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CHEMICAL ENGINEERING TRANSACTIONS 
 

VOL. 61, 2017 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Petar S Varbanov, Rongxin Su, Hon Loong Lam, Xia Liu, Jiří J Klemeš 
Copyright © 2017, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-51-8; ISSN 2283-9216 

Mathematical Modelling and Optimization for Integrated 

Production and Energy System in an Iron and Steel Plant  

Yujiao Zenga, Xin Xiaoa,*, Jie Lib, Li Sunb 

aDivision of Environment Technology and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, 

Beijing, 100190 P. R. China  
bSchool of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, M13 9PL UK 

 xxiao@ipe.ac.cn 

In this paper, we address a simultaneous optimization problem of integrated production and energy system in 

an iron and steel plant. We develop a novel multi-period mixed integer linear optimization model incorporating 

many realistic operational features such as industrial boilers, steam turbines, combined heat and power 

generation units and waste heat recovery and power generation units. A case study of a real iron and steel 

plant demonstrates that compared to the realistic operational strategy, the total operational cost is reduced by 

6.25 % using the proposed model. 

1. Introduction 

The iron and steel industry is one of the energy-intensive industries with high CO2 emissions. As reported 

(Zhang, 2008), the energy cost in the iron and steel industry accounts for about 20% of the total operating 

cost. In recent years, iron and steel industries are facing great pressure to reduce their operating cost, 

improve energy efficiency, reduce CO2 emissions, and become more competitive in the global market, which 

drives them to seek advanced techniques to improve their planning operations.  

In an iron and steel plant, production units such as coke ovens, sintering furnace, blast furnaces, hot stoves, 

basic oxygen furnaces are usually integrated with its energy system. Optimal planning of such integrated 

system has several advantages such as increasing profit margin, decreasing operating cost, improving energy 

efficiency, and reducing CO2 emissions. However, optimal planning of such integrated system is not trivial 

since it involves many production units, fuel boilers, steam turbines, combined heat and power (CHP) units 

and waste heat and energy recovery and generation (WHERG) units, resulting in many operations including 

steelmaking, rolling, steam and power generation, byproduct gas storage and distribution, and burner 

switching operations. More important, generation rates of byproduct gases and demands of byproduct gases, 

steam and electricity from production units vary from time to time, increasing the complexity of such integrated 

system. The burner switching operations involve the monitoring of number of burners whose status changes at 

each time, leading to a combinatorial problem. 

Many research efforts have been made on planning and scheduling of production processes such as 

steelmaking and continuous casting processes (Li et al., 2012) and cold rolling process (Tang et al., 2016) 

without considering the energy system. Since an iron and steel plant is energy intensive, several researchers 

have proposed some methods for the calculation of energy consumption (Ansari and Seifi, 2012) and energy 

efficiency (Wei et al., 2007). Several energy saving measures for CO2 emissions mitigation were investigated 

and their impact on productive efficiency were analyzed (Zhang and Wang, 2008). These energy saving 

measures were evaluated from a system perspective in relation to each other without optimization (Johansson 

and Söderström, 2011). Although some researchers have focused on the optimization of byproduct gas 

system considering effect of penalty factors (Zhao et al., 2015), the turn-down ratio of boiler burners (de 

Oliveira Junior et al., 2016), suitable capacity for buffer users (Yang et al., 2017), and steam and power 

generation system (Zeng and Sun, 2015) in an iron and steel plant, several realistic features are missing such 

as CHP and WHERG units for steam and electricity generation, minimum heating value requirements, ramp 

rates variations, piecewise constant demand profiles of byproduct gases, steam and electricity. In this paper, 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1761293

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Zeng Y., Xiao X., Li J., Sun L., 2017, Mathematical modelling and optimization for integrated production and energy 
system in an iron and steel plant, Chemical Engineering Transactions, 61, 1771-1776  DOI:10.3303/CET1761293  

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we develop a multi-period mixed integer linear programming (MILP) model for simultaneous optimization of 

integrated production and energy system in an iron and steel plant. Many realistic features such as byproduct 

gas distribution and storage, steam and power generation system, CHP and WHERG units, dedicated 

byproduct gasholders, boiler burner switching operations, minimum heating values, ramp rate variations, and 

piecewise constant demand profiles of byproduct gases, steam and electricity are incorporated into the model. 

