integrated model for production planning in a large iron and steel manufacturing environment

This article was downloaded by: [Linnaeus University]On: 16 October 2014, At: 13:52Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T3JH, UK

International Journal ofProduction ResearchPublication details, including instructions forauthors and subscription information:http://www.tandfonline.com/loi/tprs20

Integrated model forproduction planning in a largeiron and steel manufacturingenvironmentHong Li & J. ShangPublished online: 14 Nov 2010.

To cite this article: Hong Li & J. Shang (2001) Integrated model for productionplanning in a large iron and steel manufacturing environment, International Journalof Production Research, 39:9, 2037-2062, DOI: 10.1080/00207540110035200

To link to this article: http://dx.doi.org/10.1080/00207540110035200

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all theinformation (the “Content”) contained in the publications on our platform.However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness,or suitability for any purpose of the Content. Any opinions and viewsexpressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of theContent should not be relied upon and should be independently verified withprimary sources of information. Taylor and Francis shall not be liable for anylosses, actions, claims, proceedings, demands, costs, expenses, damages,and other liabilities whatsoever or howsoever caused arising directly orindirectly in connection with, in relation to or arising out of the use of theContent.

This article may be used for research, teaching, and private study purposes.Any substantial or systematic reproduction, redistribution, reselling, loan,sub-licensing, systematic supply, or distribution in any form to anyone is

http://www.tandfonline.com/loi/tprs20

http://www.tandfonline.com/action/showCitFormats?doi=10.1080/00207540110035200

http://dx.doi.org/10.1080/00207540110035200

expressly forbidden. Terms & Conditions of access and use can be found athttp://www.tandfonline.com/page/terms-and-conditions

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

http://www.tandfonline.com/page/terms-and-conditions

int. j. prod. res., 2001, vol. 39, no. 9, 2037 ± 2062

Integrated model for production planning in a large iron and steelmanufacturing environment

HONG LIy and J. SHANGz*

The authors have developed a production-planning model for a large steel cor-poration in China. Large systems normally require decomposition and module-interfaces, yet complicated interfaces often result in system breakdown and pre-vent it from reaching its full potential. To overcome di� culties of the linkageproblem and to synchronize the production of main products and by-products,the input-output (I± O) model was looked at. The proposed optimization model,based on the I± O concept, is capable of coordinating large number of variableswith minimum interfaces. It provides a comprehensive production managementframework. Owing to the generality of the model structure, the authors believe itis useful for both the studied company and for many other organizations.

1. Introduction

High productivity and energy e� ciency are the main objectives of today’ s iron

and steel manufacturing. The present research addresses the problem of coordinating

multiple plants in a large iron and steel complex in China. The goal is to maximizeiron and steel production while at the same time minimizing by-product gas emis-

sions. In fact, energy consumption accounts for a major part of a steel company’s

expenses. Considerable eŒorts have been undertaken to discover energy-saving alter-

natives. One of the main methods is to maximize utilization of by-product gas, which

in turn reduces gas release and related pollution. To achieve these goals one has to

manage eŒectively the operations of the production system; in the present case thismust occur through the coordination of various factories within the company.

To date, many researchers and practitioners have studied iron and steel produc-

tion management issues with varied success. The literature contains assorted tech-

niques. For example, Sato et al. (1977) applied mathematical programming to

production scheduling. Mackulak et al. (1980) and Box and Herbe (1988) developedcomputer control schemes for production planning. The system developed by Assaf

et al. (1997) was based on an implicit enumeration procedure, while Lin and Moodie

(1989) proposed a hierarchical scheduling strategy. Others such as Sztrimbely et al.

(1989), Numao and Morishita (1988) and Jimichi et al. (1990) recommended expert

systems.Owing to the need to coordinate multiplants and to synchronize steel production

with gas generation, this study forgoes the traditional planning and scheduling

International Journal of Production Research ISSN 0020± 7543 print/ISSN 1366± 588X online # 2001 Taylor & Francis Ltd

http://www.tandf.co.uk/journals

DOI: 10.1080/00207540110035200

Revision received October 2000.{ Complete Business Solutions, Inc., 111 Liberty Street, Columbus, OH 43215, USA.{ 254 Mervis Hall, Katz Graduate School of Business, University of Pittsburgh,

Pittsburgh, PA 15260, USA.* To whom correspondence should be addressed. e-mail: [email protected]

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

approach. Instead, Leontif’s Input± Output (I± O) model (1966) is investigated for its

application potential. The I± O model is predominantly concerned with the activity ofindustry sectors that consume products from other industries (inputs) while generat-

ing their own goods (outputs). Each factory site in a manufacturing system resembles

a region in the I± O model. DiŒerent factories are interdependent, just like various

regions. Based on this concept, Leontif ’s model is revised here and a dynamicoptimal plan for steel production is devised.

2. Problem description and hierarchical planningThe following subsections describe manufacturing facilities, traditional produc-

tion management approaches and limitations of the hierarchical planning systems.

2.1. Integrated manufacturing company

This study is based on Maanshan Iron and Steel Company, the ® fth largest

corporation of its kind in China. The company has multiplant sites: one cokingplant, two sinters, two iron plants, three steel rolling mills, one power plant and

more (® gure 1). DiŒerent factories have diŒerent e� ciencies, producing various

products and consuming a variety of materials. The interplant material ¯ ows are

determined by the availability of the supply and the corporation’ s dispatcher. Inputs

needed for producing a particular product are normally supplied by several factories.

This is a multi-input, -output, -stage and -site manufacturing environment.The 14 factories are connected through the interaction of steel production and

gas generation. Typically, by-product gas is generated in the processes of coke-

making, iron-making and steel-making and also is consumed in the processes. The

by-product gas generation depends on the amount and type of main products pro-

duced, whereas by-product gas supply dictates the amount of iron and steel produc-tion. As a result, gas is an output (by-product) as well as an input (fuel), and iron/

steel is a ® nal product (output) as well as an input for gas generation. E� cient use of

energy such as gas and electricity is an important steel industry objective (Cho 1981,

Lin and Moodie 1985). Currently, the steel industry consumes ¹15% of China’s

energy and is one of the largest energy consumers.Two of the main energy-saving ideas are direct rolling (DR) and hot charging

(HC), which totally or partially eliminate reheating requirements (Assaf et al. 1997).

Such approaches are suitable for mini-mills, where all the production processes are

nearby. The Japanese steel industry has successfully implemented such practices.

Yet, in the studied system, the production stream is established through a series of

factories, each of which completes only one major function. Various plants aredistributed over a large geographical area. Both DR and HC require that slabs

coming directly from the slabbing mill be inspected and charged immediately to

the hot strip mill without a cooling down cycle. With limited budget for equipment

upgrades, the modern techniques of DR and HC are not applicable to the present

problem. Adequate coordination among diŒerent production functions and pro-cesses becomes critical for the success of this integrated system.

2.2. Hierarchical production planning for steel manufacturing

Conventionally, a hierarchical approach is employed for complex problems. A

popular steel manufacturing hierarchy (® gure 2, left) relevant to our research isestablished by Purdue Laboratory for Applied Industrial Control (PLAIC)

(Williams 1985). Lin and Moodie (1989) developed a production strategy based on

2038 H. Li and J. Shang

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

a similar hierarchy (® gure 2, right). Given forecast demands, master production

scheduling (MPS) determines the weekly production and inventory level of the

® nal products. The production requirements planning (PRP) receives the MPS as

input and establishes a plan for every piece of processing equipment in a manner that

satis® es the MPS, minimizes energy consumption, and reduces WIP. At the lower

level of the hierarchy, a detailed time schedule of operations is established to fully

utilize the resources.

2039Integrated model for production planning in steel making

Slab

#3 Steel Mill

Sinter

Iron Ore Coal

Coke Coke Gas

Coking Plant*

Blast Furnace Gas

#1 Iron Plant* #2 Iron Plant*

Iron

#1 Steel Mill #2 Steel Mill

Steel

Slab Mill Wheel Mill Bar Mill

Bar Wheel & Axle

Wire Ingot Pig Iron

Coke Coke Gas

Plate

#1 Sinter Plant #2 Sinter Plant

Plate Mill Wire Mill

*Note: Gases generated and consumed internally are not shown.

