DOI: 10.3303/CET24114065 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 31 May 2024; Revised: 28 August 2024; Accepted: 5 December 2024 
Please cite this article as: Xu W., Wu L., Kang L., Liu Y., 2024, Multi-objective Design and Optimization for Supply Chain of Modular Methanol 
Productions , Chemical Engineering Transactions, 114, 385-390  DOI:10.3303/CET24114065 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 114, 2024 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Petar S. Varbanov, Min Zeng, Yee Van Fan, Xuechao Wang 

Copyright © 2024, AIDIC Servizi S.r.l. 

ISBN 979-12-81206-12-0; ISSN 2283-9216 

Multi-objective Design and Optimization for Supply Chain of 

Modular Methanol Productions 

Weibin Xua, Le Wua,*, Lixia Kangb, Yongzhong Liub 

aSchool of Chemical Engineering, Northwest University, Xi’an 710069, China 
bDepartment.of.Chemical .Engineering,Xi'an Jiaotong·University,:Xi'an,Shaanxi, .710049,·PR China 

 lewu@nwu.edu.cn 

The integration of renewable energy sources into the methanol production process is recognized as a viable 

approach to mitigate carbon emissions and promote renewable energy utilization. This study, centered on a 

modular methanol production system driven by renewable energy, is a multi-objective model encompassing 

economic and environmental objectives that is established to optimize methanol production sites and supply 

chain networks under different objectives. In order to balance economic and environmental goals, an optimal 

compromise point is set, considering both objectives equally important. Results indicate that under the scenario 

of minimizing total annual costs, the cost is 7.05×108 USD. Under the scenario of minimizing total environmental 

impact, the cost is 7.74×108 USD. At the optimal compromise point, the annual total operating cost is 7.07×108 

USD. The system's environmental impact is equivalent to approximately 1.77×105 t of methanol produced by 

coal gasification technology. In terms of economic objectives, capital costs and electricity expenses during the 

production process dominate, while the environmental impact is primarily attributed to production processes. 

The main approach to reducing environmental impact is by altering production site distribution to minimize 

transportation-related environmental effects.  

1. Introduction 

Methanol, a pivotal cornerstone of the chemical industry, finds extensive application as both a fuel source and 

in the fabrication of various commodities (Galan et al., 2023). Recently, several innovative methods for methanol 

production have emerged. These include synthesizing renewable methanol by combining green hydrogen with 

carbon dioxide, as well as producing renewable bio-methanol through the utilization of biomass or municipal 

solid waste. (Roode-Gutzmer et al., 2019). In renewable methanol synthesis systems, the production of green 

hydrogen relies predominantly on electrolyzing water using renewable energy sources. However, the 

intermittent nature, variability, and regional disparities in renewable energy availability present significant 

challenges to its efficient utilization (Qiu et al., 2022). Modular design technology involves standardizing the 

design and production of essential equipment for the manufacturing process. This approach amalgamates the 

benefits of economies of scale and economies of quantity to diminish the cost of individual devices. In order to 

effectively harness renewable energy, modular technology can act as a foundational element, in conjunction 

with corresponding energy storage systems (Zhang et al., 2019), to enable uninterrupted production driven by 

renewable energy by facilitating the initiation and cessation of production lines. Based on modular technology, 

a modular renewable energy-driven carbon dioxide to methanol synthesis system has been developed (Huang 

et al., 2022), showcasing superior economic benefits compared to large-scale counterparts. Currently, modular 

technology is predominantly used in the construction of production systems, while its application in supply chains 

remains unclear. In supply chain studies focused on traditional chemicals, production has largely been oriented 

towards large-scale operations, with adjustments in capacity primarily achieved through enhancements in 

production efficiency. Modular small-scale production allows for capacity adjustments directly through line start-

ups and shutdowns. To enhance system flexibility, production lines are permitted to adjust capacity within certain 

limits; however, deviations from rated conditions entail increased costs (Poluzzi et al., 2022). This work proposes 

a multi-objective model for supply chain design and optimization based on a modular methanol synthesis 

system, considering variations in renewable energy distribution to meet methanol demand. Unlike traditional 

385



approaches focusing solely on single objectives, the model integrates economic goals with environmental 

impacts to evaluate the performance of modular methanol synthesis systems across different objectives. The 

specific supply chain is shown in Figure 1. The objective function in different scenarios is shown in Eq. (1). 