The computational results demonstrate that the proposed model solves an industrial example to optimality 

within 2 CPU second. The total operational cost is reduced by 6.25% using the proposed model compared to 

that from actual operation.  

2. Problem definition 

Figure 1 illustrates a schematic diagram of integrated production and energy system in a typical iron and steel 

plant. There are total U (u = 1, 2, ..., U) production units, I (i = 1, 2, 3, ..., I) fuel boilers,  J (j = 1, 2, …, J) steam 

turbines, K (k = 1, 2, …, K) CHP units, and M (m = 1, 2, …, M) WHERG units. The fuel boilers in a CHP unit 

are denoted as Ik. Q (q = 1, 2, …, Q) types of energy sources such as by-product gas, coal, natural gas, and 

fuel oil can be used in fuel boilers and some production units as fuels. By-product gases generated from coke 

ovens, blast furnace, and basic oxygen furnaces are called COG, BFG, and LDG, respectively, which are 

included into a set Qg. By-product gases are either provided for production units, boilers, and CHP units as 

fuels, or stored in their dedicated gasholders. Total R (r = 1, 2, …, R) levels of steam are generated from fresh 

water in boilers, CHP and WHERG units, and consumed in production units and turbines. The electricity 

generated from turbines, CHP and WHERG units is supplied for production units. While excess electricity is 

sold to the grid, insufficient electricity is purchased from the grid. The entire problem is defined as follows, 

Given: (1) Byproduct gases data including their types, heating values, and generation rate and demand 

profiles; (2) Data on dedicated gasholders including their capacities, normal inventory levels, threshold 

inventory levels for low and high operational regions; (3) Data on fuel boilers including their inlet flow rate and 

steam generation rate limits, thermal efficiency, and minimum heating values; (4) Data on burners including 

suitable byproduct gases, feed rates, and initial status; (5) Data on steam turbines including suitable steams, 

thermal efficiency, limits on feed rates, steam and power generation rates; (6) Data on CHP units including 

thermal efficiency, limits on feed rates, steam and power generation rates, minimum heating values, (7) Data 

on WHERG units including amount of heat recovered, thermal efficiency, steam and power generation rate 

limits, (8) Data on steam and electricity demand profiles, steam enthalpy, and electricity energy content; (9) 

Economic data including coal, natural gas and electricity purchase cost, electricity sale price, penalty 

coefficients for byproduct gas emissions and burner switching operations, penalty coefficients for deviations of 

normal inventory levels and violations of threshold inventory levels of low and high operational regions in 

gasholders, maintenance cost for steam and power generation units and the planning horizon. 

 

 

Figure 1: A typical integrated production and energy system in an iron and steel plant 

Determine: (1) Selection of byproduct gases, coal, and natural gas in boilers; (2) Optimal distribution of 

byproduct gases among production units, boilers, and CHP units; (3) Inventory profiles of gasholders; (4) 

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Power generation plan; (5) Detailed operational plan for burners in boilers 

Assumptions: (1) All parameters are deterministic; (2) Byproduct gas generation rates are piecewise 

constant; (3) Demands of byproduct gases, steam, and electricity in production units are piecewise constant

Our objective is to minimize total operating cost including purchase cost of coal, natural gas, and cooling 

water, electricity cost, equipment maintenance cost, and some penalties such as penalty for byproduct gas 

emissions and penalty for burner switches. 

3. Mathematical formulation 

The entire planning horizon is divided into T periods (t = 1, 2,...,T) based on the piecewise constant generation 

rate and demand profiles of byproduct gases, steam and electricity. The length of each period t is denoted 

ast. 