Legend:

Blast furnace gas;

Material and energy flow;

Coke gas; Coke;

Input/Output product. xxxx

Figure 1. Material and energy network of iron, steel and gas products in an integrated steelcompany.

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

Many researchers directly addressed the level two optimal sequencing and sched-

uling problem in the PLAIC’s hierarchy (Box and Herbs 1988, Jacobs et al. 1988,Petermen et al. 1992). Hax and Meal (1975) introduced a widely adopted hierarchical

production planning (HPP) approach, which is based on tactical and operational

decisions in a batch production environment. Since steel manufacturing is usually

not a batch process, its discussion is omitted here.

2.3. Comments on current practice

A hierarchical approach like Lin and Moodie’s (1989) easily ® ts into the plant

management and control structure. However, there is no detailed guideline as to

product aggregation and disaggregation and for multiple-site coordination. On the

other hand, Bitran and Hax’s framework (1977) is well suited for product aggrega-

tion and disaggregation. Yet its focus on parts and assembly makes it mainly suitablefor discrete manufacturing, not for steel manufacturing, which consists of both

continuous and discrete processes.

A major weakness of the hierarchical approach lies in its interface. In dealing

with hierarchy, each individual level is decomposed into functional units so that the

burden of planning and scheduling can be shared. Though functional decomposition

is eŒective in taking on hard problems, the modules that carry out diŒerent functions

inevitably require communication, thus, interface. The more modules a hierarchyhas, the more interfaces are needed. Excess interface causes communication break-

down and hinders system performance. To overcome such di� culties, a model which

reduces the need for interface and provides an e� cient solution procedure is

proposed. The model is capable of integrating large number of variables withoutaggregation or losing any individual information. The only interfaces required are

short-term operational scheduling and long-term strategic planning. Details are

described in Sections 3 and 4.


LEVEL 4B

MANAGEMENT DATA

REPRESENTATION

« FORECAST DEMANDS & ORDERS

¯

LEVEL 4A

OVERALL PRODUCTION

PLANNING

« MASTER

PRODUCTION SCHEDULING (MPS)

®

¯

LEVEL 3

DETAILED PRODUCTION SCHEDULING

« PRODUCTION

REQUIREMENTS PLANNING (PRP)

®

¯

LEVEL 2

OPTIMIZATION

«

PRODUCTION SEQUENCING AND SCHEDULING (PSS)

®

¯

LEVEL 1

DIRECT DIGITAL CONTROL

Figure 2. Correspondence between PLAIC and Lin and Moodie’s hirarchy.

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

3. Input± output model

Leontief ’s Input± Output (I± O) model (1966) is modi® ed here to address themultisite coordination problem encountered by Maanshan Iron and Steel

Company. Although the model was originally developed to examine the interdepen-

dence among various producing and consuming sectors within a national economy,

great similarities have been observed between the structure of a ® rm and that of aneconomy. In both the national economy and the production environment, the fun-

damental problem makeup is the same: the interdependence among individual sec-

tors of an economy (or of a ® rm) can be described by a set of linear equations, and

the characteristics of such a system can be re¯ ected in the values of the linear

equations derived from empirical data.

3.1. Applying the input-outpu t model to manufacturing environmentThe information for the I± O model is contained in an interindustry transactions

table (table 1), which is the statistical basis of the I± O system. Output of each process

is distributed along a column, while the corresponding rows record the inputs. Its

application to production planning can be described as follows. Each row describes

how a particular material or semi-product is consumed by various semi- or ® nal-

products in the column. The internal ¯ ows, xij ’ s, form a square matrix. The addi-

tional column labelled `Final Demand’ records the sales of corresponding rows’products to outside markets. At the bottom of the table are the resources, such as

electricity, labour and equipment directly purchased from outside markets. These

resources are not part of the output of current production and are called primary

inputs.

The relationships between inputs (rows) and outputs (columns) can be repre-sented by the following ¯ ow balance equation:

Pnjˆ1 xij ‡ yi ˆ xi i ˆ 1; 2; . . . ; n;

Pnjˆ1 zkj ˆ zk k ˆ 1; 2; . . . ; m;

(…3:1†

where

xij amount of material or semi-product i consumed in the production of semi-

or ® nal-product j; j ˆ 1; 2; . . . ; n,yi amount of ® nal product i produced for external consumption, or available

for sale, i ˆ 1; 2; . . . ; n,


Output Intermediate demandFinal Total

Input 1 2 ¢ ¢ ¢ n demand output

Consumption 1 x11 x12 ¢ ¢ ¢ x1n y1 x1

2 x21 x22 ¢ ¢ ¢ x2n y2 x2

¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢n xn1 xn2 ¢ ¢ ¢ xnn yn xn

Purchase 1 z11 z12 ¢ ¢ ¢ z1n z1

2 z21 z22 ¢ ¢ ¢ z2n z2

¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢m zm1 zm2 ¢ ¢ ¢ zmm zm

Table 1. Input± output transaction table for material ¯ ows.

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

xi amount of product i produced, i ˆ 1; 2; . . . ; n,

zkj amount of resource k purchased for producing product j; k ˆ 1; 2; . . . ; m,zk total amount of resource k purchased, k ˆ 1; 2; . . . ; m.

(Those interested can write to the authors to obtain complete numerical information

for the studied problem.) For the sake of brevity and clarity, only part of the

complete numerical table is explained. Table 2 displays a small section of the com-

plete Xij table. The value under the title of each column is the amount of productsproduced (Xj) in the corresponding factory. Going down vertically, the table shows

how various inputs in each row are needed to produce the speci® c semi- or ® nal-

product in the column. For example, cell (9, 17) indicates 674,438 GJ of blast furnace

gas is needed to produce 88,781 tons of iron in the 1_Iron factory.

The technical coeYcient aij is de® ned as:

aij ˆxij

xj

i; j ˆ 1; 2; . . . ; n;

which is the amount of material or semi-product i directly consumed in the produc-

tion of a unit of product j. The value depends on the technical capability of each

factory, thus the name technical coe� cient. See table 3 for part of the aij ’ s.

Similarly, the purchase coe� cient dkj can be de® ned as:

dkj ˆzkj

xj

k ˆ 1; 2; . . . ; m; j ˆ 1; 2; . . . ; n;

which indicates the amount of purchased material k directly consumed in the pro-

duction of a unit of product j. See table 4 for part of the zkj ’ s and table 5 for part ofthe dkj ’ s.

Because of the interaction between the company’ s diŒerent factories (diŒerent

sites), a change in the ® nal demand for the products of one factory causes repercus-

sions throughout the whole production system. Changes in ® nal product demand not

only change the output quantity of the factory concerned, but also they impact many

of the other factories within the production system. One goal of our productionanalysis is to study the eŒects of these changes. Unfortunately, the technical coe� -

cients only show the direct (® rst-order) eŒects of changes in ® nal demand. The total

eŒects of ® rst-, second- and higher-orders can actually be summarized in the inter-

dependence coe� cients, which are derived in the following. First, (3.1) is converted

into matrix form:

AX ‡ Y ˆ X

DX ˆ Z;

¼…3:2†

where

A direct input coe� cient matrix, A ˆ …aij†n¤n,

X total product vector, X ˆ …x1; x2; . . . ; xn†T,

Y ® nal demand vector, Y ˆ …y1; y2; . . . ; yn†T,

D purchase coe� cient matrix, D ˆ …dkj†m¤n,

Z vector of purchased resources, Z ˆ …z1; z2; . . . ; zm†T.

