End of cycle

1 2 3

44 40 –

– – –

– – 44

12 20 –

– – –

– – 15

42 47 –

69 – 40

– – 39

– – 110

114 127 –

– – –

365 495 468

37 38 40 41

67 – – –

– – – 39

– 48 45 –

29 – – –

– – – 23

– 25 35 –

– – – –

87 29 94 32

– 24 – 23

107 – 100 –

– 117 – 112

– – – –

1713 1760 1825 1874

47

–

–

37

–

–

20

50

–

–

–

–

55

2018

Table 7 – Coordinates of times of commencement of technological operations for selected melts—minutes. Melt No.

1

2

3

Time of commencement of the technological operations X2,6 ¼ 158 BOF1 X1,6 ¼0 BOF2 BOF3 X3,8 ¼ 177 X2,9 ¼ 203 AR1 X1,9 ¼48 AR2 AR3 X3,11 ¼ 223 LHF2 X1,12 ¼ 163 X2,12 ¼241 X3,14 ¼ 243 LHF1 X1,14 ¼ 83 RH X3,15 ¼ 284 CCM1 X3,19 ¼ 358 CCM2 X1,20 ¼ 251 X3,20 ¼368 CCM3 End of cycle 365 495 468

37

38

40

X38,8 ¼ 1446

X40,8 ¼1507

X38,11 ¼ 1495

X40,11 ¼1553

X38,14 ¼ 1529 X38,15 ¼ 1572

X40,14 ¼1594

41

47

X37,6 ¼1388 X41,7 ¼ 1558 X47,8 ¼ 1806

X37,9 ¼1460 X41,10 ¼1605

(X37,14)0 ¼1498 X37,19 ¼1606

regard to the moment of commencement of the continuous casting process on CCM2 devices. In the case of melt No. 1, as a result of early commencement of realization of the melt in the BOF1 converter, processing of this melt was carried out twice at ladle furnace stations HLF2 and then HLF1. This was caused by the necessity to hold the melt that was made too early before transferring it to the CCM2 continuous steel casting device. In this case, the time from the commencement of steel melting in the converter to supply of this melt to the rotary tower of the CCM2 device was equal to 251 min, and for this technological route, it should be within the range of 105–125 min. The data in Tables 6 and 7 will make it possible to determine such times of commencement of steel melting processes in oxygen converters BOF 1 and BOF 2, so that devices for continuous steel casting can cast successive melts sequentially, and the time from commencement of melting to the supply of the melt to CCM devices is as short as possible. In Table 7, xi,j designates the times of commencement of technological operations of processing of melt ‘‘i’’ on device ‘‘j’’. In the case of the pairs of melts No. 37 and No. 38 as well as No. 40 and No. 41, a machine conflict occurred during realization of processing of these melts at the LHF1 ladle furnace station. In both cases, during the realization of the technological process necessary for the given grade of steel, the subsequent melt was supplied with the previous melt, and it was processed earlier and

X41,14 ¼1638 X41,15 ¼1674

X40,19 ¼1725 X38,20 ¼ 1643

1713

X46,11 ¼ 1853 X47,12 ¼ 1888

1760

X41,20 ¼1762 1825

1874

X47,21 ¼ 1963 2018

sent for further processing. It appears that the previous melt was side tracked to a reserve station during the realization of the technological process, and after the conclusion of melt processing, was subjected to the technological process in ladle furnace LHF1 again. Such realization of technological processes for the purpose of maintaining a sequential method of casting of successive melts on devices CCM1, CCM2, and CCM3 is incorrect and shows that the algorithm used for preparing the production schedule for the specified time of operation of the steel mill has no bounds for avoiding these types of situations. Fig. 7 presents a fragment of the schedule realized in real time with the arising machine conflicts. Melts No. 38 and No. 41 had to be supplied earlier to the continuous steel casting devices, which forced a break in the processing of melts No. 37 and No. 40. A target function (3.5) was formulated in Section 3 and was to ensure minimization of the time of realization of the planned production task and its execution within a strictly defined time for which the schedule was constructed, with insurance of availability of production and transport devices. Taking bounds (3.1), (3.2), (3.3), (3.4), and (3.6) into consideration, all stated errors in the production schedule realized in real time can be eliminated. Necessary corrections to the schedule: Determination of the time of commencement of steel melting in the BOF1 converter for melt No. 1: x1,6 ¼ x1,20 t14,20T1,14t9,14T1,9t6,9T1,6.