3.1 Utility generation model 

(1) Fuel boiler operational model 

   
1 1

QR
stm w

irt t r irt t i iqt t q

r q

F H F H F HV   
 

 
         

 
   i  Ik, t (1) 

min max

ir irt ir
F F F   i  Ik, r, t (2) 

min max

iq iqt iq
F F F   i  Ik, t, q  Qg (3)  

    min
g g

iqt t q iqt t i

q q

F HV F HV 
 

 
     

  
 

Q Q

 i  Ik, t (4) 

(2) Steam turbine operational model  

   in in out exhjt t jrt t jrt t jt t
r r

F F F F            j, t (5) 

   
1 1

R R
P in stm out stm exh exh

j,t t j jrt t r jrt t r jt t j

r r

P HC F H F H F H    
 

 
            

 
   j, t (6) 

in,min in in,max

jr jrt jr
F F F   j, r, t (7) 

out,min out out,max

jr jrt jr
F F F   j, r, t (8) 

min max

j jt j
P P P   j, t (9) 

(3) CHP operational model 

   
1 1k

QR
P stm w

kt t krt t r krt t k iqt t q
r i q

P HC F H F H F HV    
  

 
            

 
 

I

 k, t (10) 

k

min max

kq t iqt t kq t
i

F F F  


 
      

 


I

 k, t, q  Qg (11) 

min max

kr krt kr
F F F   k, r, t (12) 

min max

k kt k
P P P   k, t (13) 

   min
g g

k k

iqt t q k iqt t

i iq q

F HV HV F 
  

 
     

  
   

I IQ Q

 k, t (14) 

(4) WHERG operational model 

 
1

R
P stm w in

mt t mrt t r mrt t m mt

r

P HC F H F H E   


           m, t (15) 

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min max

mt mt mt
P P P   m, t (16) 

min max

mrt mrt mrt
F F F   m, r, t (17) 

3.2 Power, steam and by-product gas balances 

      exp
1 1 1

J K M
imp dem

jt t kt t mt t t t t

j k m

P P P P P P  
  

           t (18) 

         
1 1 1 1k

K M J J
in out dem

irt t krt t mrt t jrt t jrt t rt

i k m j j

F F F F F D    
    

 
          

 
    

I

  r, t  (19) 

   ( 1)
1 1

U I
Gen emission

qt q t qt t uqt t iqt t qt

u i

Inv Inv F F F Q  


 

          q  Qg, t (20) 

3.3 Gasholder operational model 

min max

,q q t q
Inv Inv Inv   q  Qg, t (21) 

N d d

qt q qt qt
Inv Inv SInv SInv

 

    q  Qg, t (22) 

L L H H

q qt qt q qt
Inv SInv Inv Inv SInv     q  Qg, t (23) 

3.4 Burner operational constraints 

iqt t iq iqt t
F F N      i, q  Qg,, t (24) 

( 1)
  

iqt iqt iq t
N N N  i, q  Qg, t  (25a) 

( 1)
  

iqt iq t iqt
N N N  i, q  Qg, t (25b) 

1 2 3
iqt iqt iqt iqt

N ibn ibn ibn
  

     i, q  Qg, t (26) 

1 2 3
iqt iqt iqt

ibn ibn ibn
  
   i, q  Qg,  t (27) 

0 1 1
iqt iqt

ibn ibn


    i, q  Qg,  t (28) 

0 2 1
iqt iqt

ibn ibn


    i, q  Qg,  t (29) 

0 3 1
iqt iqt

ibn ibn


    i, q  Qg,  t (30) 

where, 0
iqt

ibn


 is 0-1 continuous variables denoting if no burner changes its status in t; 1
iqt

ibn , 


2
iqt

ibn , 


3
iqt

ibn  

are binary variables denotes if one burner, two burners and three burners change status in t. 

3.5 Byproduct gas constraints for production units 

min max

uq uqt uq
F F F   u, q  Qg, t (31) 

dem

uqt t uq
F D   u, q  Qg, t (32) 

   min
g g

uqt t q u uqt t

q q

F HV HV F 
 

     
Q Q

 u, t, 
min

u
HV  > 0 (33) 

 
g

Dem

uqt t q ut

q

F HV E


  
Q

 u, t, 
Dem

ut
E  > 0 (34) 

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3.6 Objective function 

       

   

,
1 1 1 1 1 1

1 1

W W W W

   

   

 

     

  

           

           
   



    

   

g

g g

T I K T I K T T
w w exp exp imp imp

q iqt t i t t t t t t t
t i t i t tq

T T
emission emission L L H H d d d d

q qt q qt q qt q qt q qt

t tq q

S

q

TC C F C F C P C P

W Q SInv SInv SInv SInv

W

Q

Q Q

 

   

2 3

1 1

1 1 1 1

1 2 3 2 3

 

    

  

 

   

      
 

     

 

  

g

T I
W S S

iqt iqt iqt q iqt q iqt

t i q

T I T J K M
M PM

i it t j jt t
t i t j

ibn ibn ibn W ibn W ibn

C F C P

Q

  (35) 

We complete our mixed-integer linear optimization model (MILP) denoted as M, which comprises the objective 

function TC and constraints Eq(1) – Eq(34). The binary variables are used to model switching operations of 

burners in fuel boilers, and decisions on electricity sale and purchase. 