Matrices (3.2) may be rewritten as


Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014


Xij

CH

_C

HE

M1_

SIN

TE

R2_

SIN

TE

R1_

IRO

N2_

IRO

N1_

ST

EE

L2_

ST

EE

L

Ste

am

Co

ke

Lim

eS

inte

rL

ime

Sin

ter

Iro

nIr

on

Ste

am

OP

_S

TL

Lim

eC

V_

ST

LE

L_

ST

L

10

11

12

13

14

15

17

18

19

20

21

22

23

43

97

412

518

04

038

13

258

66

64

61

7727

988

781

75

83

50

335

41

26

07

255

59

529

4

CK

_C

HE

MC

K_

GS

110

119

88

.3S

tea

m2

25

88

41

170

1_S

INT

ER

MX

33

90

75

.834

657

.9C

ok

e4

58

45

.6L

ime

523

52

2_S

INT

ER

MX

635

704

.2C

ok

e7

55

2L

ime

84

59

.5

1_IR

ON

BF

_G

S9

67

44

38

Ste

am

10

57

00

Co

ke

11

486

98

Sin

ter

12

14

34

76

2_IR

ON

BF

_G

S1

35

26

125

Ste

am

14

18

65

0C

ok

e1

535

71

1S

inte

r1

61

25

460

1_S

TE

EL

MX

17

28

10

0.5

Ste

am

18

10

10

7L

ime

19

257

8Ir

on

20

26

16

8

2_S

TE

EL

Ste

am

21

20

50

Co

ke

22

79

5L

ime

23

20

96

27

iro

n2

43

05

22

72

0

Tab

le2.

Po

rtio

no

fth

ein

pu

t±o

utp

ut

tab

le…X

ij†.

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014


Aij

CH

_C

HE

M1_

SIN

TE

R2_

SIN

TE

R1_

IRO

N2_

IRO

N1_

ST

EE

L2_

ST

EE

L

439

74

12

51

80

40

38

132

58

666

46

177

27

988

78

17

58

35

033

541

260

72

55

59

529

4

CK

_C

HE

MC

K_

GS

10

8.0

84

26

51

00

00

00

00

00

0S

team

20

.05

88

53

0.3

28

88

64

00

00

00

00

00

0

1_S

INT

ER

MX

30

09.6

770

20.2

61

40

00

00

00

00

Co

ke

40

00

0.0

44

09

00

00

00

00

0L

ime

50

00

0.0

17

74

00

00

00

00

0

2_S

INT

ER

MX

60

00

00

0.2

014

01

00

00

00

0C

ok

e7

00

00

0.0

830

60

00

00

00

0L

ime

80

00

00

0.0

251

55

00

00

00

0

1_IR

ON

GF

_G

S9

00

00

00

7.5

966

50

00

00

0S

team

10

00

00

00

0.0

642

00

00

00

Co

ke

11

00

00

00

0.5

485

20

00

00

0S

inte

r1

20

00

00

01

.72

87

00

00

00

2_IR

ON

BF

_G

S1

30

00

00

00

69

377

60

00

00

Ste

am

14

00

00

00

00

.245

93

00

00

0C

ok

e1

50

00

00

00

0.4

70

90

00

00

Sin

ter

16

00

00

00

01

.654

38

00

00

0

1_S

TE

EL

MX

17

00

00

00

00

00

.83

78

00

0S

team

18

00

00

00

00

00

.30

13

30

00

Lim

e1

90

00

00

00

00

0.0

768

60

00

Iro

n2

00

00

00

00

00

0.8

398

10

00

2_S

TE

EL

Ste

am

21

00

00

00

00

00

00

.08

02

10

Co

ke

22

00

00

00

00

00

0.3

049

50

0L

ime

23

00

00

00

00

00

00

.08

20

10

.00

51

iro

n2

40

00

00

00

00

00

1.1

941

80.1

36

Tab

le3

.P

ort

ion

of

the

tech

nic

al

coe�

cien

tta

ble

…aij

ˆx

ij=x

i†.

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014


z ij

PL

AN

TC

K_

CH

EM

1_S

INT

ER

2_S

INT

ER

1_IR

ON

2_IR

ON

1_S

TE

EL

2P_

MX

3P

_M

X4P

_M

XS

tea

mS

tea

mC

ok

eL

ime

Sin

ter

Lim

eS

inte

rS

team

Iro

nIr

on

Ste

am

1497

63.1

828

29.8

8085

5.4

561

954

3974

125

180

403

813

2586

6646

177

279

5700

88

781

7583

50

.000

000

1

67

89

101

112

1314

151

617

1819

Ga

sC

K_

GS

111

6607

.758

523

.564

325.

19

294.

75

6774

.965

5133

dis

pa

chB

F_

GS

23

3155

.42

2681

1653

0.3

1278

08.6

115

991.

11

5909

.83

6085

42

6293

2

CV

_G

S3

162

5.3

MC

_C

KG

41

1660

858

523

.564

325.

12

584

7.2

2292

53

3190

.9

MX

_B

FG

53

3155

.42

2681

1653

0.3

13

228.

611

733

2513

.3

MX

_C

VG

61

625.

3

Pro

cur.

EL

EC

TR

79

0.9

355

50.2

939

49.0

952

408

.47

558

.62

627.

83

01.

785

3389

.865

32.4

7348

.36

637

76.8

74

reso

ur.

WS

H_

CL

817

7400

725

1

CO

AL

93

264

1535

57

492

PW

_C

L1

04

670

50

752

HV

Y_

OIL

11

Ta

ble

4.

Po

rtio

no

fth

ega

str

an

sact

ion

an

dp

urc

hase

inp

ut±

ou

tpu

tta

ble

(zij).

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014


Dij

PL

AN

TC

K_

CH

EM

1_S

INT

ER

2_S

INT

ER

1_IR

ON

2_IR

ON

1_S

TE

EL

2P

_M

X3

P_

MX

4P

_M

XS

team

Ste

am

Co

ke

Lim

eS

inte

rL

ime

Sin

ter

Ste

amIr

on

Iro

nS

team

149

763.

182

829

.88

0855

.456

195

439

741

2518

040

3813

258

666

461

7727

95

700

8878

175

835

0.0

000

001

67

89

10

11

12

1314

151

617

18

19

Ga

sC

K_

GS

10.

778

614

0.70

655

10

.79

5557

0.1

654

011.

291

102

5.2

3353

00

00

00

00

dis

pac

hB

F_

GS

20.

221

386

0.27

382

70

.20

4443

2.2

743

770

0.9

265

950

00

02.

791

193

4.0

645

53.

4671

60

CV

_G

S3

00.

019

622

00

00

00

00

00

00

MC

_C

KG

40

.77

861

0.7

0655

0.7

9556

00

06

.40

0991

0.1

729

00.

187

224

00

00

MX

_B

FG

50

.22

139

0.2

7383

0.2

0444

00

03

.27

6028

0.0

885

00.

014

177

00

00

MX

_C

VG

60

0.0

1962

00

00

00

00

00

00

Pro

cur.

EL

EC

TR

70.

000

607

0.00

060

70

.00

0607

0.0

072

690.

012

703

0.0

209

920

.07

4736

0.0

256

00.

036

848

00

.08

277

0.0

498

040

reso

ur.

WS

H_

CL

80

00

00

1.4

171

590

00

00

00

.09

5615

0

CO

AL

90

00

00

00

0.0

246

00.

086

615

00.

084

387

00

PW

_C

L10

00

00

0.1

0619

90

00

00

0.0

0877

20

0.0

099

160

HV

Y_

OIL

110

00

00

00

00

00

00

0

Ta

ble

5.

Po

rtio

no

fth

ete

chn

ica

lco

e�ci

ents

for

ga

str

an

sact

ion

an

dp

urc

ha

sed

mate

rials

(dij

ˆz i

j=x

i).

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

Y ˆ …I-A†XZ ˆ DX :

¼…3:3†

In I± O analysis, the vector of Y’s (® nal demand) is usually assumed to be exogenous,

and the goal is to determine the vector of the X’s needed. Matrices (3.3) can be

reorganized into

X ˆ …I-A† 1Y

Z ˆ D…I-A† 1Y :

(…3:4†

The coe� cients …I-A† 1 are the interdependence coeYcients. Matrix (3.4) indicatesthat if market demand Y is known, both the corresponding total output X to be

produced and the related resources Z to be purchased can be easily determined. The

numerical example of the interdependence coe� cients is in table 6. Table 7 shows

part of the interdependence coe� cients for purchased materials and gas dispatching.