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Table 8 – Average processing and flow times in the steel production process line for converter BOF1. Statistics for 731 melts (times given in minutes) Device symbol

Average from test

UFN

MIN

MAX

Average for 1a ¼ 0.995

Mill data

Dt

BOF1 BOF3 BOF1-AR1 BOF3-AR3 AR1 AR3 AR1-LHF1 AR1-LHF2 AR3-LHF1 AR3-LHF2 LHF1 LHF2 LHF1-WO1 LHF1-WO2 LHF2-WO1 LHF2-WO2 LHF2-WO3 LHF1-RH LHF2-RH RH RH-WO1 RH-WO2 CCM1 280  400 CCM2 160  160 CCM3 2030  220

43.3 43.7 4.6 4.8 20.1 22.1 14.1 19.7 13.5 20.3 57.1 64.0 26.1 26.6 25.5 23.1 14.9 3.6 14.9 37.1 26.6 23.8 108.07 103.4 68.5

1.2 1.0 0.48 0.48 1.5 1.7 1.7 1.9 3.6 1.9 5.1 5.9 1.8 2.1 2.1 2.5 7.1 0.9 7.1 3.2 1.9 2.4 3.7 4.3 7.6

43 43 4.0 4.0 19.0 21.0 13.0 18.0 10.0 19.0 53.0 59.0 25.0 25.0 24.0 21.0 12.0 3.0 4.0 34.0 25.0 23.0 106.0 100.0 62.0

44 44 5.0 6.0 21.0 23.0 15.0 21.0 17.0 22.0 62.0 69.0 27.0 28.0 27.0 25.0 21.0 4.0 99.0 40.0 28.0 26.0 112.0 107.0 76.0

43.4 43.4 5.0 4.7 20.1 22.1 14.1 19.3 12.3 20.4 57.4 63.3 26.3 26.7 25.6 22.5 17.8 3.3 14.5 36.8 26.3 24.5 109.2 103.6 68.8

40.0 40.0 5.0 5.0 10.0 10.0 10.0 10.0 10.0 10.0 40.0 40.0 20.0 20.0 20.0 20.0 10.0 3.0 15.0 30.0 20.0 20.0 105.0 98.0 60.0

3.4 3.4 0.0 0.3 10.1 12.1 4.1 9.3 2.3 10.4 7.8 23.3 6.3 6.7 5.6 2.5 7.8 0.3 0.5 6.8 6.3 4.5 4.2 5.6 8.8

After substituting the average numerical values of times of duration of technological processes for individual devices and transition times of the melt between these devices, as presented in Table 8, calculated on the basis of statistical tests, it can be calculated that: (x1,6)0 ¼76 that is, the time of commencement of realization of melt No. 1 in the BOF1 converter can be shifted by 76 min later than was determined in the schedule and recorded in Table 8 as x1,6 ¼0. Determination of the time of commencement of steel melting in the BOF1 converter for melt No. 2: x2,6 ¼ x2,20 t14,20T2,14t9,14T2,9t6,9T2,6. After substituting average time values analogously, as in the case of calculation of the value of x1,6, the following value will be obtained: (x2,6)0 ¼193, therefore, the moment of commencement of realization of melt No. 2 on the BOF1 converter may take place in the 193rd minute, that is, 35 min later than planned in the initial schedule. Calculation of the total cycle time as the technological operations for a given grade of steel: Tc ¼Tc1þTc2, where Tc1 is the total time of melting and post-furnace processing of the melt; Tc2 is the total casting time of the melt on the CCM device. For melt No. 1, Tc1 ¼ 175 min and Tc2 ¼114 min; thus, the total cycle time is equal to: Tc ¼289 min. After such a correction of the times of commencement of the steel melting process in the BOF1 converter, the clock time of commencement of the schedule can be shifted from 18:47 to 20:03. Removal of the machine conflict for the LHF1 device between melts No. 37 and No. 38 is to be carried out in accordance with condition (3.1) xwnði;jÞ;j 2xi;j ZTi;j