( )

( )

( )







-

    

    

    s h

scenario

EI scenario

M m

b

in TAC in minimu TAC

Min T in minimum TEI

Max in e e scenao riost compr mis

 (1) 

 

Figure 1: Renewable supply chain framework 

2. Mathematic model 

2.1 Economic objectives 

The economic objective function is defined by the Total Annual Cost (TAC), encompassing both capital and 

operational expenditures, as articulated in Eq. (2). 

= +TAC TCC TOC  (2) 

2.2 Total capital cost 

The total capital costs primarily stem from the construction expenses of modular methanol production lines at 

various production sites, as delineated in Eqs. (3) to (5). 

=C ( )S

p p csC n C   (3) 

=  C

p p

p

TCC CRF C Z  (4) 

+
=

+ −

(1 )

(1 ) 1

f

f

r r
CRF

r
 (5) 

2.3 Total operating cost 

Methanol transportation costs are articulated in Eqs. (6) to (7); electricity consumption costs and initial hydrogen 

expenses within the methanol production system are delineated in Eqs. (8) to (11); raw material consumption 

expenses are expressed in Eqs. (12) to (15); the annual total operating cost is represented by Eq. (16). 

=T,

, , ,

MeOH MeOH

p d p d p d kC F D P  (6) 

= T,

, ,

T MeOH

p d p d

p d

C C Z  (7) 

  
= + +  −  

   
1 1.3 1

v
E f v

p p f p ff

Cap
C n C n C

Cap
 (8) 

=E E

p p

p

C C Z  (9) 

=2

2

H

p p HC n P  (10) 

=2 2H H

p p

p

C C Z  (11) 

=
2

2

2 2

CO
CO MeOH

p p CO COMeOH

M
Dem Cap

M Sel X
 (12) 

386



=2 2

2

,R CO CO

p p COC Dem P  (13) 


= 

2

2

2

, 3
H O

R H O MeOH

p p H O MeOH

M
C Cap P

M
 (14) 

= + 2 2, ,( )R H O R COR

p a p

p

C C C Z  (15) 

= + + +2HT E RTOC C C C C  (16) 

2.4 Environmental objectives 

Employing the Eco-indicator 99 (Goedkoop and Spriensma, 2000) methodology facilitates the quantitative 

assessment of environmental impacts across the supply chain continuum. The impact of electricity consumption 

during production is explicated in Eqs. (17)-(18); the impact of methanol products is delineated in Eqs. (19)-(20); 

the impact of the transportation process is elucidated in Eqs. (21)-(22); the impact of initial hydrogen is outlined 

in Eqs. (23)-(24); and the total annual environmental impact is succinctly represented in Eq. (25). 

=

E

pE E

p

E

C
EI e

p
 (17) 

=E E

p p

p

EI EI Z  (18) 


= +  −

2

2 2 23
H O

CO CO H OR MeOH MeOH MeOH

p p p pMeOH

M
EI Dem e Cap e Cap e

M
 (19) 

=R R

p p

p

EI EI Z  (20) 

=T

, , ,

MeOH T

p d p d p d kEI F D e  (21) 

= T

, ,

T

p d p d

p d

EI EI Z  (22) 

=
2

2 2

2

H

pH H

p

H

C
EI e

p
 (23) 

=2 2H H

p p

p

EI EI Z  (24) 

= + +E R TTEI EI EI EI  (25) 

2.5 Mass balance 

Quality balance must be maintained between the flow of production and demand. 

= MeOH

,

MeOH

p d p

d

F Cap  (26) 

= MeOH

,

MeOH

p d d

p

F Dem  (27) 

2.6 Constraints  

The constraints mainly include the limitation of the maximum number of modular methanol production lines in a 

certain area, as shown in Eqs. (28)-(29), the limitation of modular methanol production lines operating below full 

load as shown in Eq. (30), the limitation between modular production quantity and capacity as shown in Eqs. 

(31)-(32), and the limitation between methanol production and demand within the cycle as shown in Eq. (33). 