Both tables involve the T matrix (see below).

3.2. Use of multiregional I± O model to coordinate multisites

Each plant in a distributed production environment is comparable to a region in

a larger economy. In this subsection, we modify the Multi-regional Chenery± Moses

I± O model and adapt it to the multiplant production environment.

3.2.1. Modifying the Chenery± Moses model for multisited production planning and

scheduling

Given that the manufacturing system has s factories, and there are m…q† types of

inputs consumed, and n…q† types of output produced by factory q, the local technical

coe� cient a…q†ij for factory q can be de® ned as:

a…q†ij ˆ

x…q†ij

x…q†j

i ˆ 1; 2; . . . ; m…q†j ˆ 1; 2; . . . ; n…q†q ˆ 1; 2; . . . ; s;

…3:7†

where

x…q†ij amount of material or semi-product i consumed by semi-product or ® nal

product j in plant q; and

x…q†j amount of semi-product or ® nal product j produced by plant q.

The dispatch coe� cient tpq

l…p†k…q†, known as the trade coe� cient in Chenery± Moses

model, can be computed by the following formula:

tpq

l…p†k…q† ˆrpqk…q†

rqk…q†

l…p† ˆ k…q†

0 l…p† 6ˆ k…q†

l…p† ˆ 1; 2; . . . ; n…p†k…q† ˆ 1; 2; . . . ; m…q†p; q ˆ 1; 2; . . . ; s;

8><

>:…3:8†

where

l…p†; k…q† subscripts denoting the products made by plants p and q respectively,

where l…p† ˆ k…q† indicates the same product from diŒerent plants,and l…p† 6ˆ k…q† otherwise;

rpqk…q† amount of item k supplied by plant p to plant q; and


Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014


(1±

TA

)1

CK

_C

HE

M1_

SIN

TE

R2_

SIN

TE

R1

_IR

ON

2_IR

ON

1_

ST

EE

L2_

ST

EE

L

Ste

am

Co

ke

Lim

eS

inte

rL

ime

Sin

ter

Ste

am

Iro

nIr

on

Ste

am

OP

_S

TL

Lim

eC

V_

ST

LE

L_

ST

L

10

11

12

13

14

15

16

17

18

19

20

21

22

23

Po

wer

CK

_G

S1

08

.084

30

9.3

56

43

0.6

714

59

0.0

16

89

10

0.4

97

06

33

3.8

34

85

60

3.3

40

127

2.4

65

28

24

.59

33

55

0.5

22

41

4

pla

nt

BF

_G

S2

00

00

00

07

.59

66

46

6.9

37

76

50

5.8

26

39

08

.28

49

27

0.9

43

55

7

CV

_G

S3

00

00

00

00

00

00

00

1S_

MX

4

2S_

MX

50

00

00

0.2

01

40

10

0.0

47

38

90

.33

31

94

00

.27

98

19

00

.39

78

93

0.0

45

31

5

2P

_M

X6

00

00

00

00

00

0.8

37

796

00

0

3P

_M

X0

00

00

00

00

00

00

00

4P

_M

X8

00

00

00

00

00

00

00

ST

EA

M9

00

00

00

00

0.2

45

92

90

0.5

07

866

00

.37

38

89

0.0

33

44

7

CK

_C

HE

MS

TE

AM

10

1.0

62

53

0.3

49

50

0.0

15

41

0.0

290

25

0.0

00

73

00

.21

48

62

0.1

65

76

70

0.1

44

381

0.1

06

56

50

.01

98

55

40

.02

25

82

CO

KE

11

01

00

.04

40

90

.09

30

57

0.0

02

08

90

0.6

14

85

30

.47

43

60

0.4

13

164

0.3

04

94

90

.56

81

85

0.0

64

62

1

1_S

INT

ER

LIM

E12

00

10

.01

77

40

00

0.0

26

49

20

00

00

.06

41

60

.00

39

9

SIN

TE

R13

00

01

00

01

.49

34

05

00

00

00

2_S

INT

ER

LIM

E14

00

00

10

.02

51

55

00

.00

59

19

0.0

41

61

60

0.0

73

917

00

.06

65

0.0

06

70

5

SIN

TE

R15

00

00

01

00

.23

52

98

1.6

54

38

10

1.3

89

363

01

.97

56

26

0.2

25

00

1

1_IR

ON

ST

EA

M16

00

00

00

10

.06

42

03

00

00

00

IRO

N17

00

00

00

01

00

00

00

2_IR

ON

IRO

N18

00

00

00

00

10

0.8

39

808

01

.19

41

78

0.1

36

00

3

1_S

TE

EL

ST

EA

M19

00

00

00

00

01

00

00

OP

_S

TL

20

00

00

00

00

00

10

00

S_

ST

EE

LL

IME

21

00

00

00

00

00

0.0

37

894

10

.00

10

43

6.4

9E

-05

CV

_S

TL

22

00

00

00

00

00

00

10

EL

_S

TL

23

00

00

00

00

00

00

01

3_S

TE

EL

LIM

E24

00

00

00

00

00

00

00

CV

_S

TL

25

00

00

00

00

00

00

00

RG

H_

RO

LB

ILL

ET

26

00

00

00

00

00

00

00

1_R

OL

LW

HE

EL

27

00

00

00

00

00

00

00

HO

OP

28

00

00

00

00

00

00

00

Ta

ble

6.

Po

rtio

no

fth

ein

terd

epen

den

ceco

e�ci

ent

(I±

TA

)1.

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014


D(I

±TA

)1

Po

wer

pla

nt

CK

_C

HE

M1_

SIN

TE

R2_

SIN

TE

R

CK

_G

SB

F_

GS

CV

_G

S1

S_M

X2S

_M

X2P

_M

X3P

_M

X4

P_

MX

Ste

amS

team

Co

ke

Lim

eS

inte

rL

ime

Sin

ter

1011

988

1200

563

1625

.37

3733

.735

704.

21

4976

3.1

8282

9.8

8085

5.4

56

195

4397

41

2518

04

038

1325

86

664

617

7279

12

34

56

78

91

01

21

31

41

5

Ga

sC

K_

GS

10

00

6614

628

0.9

296

080

.77

8614

0.7

065

510

.79

5557

0.1

654

011.

371

838

4.7

823

56

4.0

0988

2.6

537

090

.39

721

0.1

772

32

dis

pa

tch

BF

_G

S2

00

00.

338

537

0.0

703

920

.22

1386

0.2

738

270

.20

4443

2.2

743

770

0.92

659

53

.27

6-31

0.1

874

610

.07

6961

0.0

161

13

CV

_G

S3

00

00

00

0.0

196

220

00

00

00

0

MX

_C

KG

40

00

6.6

146

30.

929

610.

778

610.

706

550.

795

560

00

57.6

089

2.57

810

0

MX

_B

FG

50

00

0.3

385

40.

070

390.

221

390.

273

830.

204

440

00

00

00

MX

-CV

G6

00

00

00

0.0

1962

00

00

00

00

Pro

cur.

EL

EC

TR

70

0.0

0037

30

0.00

060

70

.00

0607

0.0

006

070

.00

0607

0.0

006

070

.00

7269

0.01

349

70.

0254

31

0.0

806

120

.02

8277

0.0

021

120

.03

7024

reso

ur.

WS

H_

CL

80

00

00

00

00

01.

4171

59

00

.06

2481

0.1

177

060

.00

2961

CO

AL

90

00

00

00

00

00

00

.02

4618

00

.08

6615

PW

_C

L1

00

00

00

00

00

0.1

128

40.

0371

12

00

.00

1636

0.0

030

820

HV

Y_

OIL

11

00

00

00

00

00

00

00

0

Tab

le7.

Po

rtio

no

fth

eg

as

tra

nsa

ctio

na

nd

pu

rch

ase

inte

rdep

end

ence

coe�

cien

tta

ble

D(1

±T

A)

1

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

rq

k…q† amount of product k needed by plant q, including both the internal

consumption and the ® nal demand (external sales).