where xwn(i,j),j—the time of commencement of the processing of the closest possible melt after melt ‘‘i’’ on device ‘‘j’’ x39,14x37,14ZT37,14; that is 31o57.1 Condition (3.1) is not fulfilled; therefore, melt No. 37 realized in the BOF1 converter should be started earlier. As it results from the data in Tables 2, 3, and 4, melting can be started 20 min earlier and should last 44 min, that is, as long as the average time for this operation in the BOF1 converter: (x37,6)0 ¼ 1368, (x37,9)0 ¼1440, (x37,14)0 ¼ 1478. For the BOF3 converter and melt No. 38: (x38,14)0 ¼ 1550, (x38,15)0 ¼ 1560. After execution of these operations, condition (3.1) is fulfilled, that is, the machine conflict on the LHF1 ladle furnace was removed, and simultaneously, the liquid will still be supplied to CCM devices according to the initially specified time so as to ensure sequential casting. Analogously, new times of commencement of technological operations for the processing of melts No. 40 and No. 41 were calculated in order to remove the machine conflict on the LHF ladle furnace. The new numerical values of the times of commencement of technological processes of the processing of melt ‘‘i’’ on individual devices ‘‘j’’ have been given in Table 9 as (xi,j)0 . Fig. 8 presents a schedule for 47 melts after removal of machine conflicts and correction of time of commencement of technological processes for steel melting in the BOF1 converter. The changes made in the analyzed production schedule of the steel mill for the production of 47 melts caused that the

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Table 9 – Coordinates of times of commencement of technological operations for selected melts after corrections and removal of machine conflicts – in minutes. Melt No.

1

2

Time of commencement of the technological operations (X2,6)0 ¼ 193 BOF1 (X1,6)0 ¼ 76 BOF2 BOF3 (X2,9)0 ¼ 241 AR1 (X1,9)0 ¼ 124 AR2 AR3 LHF2 LHF1 RH CCM1 CCM2 CCM3 End of cycle

3

37

38

40

X38,8 ¼ 1446

X40,8 ¼ 1507

X38,11 ¼ 1495

X40,11 ¼1553

(X38,14)0 ¼ 1550 (X38,15)0 ¼ 1610

(X40,14)0 ¼ 1620

41

47

(X37,6)0 ¼1368 X41,7 ¼ 1558 X3,8 ¼ 177

X47,8 ¼ 1806

(X37,9)0 ¼1440 X41,10 ¼1605 X3,11 ¼223

(X1,12)0 ¼ 164

X46,11 ¼ 1853 X47,12 ¼ 1888

(X2,12)0 ¼ 281 X3,14 ¼243 X3,15 ¼284 X3,19 ¼358

X1,20 ¼ 251

X3,20 ¼ 368

365

495

(X37,14)0 ¼ 1478 X37,19 ¼ 1606

X40,19 ¼1725 X38,20 ¼ 1643

468

1713

(X41,14)0 ¼ 1670 X41,15 ¼1674

1760

X41,20 ¼1762 1825

1874

X47,21 ¼ 1963 2018

Fig. 8 – Schedule for 47 melts after removal of machine conflicts and correction of the time of commencement of technological processes.

time of realization of the planned production tasks was shortened by 83 min, which constitutes 4.1% of the entire time of realization of the production task. This will make it possible to realize two additional melts within the time planned earlier. Detailed analysis of the times of realization of individual technological processes for both studied schedules has been presented in Table 10. In Table 9, the H column designates the number of the analyzed schedule, and the HT column with rows from HT1 to HT5 designate, respectively: HT1—the time of commencement of technological operations on individual process devices for the first melt in the analyzed schedule; HT2—the time of conclusion of technological operations on individual process devices for the last melt in the analyzed schedule;

HT3—time from the commencement of processing of the first melt on a given technological device to the conclusion of processing of the last device within the framework of the analyzed schedule; HT4—time of actual operation of the process device during processing of all melts realized within the framework of the analyzed schedule; HT5—HT4 to HT3 ratio expressed as a percentage. The data in the rows from HT1 to HT5 for schedule 1 are for the schedule realized in real time as shown in Fig. 6 and analogous for schedule 2 for the schedule shown in Fig. 8 after removal of machine conflicts and correction of the times of commencement of technological processes according to the scheduling procedure presented in Section 3. As it results from the presented data, a slight increase in the exploitation of technological devices took place during the time of realization of production tasks.

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Table 10 – Comparison of the times of duration of technological processes in schedules 1 and 2. H