= −MN ( 0.5)
E

p

p

PV
round  (28) 

 Mp pn N  (29) 

 0.85 f v fCap Cap Cap  (30) 

= +f v

p p pn n n  (31) 

= +MeOH f f v v

p p pCap n Cap n Cap  (32) 

= MeOH MeOH

p d

p d

Cap Dem  (33) 

387



2.7 Tradeoffs between economic and environmental objectives  

For multi-objective optimization problems, the multi-objective model needs to be normalized to obtain the optimal 

result points under different objective weights. In this work, the evaluation function method is adopted for 

normalization, as shown in Eqs. (34)-(35). 

 − −

− − − − −
= − −max max min( ) / ( )s h s h

o h o h o h o h o hO O O O  (34) 

  − −

− −

−

=s h s h

o h o h

o h

 (35) 

3. Case study 

This work employs Shandong Province, a prominent hub for methanol consumption in northern China, as a case 

study. Specifically, the analysis focuses on conventional methanol consumption sectors, including formaldehyde 

and methanol fuel industries. 

3.1 Base parameters 

Through computational and statistical methodologies, a comprehensive assessment reveals a total of 16 

methanol demand sites. The photovoltaic power generation aggregate across various locales in Shandong 

Province was derived from statistical analyses (CLOUD, 2023). Factoring in the minimal operational energy 

constraints inherent to production systems, a discerning process identified 46 prospective sites conducive to 

methanol production. Three methanol transportation methods have been established, including truck, train, and 

pipeline. The distances between each production site and its corresponding demand location were obtained on 

a map. The aforementioned design and optimization model for the multi-objective supply chain of renewable 

energy-driven modular methanol production is formulated as a mixed-integer nonlinear programming (MINLP) 

problem. The model comprises 8,188 variables and 6,237 constraints. Solution computations were conducted 

using GAMS 24.1.3, employing SCIP as the solver for MINLP models, CONOPT for NLP, and CPLEX for MIP.  

3.2 The optimal supply chain 

The optimal actual supply chain diagrams in different scenarios are shown in Figure 2 

  

Figure 2: The optimal actual supply chain diagrams in different scenarios. (a Minimum TAC; b Minimum TEI;c 

Best compromise) 

The total annual cost breakdown for different scenarios is presented in Table 1. The total environmental impact 

for different scenarios is detailed in Table 2. In Table 2, the unit PT is an abbreviation for "point" and represents 

the result obtained from quantifying environmental impacts using Eco-indicator 99. It represents one-thousandth 

of the average annual environmental burden per person. The material balance, energy consumption, and 

methanol cost are shown in Table 3. Considering the selectivity of carbon dioxide and the efficiency of water 

electrolysis, material imbalances at the inlet and outlet were observed. 

Table 1: The total annual cost for different scenarios 

Item Minimum TAC Cost/USD Minimum TEI Cost/USD Best compromise Cost/USD 

Construction 3.29×108 4.00×108 3.32×108 

Initial hydrogen 1.61×105 1.61×105 1.61×105 

CO2 1.13×108 1.13×108 1.13×108 

H2O 4.25×106 4.25×106 4.25×106 

Transport cost 7.32×106 4.99×106 6.48×106 

Electricity 2.51×108 2.51×108 2.51×108 

Total annual cost 7.05×108 7.74×108 7.07×109 

388



Table 2: The total environmental impact for different scenarios 

Item Minimum TAC Impact/PT Minimum TEI Impact/PT Best compromise Impact/PT 

Methanol product 5.68×107 5.68×107 5.68×107 

Production process 1.38×107 1.38×107 1.38×107 

Transport Process 5.94×105 3.98×105 5.42×105 

Initial hydrogen 2.74×104 2.74×104 2.74×104 

Total environmental impact 7.13×107 7.11×107 7.12×107 

Table 3: material balance, energy consumption and methanol cost 

Item  Item  Item Methanol cost/USD⋅t−1 

Carbon dioxide 

input/t⋅y−1 

2436667 Electrolyzer/MW 
13.1 

Minimum TAC case  489.04 

Water input/t⋅y−1 9133300 Compressor/MW 0.479 Minimum TEI case  536.90 

Methanol 

output/t⋅y−1 

1441600 Heater/MW 
0.933 

Best compromise case  490.43 

Waste water 

output/t⋅y−1 

3054353 Cooler/MW 
2.488 

  