Part of R and T matrices can be found in tables 8 and 9.

Based on equation (3.8), the local supply function, from plant p to q, can be

written in a matrix form as:

R…pq† ˆ T …pq†R…q† p; q ˆ 1; 2; . . . ; s; …3:9†

where

R…pq† ˆ …r…pq†1 ; r

…pq†2 ; . . . ; r

…pq†n…p††

T

and

R…q† ˆ …r…q†1 ; r

…q†2 ; . . . ; r

…q†m…q††

T:

In equation (3.9), matrix T…pq† is not a squared one (36*47 in our case) like its

counterpart in the original Chenery± Moses model. Its row catalogue is the sameas the product catalogue of plant p, and its column catalogue is equivalent to the

consumption catalogue of plant q. That is:

T …pq† ˆ

t…pq†11 t

…pq†12 ¢ ¢ ¢ t

…pq†lm…q†

t…pq†21 t

…pq†22 ¢ ¢ ¢ t

…pq†2m…q†

..

. ... ..

.

t…pq†n…p†1

t…pq†n…p†2 ¢ ¢ ¢ t

…pq†n…p†m…q†

0

BBBBBB@

1

CCCCCCAˆ …t…pq†

t…p†k…q††n…p†¤m…q†: …3:10†

By using equation (3.7) for local technical coe� cient a…q†ij , the local net demand

function in matrix form becomes:

R…q† ˆ A…q†Z…q† q ˆ 1; 2; . . . ; s; …3:11†

where

A…q† ˆ

a…q†11 a

…q†12 ¢ ¢ ¢ a

…q†ln…q†

a…q†21 a

…q†22 ¢ ¢ ¢ a

…q†2n…q†

..

. ... ..

.

a…q†m…q†1 a

…q†m…q†2 ¢ ¢ ¢ a

…q†m…q†n…q†

0

BBBBBB@

1

CCCCCCA;

X …q† ˆ …X …q†1 ; X

…q†2 ; . . . ; X

…q†n…q††

T:

Note, the local transactions matrix A…q† is not a square matrix either (47*36 in our

case). The ® nal products of the plant from its plant p are counted in the local

production function, which is:

X …p† ˆXs

qˆ1

R…pq† ‡ Y …p† p ˆ 1; 2; . . . ; s; …3:12†

where Y…p† is plant p’ s ® nal product demand vector, and


Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014


Rij

CK

_C

HE

M1

_S

INT

ER

2_

SIN

TE

R1_

IRO

N2_

IRO

N1_

ST

EE

L

CK

_G

SS

team

Mx

Co

ke

Lim

eM

XC

ok

eL

ime

BF

_G

SS

tea

mC

ok

eS

inte

rG

F_

GS

Ste

am

Co

ke

Sin

ter

MX

Ste

am

Lim

e

12

34

56

78

91

01

11

21

31

41

51

61

71

81

9

10

11

98

64

37

58

73

73

45

84

5.6

23

52

35

70

45

52

445

9.5

67

44

38

57

00

48

69

81

53

47

65

26

12

5.4

18

65

03

57

11

12

54

60

28

10

11

01

07

25

78

Po

wer

CK

_G

S1

10

11

98

8

pla

nt

BF

_G

S2

67

44

38

52

61

25

.4

CV

_G

S3

1S

_M

X4

73

73

4

2S

_M

X5

35

70

4

2P

_M

X6

28

10

1

3P

_M

X7

4P

_M

X8

Ste

am

91

86

50

10

10

7

K_

CH

ES

team

10

43

75

8

Co

ke

11

58

45

.65

52

48

69

83

57

11

_S

INT

EL

ime

12

23

52

Sin

ter

13

13

25

86

2_S

INT

EL

ime

14

445

9.5

13

07

Sin

ter

15

20

89

01

25

46

0

1_IR

ON

Ste

am

16

57

00

Iro

n1

7

2_IR

ON

Iro

n1

8

1_S

TE

EL

Ste

am

19

OP

_S

TL

20

2_S

TE

EL

Lim

e2

11

27

1

CV

_S

TL

22

EL

_S

TL

23

3_S

TE

EL

Lim

e2

4

CV

_S

TL

25

Ta

ble

8.

Po

rtio

no

fth

ere

gio

na

ltr

an

sfer

(dis

pa

tch

ing

)in

pu

t±o

utp

ut

tab

le.

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014


T

CK

_C

HE

M1_

SIN

TE

R2

_S

INT

ER

1_

IRO

N2_

IRO

N1

_S

TE

EL

CK

_G

SS

tea

mM

xC

ok

eL

ime

MX

Co

ke

Lim

eB

F_

GS

Ste

am

Co

ke

Sin

ter

GF

_G

SS

tea

mC

ok

eS

inte

rM

XS

tea

mL

ime

12

34

56

78

91

01

11

21

31

41

51

61

71

81

9

10

11

98

64

37

58

737

34

58

45

.62

35

23

57

04

55

24

45

9.5

67

44

38

57

00

48

69

81

53

47

65

26

12

5.4

18

65

03

57

11

12

54

60

28

10

11

01

07

25

78

Po

wer

CK

_G

S1

10

00

00

00

00

00

00

00

00

0

pla

nt

BF

_G

S2

00

00

00

00

00

00

00

00

00

0

CV

_G

S3

00

00

00

00

00

00

00

00

00

0

1S

_M

X4

00

10

00

00

00

00

00

00

00

0

2S

_M

X5

00

00

01

00

00

00

00

00

00

0

2P

_M

X6

00

00

00

00

00

00

00

00

10

0

3P

_M

X7

00

00

00

00

00

00

00

00

00

0

4P

_M

X8

00

00

00

00

00

00

00

00

00

0

Ste

am

90

00

00

00

00

00

00

10

00

10

K_

CH

ES

tea

m1

00

10

00

00

00

00

00

00

00

00

Co

ke

11

00

01

00

10

00

10

00

10

00

0

_S

INT

EL

ime

12

00

00

10

00

00

00

00

00

00

0

Sin

ter

13

00

00

00

00

00

00

.86

38

88

00

00

00

0

2_S

INT

EL

ime

14

00

00

00

01

00

00

00

00

00

0.5

07

Sin

ter

15

00

00

00

00

00

00

.13

61

12

00

01

00

0

1_IR

ON

Ste

am

16

00

00

00

00

01

00

00

00

00

0

Iro

n1

77

00

00

00

00

00

00

00

00

00

0

2_IR

ON

Iro

n1

87

00

00

00

00

00

00

00

00

00

0

1_S

TE

EL

Ste

am

19

70

00

00

00

00

00

00

00

00

00

OP

_S

TL

20

70

00

00

00

00

00

00

00

00

00

2_S

TE

EL

Lim

e2

10

00

00

00

00

00

00

00

00

00

.49

3

CV

_S

TL

22

70

00

00

00

00

00

00

00

00

00

EL

_S

TL

23

70

00

00

00

00

00

00

00

00

00

3_S

TE

EL

Lim

e2

47

00

00

00

00

00

00

00

00

00

0

CV

_S

TL

25

70

00

00

00

00

00

00

00

00

00

Ta

ble

9.

Po

rtio

no

fth

etr

ad

e(d

isp

atc

hin

g)

coe�

cien

tta

ble

…Tij

ˆR

ij=R

j†.

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

Y …p† ˆ …y…p†1 ; y

…p†2 ; . . . ; y

…p†n…p††

T;

By combining equations (3.9), (3.11) and (3.12), the global production function can

be obtained as follows:

X …p† ˆXs

qˆ1

T …pq†A…q†X …q† ‡ Y …p† p ˆ 1; 2; . . . ; s: …3:13†

Note that inconsistencies, gaps and redundancies in statistical system of a plant can

easily be revealed in the process of compiling the above table. The creation of I± O

tables has no doubt led to improved statistics in the entire company where such

tables are prepared.