HT

Technological devices BOF1

BOF2

BOF3

AR1

AR2

AR3

LHF2

LHF1

RH

CCM1

CCM2

CCM3

Schedule 1

HT1 HT2 HT3 HT4 HT5

18:47 23:26 1699 882 51.9%

00:50 21:24 1234 407 32.9%

21:44 01:30 1666 1053 63.2%

19:35 23:25 1680 317 18.9%

01:52 21:55 1153 173 15.1%

22:30 02:00 1650 436 26.4%

20:10 03:05 1855 1544 83.2%

21:31 00:36 1613 1169 72.5%

23:31 01:16 1549 324 20.9%

00:45 01:02 1457 1425 97.8%

22:59 03:52 1733 1608 92.8%

04:00 03.28 1408 1030 73.2%

Schedule 2

HT1 HT2 HT3 HT4 HT5

20:03 23:26 1623 882 54.4

00:50 21:24 1234 407 32.9%

22:30 01:30 1620 1053 65.1%

20:51 23:25 1604 317 19.8%

01:52 21:55 1153 173 15.1%

23:30 02:00 1590 436 27.4%

21:55 03:05 1750 1544 88.2%

22:50 00:36 1534 1169 76.2%

23:31 01:16 1549 324 20.9%

00:45 01:02 1457 1425 97.8%

22:59 03:52 1733 1608 92.8%

04:00 03.28 1408 1030 73.2%

2.5%

No change

1.9

0.9%

No change

1.0%

5.0%

3.7%

No change

No change

No change

No change

Change

6.

Conclusion

From the point of view of production scheduling and searching for the best possible parameters for exploitation of all devices operating in the steel mill, the most significant factor is the operation of the steelworks, that is, subsystems HS4, HS5, and HS6. For production nearing production capacity, the scheduling process is difficult due to the possibility of occurrence of ‘‘machine conflicts’’. For limited production resulting from a decreased number of orders, the scheduling process is simple; however, there are problems with exploitation, which must be realized so that there is no technical degradation of technological devices. It is necessary to use production scheduling algorithms in continuous steel casting devices CCM1, CCM2, and CCM3, which will optimally determine what sections and with what speed will be the case in specific sequences. The algorithms take into account the realization of production orders, especially in the scope of transfer of cast strands with the highest possible temperature to the hot rolling mills RMI and RMII, while ensuring optimal exploitation of oxygen converters, post-furnace processing devices, and steelwork ladles, minimizing the time during which liquid steel is kept in them. Production schedules were constructed on the basis of the elaborated steel production model, minimizing the time of realization of planned production tasks while eliminating the possibility of occurrence of machine conflicts. The studies conducted on the basis of the schedule realized in real time showed the suitability of the elaborated model for removing machine conflicts and shortening the time of realization of production tasks planned in the schedule. Schedules constructed using the elaborated model also allows for such planning of production tasks on individual technological devices so as to ensure their optimal exploitation. By eliminating excessively lengthy intervals, while expecting the realization of processing of subsequent melts, they also

ensure necessary breaks for the preparation of devices between melts. A priority in the construction of schedules ensures sequential casting in continuous steel casting devices. Using the elaborated model for building schedules, the realization of this task can be ensured.

r e f e r e n c e s

[1] P. Cowling, W. Rezig, Integration of continuous caster and hot strip mill planning for steel production, Journal of Scheduling 3 (2000). [2] B. Karwat, Analysis of materials’ flow in a steel mill in order to determine exploitation parameters of technological line’s devices, scientific problems of machines operation and maintenance, Zagadnienia Eksploatacji Maszyn PAN 4 (156) (2008) 43. [3] B. Karwat, Production scheduling in a steel working plant, scientific problems of machines operation and maintenance, Zagadnienia Eksploatacji Maszyn PAN 2 (154) (2008) 43. [4] B. Karwat, Modelowanie zintegrowanego systemu wytwarzania stali, Biblioteka Problemo´w Eksploatacji, Wydawnictwa Naukowe Instytutu Technologii Eksploatacji PIB, Radom 2010. [5] S. Li, Z. Chan, Mathematical models of logistics decision in slab yard in an iron and steel complex, Journal of University of Science and Technology, Beijing (English edition) 7 (4) (2000) 301–304. [6] J. Majewski, Informatyka dla logistyki, Biblioteka Logistyka, Poznan´, 2002. [7] E. Michlowicz, Podstawy logistyki przemysłowej, Uczelniane Wydawnictwa Naukowo–Dydaktyczne AGH, Krako´w, 2002. [8] S. Park, Y. Sohn, The development of synchronized scheduling system for steel making & hot rolling process, RIST Journal of R&D (South Korea) 17 (2) (2003) 190–196. [9] F. Pettersson, M. Slotte, T. Haggblad, J. Koistinen, H. Saxen, A system for optimal melt shop production planning, in: Proceedings of the Iron and Steel Society/AIME 84th Steelmaking Conference, Baltimore, 2001, pp. 517–523. [10] T. Siwak, Optymalizacja dyskretna w elastycznych systemach produkcyjnych, WNT, Warszawa, 1992.