Purge gas 

output/t⋅y−1 

916306     

In the scenario of minimum TAC, out of 46 regions capable of producing methanol, only 16 are selected for 

production, indicating a more concentrated methanol production. In the scenario of minimum TEI, 34 are 

selected for methanol production, indicating a more dispersed methanol production. Compared to the minimum 

TAC scenario, in this scenario, there are fewer methanol production facilities in each location. This results in a 

sharp increase in construction costs in each location, and the dispersed distribution of production sites also 

leads to a decrease in transportation costs. The variation in TEI mainly reflects the reduction in environmental 

impact caused by transportation. It can be concluded that the main means of reducing TEI in the supply chain 

model is by changing the distribution of production sites to make them more dispersed, bringing them closer to 

demand locations, and reducing the environmental impact of methanol commodity transportation to lower the 

overall system's environmental impact. In the scenario of the best compromise, only 18 regions are selected for 

methanol production. Compared to the minimum TAC scenario, this scenario includes two additional production 

sites. It is worth noting that there is a phenomenon of long-distance transportation in this scenario. Because of 

the low volume, the economic and environmental impact of using long-distance transportation is much lower 

than if places with large demand switch to more distant supply locations, leading to the phenomenon of long-

distance transportation, all of which are routes for methanol transportation by trucks. The environmental impact 

of the system equates to approximately 1.77×105 t of methanol produced by coal gasification technology, 

indicating that modular methanol production is more eco-friendly. 

4. Conclusions 

In this study, a multi-objective model combining economic and environmental goals was proposed based on 

modular methanol production lines driven by renewable energy sources. The optimal supply chain solutions 

under different objectives were ultimately obtained. According to the analysis of actual cases, the largest 

proportion of annual total costs in each scenario is construction costs, while the largest proportion of 

environmental impact is methanol products. The main way to reduce environmental impact is by altering the 

distribution of production sites, bringing them closer to demand areas to reduce the environmental impact of 

transportation. However, this also leads to an increase in construction costs. An optimal compromise point was 

set, considering economic and environmental goals equally important. At the optimal compromise point, the 

annual total cost is 7.07×109 USD, and the total environmental impact is 7.12×107 PT. 

For supply chain issues, solely considering economic objectives is not comprehensive. In future research, 

emphasis should be placed on studying the reduction of environmental impact in the methanol production 

process and developing related multi-period multi-objective models to comprehensively examine the economic 

benefits and environmental impact of renewable energy-driven modular methanol production lines.  

Nomenclature

Variable 

C – total construction cost, USD 

Cap – capacity, t/y 

CRF – the capital recovery factor, /y 

389



Dem – demand, t/y 

D – distance, km 

E – the energy consumption of a single methanol 

production line, MW 

EI – the total impacts, PT 

e – environmental impact per unit consumption, 

PT/per unit 

F – mass flow rate, t/y 

f – the operation unit life, - 

M – molar mass, g/mol 

MN – the maximum number of production lines, - 

n – the number of production lines, - 

O – solution, - 

P – the unit prices of raw material, USD/ per unit 

PT – an abbreviation for point, is used to quantify 

environmental impact, representing one-

thousandth of the average annual environmental 

burden per person, - 

PV – photovoltaic power, MW 

p – the unit prices, USD/ per unit 

r – the interest rate, - 

S –the scale up factor, - 

Sel – selectivity, - 

TAC –total annual cost, USD/y 

TCC – total capital cost, USD/y 

TEI – the total annual environmental impact, PT 

TOC – total operating cost, USD/y 

Z – the binary variable, - 

µ– the compromise number, - 

ω – the weight of objective function, - 

Superscript 

C – construction 

CO2 – carbon dioxide 

E – electricity 

f – full-load production line 

H2 – hydrogen 

H2O – water 

max – maximum 

min – minimum 

MeOH – methanol 

R – raw material 

s-h – the s-th solution 

T – transportation 

v – variable production line 

Subscript 

CO2 – carbon dioxide 

d – demand site 

f – full-load production line 

H2 – hydrogen 

H2O – water 

k – mode of transportation 

o-h – the o-th objective function 

p – production site  

sc – single modular methanol production line 

Acknowledgments 

The authors gratefully acknowledge funding by the projects (22238006 and 22378328) sponsored by Natural 

Science Foundation of China (NSFC). 

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