Equation (3.13) indicates that products X …p† of plant p will satisfy materialrequirements,

Psqˆ1 T …pq†A…q†X …q†, from all plants including its own, and also provide

the company with its ® nal (external) demand, Y …p†. Equation (3.13) can be reorga-

nized as:

X ˆ TAAX ‡ Y ; …3:14†

where

T ˆ

T …11† T …12† ¢ ¢ ¢ T …1s†

T …21† T …22† ¢ ¢ ¢ T …2s†

..

. ... ..

.

T …s1† T …s2† ¢ ¢ ¢ T …ss†

0

BBBB@

1

CCCCA

AA ˆ diag …A…1†; A…2†; . . . ; A…s††;

X ˆ …X …1†; X …2†; . . . ; X …s††T

and

Y ˆ …Y …1†; Y …2†; . . . ; Y …s††T:

Matrix (3.14) provides an e� cient production planning and scheduling model that

possesses the following edges.

(1) The I± O model is capable of dealing with interplant material ¯ ows. It caneffectively coordinate all factories and products and ensure overall system

equilibrium.

(2) It acknowledges the fact that corporate’s material dispatching practice

(matrix T) is independent of the production planning procedure exercised

at the individual factory level.

(3) It offers a handy link for bridging both the corporate and the factory man-

agement.(4) It possesses a compact and standard structure that can be easily adjusted.

(5) If local production costs and material handling costs are available, one can

easily calculate the total product (X) costs and the ® nal product (Y) costs.

In the original Chenery± Moses Model, both diagonal matrix A…q† in A and block

matrix T …pq† in T are square matrices (Sohn 1986, Miller 1989), which expands the

matrix dimension swiftly at the rise of factory sites or product types. By using model


Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

(3.14), the complete model technical structure for plant q, any changes in a plant will

not aŒect the remaining plants. As a result, if the number of the product typesincreases by n, the overall matrix dimension will increase by `n’ instead of

`n £ ñ total number of plants’ . Therefore, model (3.14) is more practical and man-

ageable.

3.3. Modify the negative input method for by-produc t management

Coordination between the production of main products and their by-products is

a very critical issue. O’ Conner (1975) presented a specially structured transactionstable where he lists negative values of by-products on the column of its associated

main products. By introducing a negative I± O technical coe� cient into the direct

input coe� cient matrix, he quanti® ed the relationship between the main product and

its by-product. However, it results in a coe� cient matrix that no longer preserves the

non-negative property of the original structure of the I± O matrix, A. As a result, the

non-singularity of the matrix (I± A) is no longer guaranteed, and the interdependencecoe� cient (I-A† 1 matrix is not attainable. (Note: a matrix can only be inverted if it

is non-singular. Chen and Li (1985) showed that a necessary condition for a matrix

to be non-singular is when the matrix’s coe� cients are non-negative. ) In modelling

the relationship between iron/steel products and their by-products, we modify the

original negative input method to ensure the non-negativity of matrix (I± A), and

maintain the true relationship between the main products and their by-products.The `modi® ed negative input method’ in this subsection is illustrated through the

numerical example in table 10. In table 10a, we record the by-product gas volume at

the intersection of the by-product rows and the main product columns. For example,

the numerical value 674 437.8 GJ in cell (9, 17) is the total output of blast furnace gas

(BFG) generated during iron-making in the 1_Iron factory. In cell (2, 17) the nega-tive number -360 854 GJ shows the net BFG output from iron making in 1_Iron

factory. This is less than the total gas 674 437.8 GJ generated since iron production

consumes BFG during its own production processes. The positive numbers in table

10b represent gas consumed while making the product in the speci® c column. For

example, the mixed-gas station consumes 33 155.4, 22 681 and 16 530.3 GJ (see cells(2,6), (2,7), and (2,8)) of BFG to produce the mixed BFG in cells (5,6), (5,7), (5,8)).

Factories 1_Sinter and 2_Sinter consume speci® c amount of mixed BFG in its pro-

duction process as seen in cells (5,12), (5,13) and (5, 15). Such an arrangement makes

it possible to handle each gas-mixing station independently. In summary, the by-

product gases in Xij table are always positive, and they are the outputs from the

corresponding columns. In Zij table, the positive numbers are the inputs to thecorresponding column production. The negative numbers in the gas dispatching

area are the net outputs from the corresponding columns.

Now return to table 3 to examine the meaning of the technical coe� cients of the

by-product gas. The technical coe� cients aij ’ s are the direct output coeYcients.

For example, 7.59665 [5 674 437.8/88 781] in cell (9,17)] is the direct outputcoeYcients of BFG when producing iron in 1_Iron. In cell (2,17) of table 5,

the -4.06455 (-360 854/88 781) is the net output coeYcients of the BFG, which

is the result of [ (674 437.8 internal consumption)/(88 781)]. The I± O tables

and their derivations in our ® nal table (not given) provide complete technical

description of the integrated steel plant. Owing to the use of the negative inputmethod, we can manage the main products and the by-product gas operations

simultaneously, making synchronization planning possible.


Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014


(a)

Xij

Pla

nt

CH

_C

HE

M1_

SIN

TE

R2_

SIN

TE

R1_

IRO

N1_

IRO

N2_

IRO

N

2P_

MX

3P

_M

X4P

_M

XS

tea

mS

tea

mC

ok

eL

ime

Sin

ter

Lim

eS

inte

rS

tea

mIr

on

Iro

n6

78

91

011

1213

141

51

61

71

814

976

3.1

828

29.8

8085

5.4

561

954

3974

125

180

403

813

2586

664

617

7279

5700

8878

17

5835

CK

_C

HE

MC

K_

GS

11

0119

88.3

Ste

am2

2588

4117

0

1_S

INT

ER

MX

33

9075

.83

4657

.9C

ok

e4

5845

.6L

ime

52

352

2_S

INT

ER

MX

635

704.

2C

ok

e7

552

Lim

e8

445

9.5

1_IR

ON

BF

_G

S9

6744

37.

8S

team

105

700

Co

ke

1148

698

Sin

ter

121

5347

6

2_IR

ON

BF

_G

S13

526

125.

4S

team

141

8650

Co

ke

153

5711

Sin

ter

1612

5460

(b)

Zij

Pla

nt

CH

_C

HE

M1_

SIN

TE

R2_

SIN

TE

R1_

IRO

N1_

IRO

N2_

IRO

N

2P_

MX

3P

_M

X4P

_M

XS

tea

mS

tea

mC

ok

eL

ime

Sin

ter

Lim

eS

inte

rS

tea

mIr

on

Iro

n14

976

3.1

828

29.8

8085

5.4

561

954

3974

125

180

403

813

2586

664

617

7279

5700

8878

17

5835

67

89

10

1112

1314

15

16

17

18

Gas

CK

_G

S1

1166

07.

75

8523

.564

325.

19

294.

756

774.

965

5133

.4d

isp

ach

BF

_G

S2

331

55.4

2268

116

530.

31

2780

8.6

1159

91.1

1590

9.8

360

854

262

932.

3C

V_

GS

316

25.3

MX

_C

KG

411

660

7.7

585

23.5

6432

5.1

258

47.2

229

24.9

3319

0.9

MX

_B

FG

53

3155

.422

681

1653

0.3

132

28.6

11

733

251

3.3

MX

_C

VG

616

25.3

Pro

cur.

EL

EC

TR

79

0.9

355

50.

293

949

.09

524

08.4

755

8.6

2627

.83

01.7

85

3389

.78

96

532.

473

48.3

66

377

6.8

74re

sou

rW

SH

_C

L8

177

400

7251

CO

AL

93

264

153

557

492

Tab

le1

0.

Illu

stra

tio

no

fth

en

ega

tiv

ein

pu

tm

eth

od

.

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

4. Input± output model for dynamic production planning and scheduling

We have established a quantitative basis for production planning. However, themodel so far is static. A practical system must be dynamic and its problem size does

not grow exponentially with the number of product types or factory sites. This

section presents a dynamic model based on the techniques discussed above.