4. Computational results 

We use the proposed model M to solve an industrial example from an iron and steel plant in China. This 

industrial plant consists of 4 coke ovens, 2 blast furnaces, and 5 basic oxygen furnaces. The energy system is 

made up of 4 boilers (B1 - B4), 2 steam turbines (TB1 - TB2), 2 CHP units (CHP1 - CHP2), and 2 CDQ units 

(CDQ1 - CDQ2). Three levels of steams are generated from the boilers, which are high-pressure steam S1 

(3.5 MPa), medium-pressure steam S2 (1.0 MPa) and low-pressure steam S3 (0.4 MPa). Three types of 

byproduct gases are generated, which are COG, BFG, and LDG. Prices of natural, coal, fresh water are 3.5 

¥/m3, 500 ¥/t and 10 ¥/t. The horizon is about 6 h and divided into 6 identical periods based on energy 

demand profiles. This example is solved using CPLEX 12.6.1.0/GAMS 24.4.2 on a Dell Insprion15 5000 of 

Intel Core i7-4510U CPU 2.0 GHz with 8GB RAM memory running Windows 7. The optimization model 

contains 438 binary variables, 918 continuous variables, and 2,293 constraints. The optimal solution of 

¥1,285,132 is obtained within 2 CPU s. The optimal distribution of by-product gases in production units and 

gasholders are illustrated in Figure 2. It is noted that the inventory level of each dedicated gasholder at any 

time is maintained around its normal operation level. The comparative results from the proposed approach 

and the actual operation are given in Table 1. The total cost of ¥1,370,252 from the actual operation is 

reduced by 6.25 % compared to that of ¥1,285,132 using the proposed model. The purchase cost of electricity 

and coal from the market, and the penalty cost for gasholder deviation from the normal level and burner 

switches are significantly reduced using the proposed model, although the equipment maintenance cost is 

slightly increased. 

 

Figure 2: The optimal distribution of byproduct gases in production units and gasholders: (a) COG, (b) BFG, 

(c) LDG, (d) Inventory profiles of gasholders 

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Table 1: Comparative results from the proposed model and actual operation  

Item Actual Operation Proposed Model 

Coal cost (¥) 858,560 804,776 

Natural gas cost (¥) 0 0 

Water cost (¥) 80,246 72,585 

Penalty for byproduct gas emissions (¥) 0 0 

Penalty for violation of high levels in gasholders (¥) 0 0 

Penalty for violation of low levels in gasholders (¥) 0 0 

Penalty for deviation of normal levels in gasholders (¥) 15,045 5,089 

Penalty for burner switches (¥) 36,800 24,400 

Equipment maintenance cost (¥) 316,197 327,588 

Electricity purchase cost (¥) 63,404 50,694 

Electricity sale revenue (¥) 0 0 

Total cost (¥) 1,370,252 1,285,132 

5. Conclusions 

In this paper, a novel multi-period MILP planning model was developed for simultaneous optimization of 

integrated production and energy system in an iron and steel plant. The proposed model incorporated many 

realistic operational features such as byproduct gas distribution, boilers and turbines, CHP and WHERG units, 

dedicated byproduct gasholders, burner switching operations, minimum heating values, ramp rate variations, 

and piecewise constant demand profiles of byproduct gases, steam and electricity. The results indicate that a 

reduction of 6.25 % in total operational cost was successfully achieved compared to that from actual 

operation. 

Acknowledgments  

Yujiao Zeng would like to acknowledge financial support from the National Natural Science Foundation of 

China (61603370) and Major Science and Technology Program for Water Pollution Control and Treatment 

(2015ZX07202013-003). Jie Li is thankful from the National Natural Science Foundation of China (21206174). 

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