4.1. Dynamic approach for daily production planning and scheduling

The idea of having products consumed later than they were produced indicates

that the production system needs dynamic balance, both horizontally (i.e. within 1

day if daily production is in question) and vertically (i.e. a stretch of many days). To

solve the dynamic problems, we allow the variables of current ® nal products (Yt) to

be negative when current demand exceeds current supply and then establish balancedproduction relations for diŒerent time periods. A dynamic model with the I± O

matrix as its main component is introduced below:

TtAAtXt ‡ Yt ˆ XtPt½ˆ1 Y½ ‡ So ¶ 0;

t ˆ 1; 2; . . . ; T ;

(…4:1†

where

t; ½; T time parameters,Tt; At dispatch matrix and technical matrix in time t respectively,

Xt; Yt total product vector (total production) and ® nal product (external

demand) vector in time t respectively,

So inventory vector at time 0 (at the beginning of the planning horizon).

The ® rst equation in (4.1) shows the balanced relationship at time t, while the secondequation ensures the balanced relationship of each time period. The second equation

guarantees that the amount of the shortage occurring at time t can be satis® ed by

previous supplies, including the beginning inventory. This implies that the system

does not allow backorder.

A typical dynamic I-O model uses diŒerence equations to describe the verticalrelationships across diŒerent time periods in question (Chen and Li 1985, Miller

1989). Consequently, complicated modelling structures and numerous variables

are inevitable. Developing a model for on-line management, (4.1) not only prevents

a dynamic model from becoming a ® nite diŒerence equation, but also it helps reduce

new variables and coe� cients. It lays a solid foundation for constructing the optimal

model below.

4.2. Dynamic and optimal planning model

Through the combination of a multiregional column model, negative input

method and dynamic balance concepts, we form a dynamic optimum model.Management at the Iron and Steel Complex has chosen two objectives for the

production system: (1) maximizing the ® nal products’ daily production value and

(2) minimizing the daily release of gases in an eŒort to reduce pollution. The ® rst

goal of maximizing the production objective can be expressed as:

max Z ˆXT

½ˆ1

Y½ ¢ p½ ; …4:2†


Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

where p½ is the price vector of the ® nal products at time ½ . The second objective is the

gas release control and is de® ned as follows:

min Z ˆXT

½ˆ1

…CR½ ‡ BR½†; …4:3†

where

½; T time indicator and its upper limit; and

CR½ ; BR½ the amount of coke oven gas and blast furnace gas released duringtime ½ .

Among the constraints of the model, the daily production capacity can be expressed

as:

XLt µ …I-TtAAt† 1Yt µ XHt: t ˆ 1; 2; . . . ; T ; …4:4†

where

XLt; XHt lower and upper capacity limits at time t;Tt dispatch matrix at time t; and

AAt technical matrix at time t.

The lower limit XLt above is set for technical and/or economical reasons. In the steel

plant, every large piece of equipment has a break-even point. Any amount less than

the break-even point (lower limit) is unacceptable. XLt and XHt are also used tosignify the direct in¯ uence of equipment maintenance or machine breakdown.

The equilibrium condition of gas generation and consumption is established by

using the interdependence coe� cients …I-TA† 1, and the equilibrium coe� cients

D…1-TA† 1. According to the interdependence structure of the I± O table in tables

6 and 7, the constraint can be presented as:

Dg;t…I-TtAAt†1Yt ‡ Yg;t ‡ GRt ‡ »»g;t…I-TtAAt†

1g Yt ˆ 0; t ˆ 1; 2; . . . ; T ; …4:5†

where

Dg;t technical coe� cient matrix of gases (such as those in ® rst tosixth rows in table 5);

Dg;t…I-TtAAt† 1 equilibrium matrix of the by-product gases (such as those in

® rst to sixth rows in table 7);

Yg;t gas supply to outside customers at time t;GRt amount of released gas vector at time t, GRt ˆ …CRt; BRt†T;

…I-TtAAt†1

g block matrix of …I-TtAAt†1, which consists of the rows of the

total output coe� cients of the by-product gases; and

»»g;t error control diagonal matrix which re¯ ects the percentage of

gas losses on the network and measurement errors, etc. »»g;t

re¯ ects the actual circumstances of a gas-dispatching opera-

tion.

The constraint for purchased electricity is:

De;t…I-TtAAt† 1Yt µ …1-»»e;t†EHt -Yet t ˆ 1; 2; . . . ; T ; …4:6†

where


Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

De;t technical coe� cient matrix of purchased electricity at time t;

De;t…I-TtAAt† 1 total input coe� cients of electricity;

»»e;t error control percentage of electricity dispatching operation;EHt electricity peak limit at time t; and

ye;t electricity supply to outside systems.

Since coal can be stored, its constraint may be computed directly for the entire

planning horizon:

XT

½ˆ1

Dc;½ …I-T½ AA½†1Y½ µ CH; …4:7†

where

Dc;½ technical coe� cient matrix of purchased coal at time ½ ;

Dc;½ …I-T½ AA½ † 1 total input coe� cients of coal; and

CH supply or storage limit for coal during the planning period.

The constraint of the ® nal products is:

XT

½ˆ1

Y½ ¶ YM ‡ ST‡1-So; …4:8†

where

YM demand matrix for the semi- or ® nal-products during the planning

horizon, ½ ˆ 1; 2; . . . ; T ; and

ST‡1; So amount of inventory required for the next planning period, and the

inventory remaining from the last planning period, respectively.

The dynamic constraint is:

Xt

½ˆ1

Yt ¶ -So t ˆ 1; 2; . . . ; T : …4:9†

Using equations (4.2) and (4.4± 4.9), we establish a dynamic optimum model as

follows:

MaxXT

½ˆ1

Y½p½

S.t.

…I-TtAAt† 1Yt ¶ XLt

…I-TtAAt† 1Yt µ XHt

‰…Dg;t…I-TtAAt† 1 ‡ »»g;t…I-TtAAt† 1g ŠYt-GRt ˆ Yg;t

De;t…I-TtAAt† 1Yt µ …1-»e;t†EHt ye;tPT

½ˆ1 Dc;½ …I-T½ AA½† 1Y½ µ CHPT

½ˆ1 Y½ > YM ‡ ST‡1 SoPT½ˆ1 Y½ ¶ So

GRt ¶ 0 t ˆ 1; 2; . . . ; T :

9>>>>>>>>>>>>>>>>=

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

…4:10†


Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

The model described here takes the ® nal products as variables and the by-product

equilibrium coe� cients as parameters. After solving (4.10), we use the objective

function and its optimal value as an additional constraint and solve (4.10) againby replacing the objective function with (4.3): min

PT½ˆ1…CR½ ‡ BR½†, to minimize

the by-product gas discharge.

4.3. Use the dynamic model in a production planning hierarchyModel (4.10) provides communication channels for all parties involved in the

management of a hierarchical production planning system (see ® gure 2). A working

mechanism for integrating (4.10) into a hierarchy is demonstrated in ® gure 3.

First, the marketing department sends customer order or sales forecasts (denoted

as YM) to the production planner. The local technical coe� cients, would come fromeach factory. Data such as XL

…p†t and XH

…p†t are from the equipment maintenance

division that provides maintenance plans and equipment capacities. The dispatching

plan T…pq†t data are collected from the system planner. Thereafter, the planning model

is ready for execution and for carrying out detailed plans.

The planner can then follow the principle proposed by Bitran and Hax (1977) foraggregation and disaggregation of YM. By allowing all products to stay in the same

I± O table, the computational eŒorts are greatly reduced. If the initial parameters


Business Management Yt

(p) YM

Planner GRt

Yt(p) Tt

(pq)

The Input-Output Xt(p)

Production Planning & Equipment

Scheduling Model Maintenance XLt

(p) XHt

(p) Dt

(p) Xt

(p)

At(p)

Factory p

Figure 3. Input± Output model in a production management and control hierarchy.

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

result in infeasible solution, the planner could provide adjustments on the initial

parameters. It is possible that a bottleneck exists in the current system and achange in XL

…p†t and XH

…p†t becomes necessary. The planner may ask the factory

involved to rearrange its operational procedure so as to ease the bottleneck, where

the detailed plans will be decided according to particular circumstances.

5. Model evaluation

The proposed model was constructed with the historical data supplied by

Maanshan Iron and Steel Complex. Other sets of data were later obtained from

the organization to validate the proposed procedure. The model’s capability was

tested based on the plant’ s normal daily operation. Overall, the proposed modelincreases Maanshan’ s energy savings by almost 24% . As a result, the iron and

steel production rate increases by ¹20% due to the additional supply of the by-

product gas energy.

In other situation when set-up times and costs are involved, the zij table (table 4)

can record the amount of the time (or resource) needed to set up a machine fromproducing product i to product j. To calculate the costs of direct input, either

material or semi-product, the I± O model only needs to measure them by their

dollar values, instead of physical measurement, in formulating technical coe� cient,

aij . It is important to understand that the I-O model by itself is a balanced design. It

only discloses whether each constituent in the table maintains a su� cient amount.The optimization model is the very one that helps adequately allocate the excess gas

to various production units, thus enhancing overall system e� ciency.

Through the experiments, we found that the proposed model not only meets the

requirements of the hierarchical planning and control in Maanshan, but it is also

capable of identifying the bottleneck of the operational structure, including a feasi-

bility study of the long-run production plan. It provides, within a very reasonablecomputation time, comprehensive and optimal results in terms of iron and steel

production, by-product gas utilization and equipment maintenance plans.

6. Summary and conclusionThe major contributions of this research can be summarized as follows.

(1) It improves performance. Since the proposed model is capable of unifying

both global and local prospects within one integrated structure, complex

interactions and iterations between various levels as seen in conventional

decompositions are eliminated. Therefore, the model not only improvescomputational ef® ciency, but also helps obtaining global optimum.

(2) It provides a useful communication tool. Since the proposed model consis-

tently preserves the global view, it closely mimics the reality. Such ability

helps management of the company understand the model structure. As a

result, management is more willing to accept the proposed model.(3) It identi® es bottlenecks. The calculation as seen in constraint (4.4),

ZHt …I TtAAt† 1Yt, helps identify bottlenecks. By using market demand

Yt, and system capacity XHt, the negative difference found above will reveal

that bottlenecks are present in the system. (Positive outcome indicates suf® -

cient system capacity.) This approach is demand driven and only involvesstandard matrix calculation. No optimization procedure is needed prior to

the identi® cation of bottlenecks.


Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

Models developed based on the speci® c structures of the manufacturing facility

signi® cantly increase overall system e� ciency. In conducting this research, we spenta large amount of time identifying the problem and de® ning the data before the I± O

model was chosen. The approach takes account of the geographically dispersed

situation and the need to synchronize the production of main products and by-

product gas. The dispatch matrix, Tt, and technical matrix, AA can capture andmodel both the individual and the global aspects of the problem without arti ® cially

decompose a system. Since this modelling approach preserves the `global view’,

physical ¯ ow in the network is well represented. It not only maximizes system

output and minimizes environmental pollution, but also provides resource consump-

tion information. Hence, it adds to the accuracy of product cost calculation. As a

consequence, it is eŒective in addressing practical and complicated manufacturing

management issues.The model itself is easy to implement and guarantees good results. Although the

procedure presented in this paper was developed speci® cally for Maanshan, due to

its general structure, we believe the proposed framework is useful for managing

systems involving by products. In particular, it is suitable for managing various

centralized and decentralized supply chain networks, due to their similarity in struc-ture to the studied problem. Bene® ts of the model may be best observed when

members of the manufacturing network play the role of the supplier and consumer

simultaneously. For example, the proposed framework is useful in modelling the

problem of Ford Explorer’s recall of Firestone tires. The returned tires will be

recycled and part of the recycled materials may later become inputs. This turnsthe supplier of the output (tires) into the consumer of its own product (recycled

tires). Traditional production management approach is incapable of handling such

loop situations, while the proposed model could analyse such supply-demand rela-

tionships e� ciently.

Despite similarity between the structure of ® rms and the composition of indus-

tries in an economy, no researchers have thus far taken advantage of I± O analysisand applied it to production/operations management domain. This research pro-

mises to be an innovative application of economics theory, and hopefully it will

provide a new and useful tool for researchers in the area of production and opera-

tions management.

Acknowledgement

This research was partially supported by an Institute for IndustrialCompetitiveness grant.

References

ASSAF, I., CHEN, M. and KATZBERG, J., 1997, Steel production schedule generation.International Journal of Production Research, 35, 467± 477.

BITRAN, G. and HAX, A., 1977, On the design of hierarchical production planning systems.Decision Sciences, 8, 25± 55.

BOX, R. and HERBE, D., JR, 1988, A scheduling model for LTV Steel’s Cleveland Works’ twinstrand continuous slab caster. Interfaces, 18, 42± 56.

CHEN, X. and LI, B., 1985, Economic-Mathematic Methods and Models (PR China: Financeand Economics Press).

CHO, C. H., 1981, Energy Management Applications for the Steel Industry, Iron and SteelEngineer, 8, 54± 60.


Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

HAX, A. and MEAL, H., 1975, Hierarchical Integration of Production and Scheduling. In M.A. Geisler (ed.), Studies in the Management Sciences, 1, Logistics (Amsterdam: North-Holland and American Elsevier), pp. 53± 69.

JACOBS, T., WRIGHT, J. and COBBS, E., 1988, Optimal inter-process steel production sched-uling. Computers and Operations Research, 15, 497± 507.

JIMICHI, Y., HORI, A., ISHIHARA, H. and ODAIRA, T., 1990, An expert system of automaticslab assignment for hot strip mill. ISIJ International, 30, 155± 160.

LEONTIF, W., 1966, Input± Output Economics (New York: Oxford University Press).LIN, C. W. and MOODIE, C. L., 1985, An Energy-EVective Production Scheduling Strategy for

Hierarchical Control of Steel Manufacture. PLAIC Report no. 147 (West Lafayette:Purdue Laboratory for Applied Industrial Control, Purdue University).

LIN, C. W. and MOODIE, C. L., 1989, Hierarchical production planning for a model steelmanufacturing system. International Journal of Production Research, 27, 613± 628.

MACKULAK, G. T., MOODIE, C. L. and WILLIAMS, T. J., 1980, Computerized hierarchicalproduction control in steel manufacture. International Journal of Production Research,18, 455± 465.

MILLER, R. E., POLENSKE, K. R. and ROSE, A. Z. (eds), 1989, Frontiers of Input± OutputAnalysis (New York: Oxford University Press).

NUMAO, M. and MORISHITA, S., 1988, Scheplan Ð a scheduling expert for steel-making pro-cess. Proceedings of the International Workshop on ArtiWcial Intelligence for IndustrialApplications, 25± 28 May, Hitachi, pp. 467± 472.

O’ CONNOR, R. and HENRY, E. W., 1975, Input-output analysis and its applications. InGriYn’ s Statistical Monographs and Courses, 36 (Hafner).

PETERMEN, C. SORENSEN, K. and VIDAL, R., 1992, Inter-process synchronization in steelproduction. International Journal of Production Research, 30, 1415± 1425.

SATO, S., YAMAOKA, T., AOKI, Y. and UEDA, T., 1977, Development of integrated productionscheduling system for iron and steel works. International Journal of ProductionResearch, 15, 539± 552.

SOHN, I. (ed.), 1986, Readings in Input± Output Analysis, Theory and Applications (New York:Oxford University Press).

SZTRIMBELY, W., WEYMOUTH, P. and PONZO, T., 1989, An expert systems approach to rule-based dynamic process plant scheduling. In M. Y. Demeri (ed.), Expert SystemApplications in Materials Processing and Manufacturing (Minerals, Metals &Materials Society).

WILLIAMS, T. J. (ed.), 1985, Design of Hierarchical Control Systems: With Special Reference toSteel Plant Operations (PLAIC and Elsevier).

2062 Integrated model for production planning in steel making

Dow

nloa

ded

by [

Lin

naeu

s U

nive

rsity

] at

13:

53 1

6 O

ctob

er 2

014

integrated model for production planning in a large iron and steel manufacturing environment

Documents