DOI: 10.3303/CET2188009
Paper Received: 24 May 2021; Revised: 29 July 2021; Accepted: 10 October 2021
Please cite this article as: How B.S., Benjamin M.F.D., Lim C.H., 2021, VIKOR - P-graph Method for Optimal Synthesis of Philippine
Agricultural Waste-Based Sustainable Integrated Biorefinery, Chemical Engineering Transactions, 88, 55-60 DOI:10.3303/CET2188009
CHEMICAL ENGINEERING TRANSACTIONS
VOL. 88, 2021
A publication of
The Italian Association
of Chemical Engineering
Online at www.cetjournal.it
Guest Editors: Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš
Copyright © 2021, AIDIC Servizi S.r.l.
ISBN 978-88-95608-86-0; ISSN 2283-9216
VIKOR - P-graph Method for Optimal Synthesis of Philippine
Agricultural Waste-Based Sustainable Integrated Biorefinery
Bing Shen Howa,*, Michael Francis D. Benjaminb, Chun Hsion Limc
a Biomass Waste-to-Wealth SIG, Research Centre for Sustainable Technologies, Faculty of Engineering, Computing and
Science, Swinburne University of Technology, Jalan Simpang Tiga, 93350, Kuching, Sarawak, Malaysia
b Research Center for the Natural and Applied Sciences / Chemical Engineering Department, University of Santo Tomas,
España Blvd., 1015 Manila, Philippines
c Universiti Tunku Abdul Rahman, Department of Chemical Engineering, Jalan Sungai Long, Bandar Sungai Long, Cheras
43000 Kajang, Selangor, Malaysia
bshow@swinburne.edu.my
A sustainable integrated biorefinery (SIBR) is a biomass processing facility that converts agricultural wastes or
residues into a wide range of valuable products where both economic sustainability and environmental
sustainability are optimized. This work proposed a hybrid method that incorporates Vlsekriterijumska
Optimizacija I Kompromisno Resenje (VIKOR), a widely used multi-criteria decision-making (MCDM) tool with
the P-graph (process-graph) framework. The proposed VIKOR - P-graph model can (i) generate a set of
combinatorically feasible solutions, and (ii) rank the solution sets using VIKOR method, simultaneously in the
same P-graph model. In other words, all the drawbacks attributed to the sequential optimization methods can,
therefore, be avoided. To demonstrate the effectiveness of the proposed hybrid methodology, a case study in
the Philippines is presented in this paper. The hybrid P-graph model generated a total of 7 feasible solutions
with different configuration for the SIBR based on the overall profit (i.e., economic goal) and carbon emissions
(i.e., environmental goal). Results show that the best compromised solution can be obtained when majority (70
%) of the rice husk is used to produce bioethanol, where the required power is supplied by combusting the
remaining rice husk and by importing external power. It offers an hourly profit of 161 $/h with a lower (~38.6 %)
carbon emissions as compared to the most profitable option (3.504 tCO2-eq/h). This research is essentially a
guide for policymakers to make informed decisions that can maximise the benefits of SIBR on a national scale.
1. Introduction
The utilization of biomass to produce bioenergy and other high-value added products is an important step of a
country to increase local energy supply and thus lessen its dependence on imported fuels. One way of achieving
this is via the development of sustainable integrated biorefineries (SIBR). SIBR is a processing facility that use
biomass as feedstock to produce various bioenergy products. Biomass raw materials are converted to biofuels
or biochemicals via mechanical, thermochemical, or biochemical processes. The efficiency of this system is
further enhanced using process integration by identifying potential material or energy synergies between
process units. Aside from this, economic and environmental benefits consideration are possible through
integration of process units that could increase farmer revenues and decreased carbon emissions, respectively.
Among the available biomass, lignocellulosic materials such as wood waste, herbaceous crops, and residues
from agricultural processes can be used in SIBR. In the Philippines and Asia in general, a huge amount of
agricultural waste (i.e., from harvesting rice, corn, or sugarcane) remains to be tapped for bioenergy production.
In particular, residues from rice production and processing can be utilized as these comprise largely the available
waste (Sangalang et al., 2021). About 20 Mt of rice are annually produced and its residues, straw, husk, and
bran are potential feedstock for the SIBR (PSA, 2019). The establishment of a SIBR is a novel work in the
Philippines as there are limited studies on this research area and agricultural waste are yet to be utilized for
bioenergy production in the country.
The design and synthesis of SIBR are challenging tasks and not straightforward as this will entail factors such
as type of biomass, products to be generated, the capacity of process units, network topology, and cost
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parameters. Traditional mathematical programming approaches are usually employed to deal with this process
network synthesis (PNS) problem. The P-graph method which was developed by Friedler et al. (1992), has been
used to solve various PNS problems given the versatility of this approach. Its extended applications were
outlined in Friedler et al. (2019). Recent works on the application of P-graph to design various systems include,
but not limited to, solid waste management (Fan et al., 2020), oil supply chains (Wang et al., 2020), and
biohydrogen network (Lee et al., 2020). Various efforts have been committed to extending P-graph framework
into multi-objective optimization, e.g., TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution)
(Lim et al., 2021), weighted-sum approach (Lam et al., 2017), and fuzzy optimization (Aviso and Tan, 2018).
VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) is one of the widely applied multi-criteria
decision-making (MCDM) methods where the optimality of each alternative is measured based on the measure
of “closeness” to the “ideal” solution (Opricovic, 1998). In general, VIKOR stands out from the other MCDMs
since it derives the ranking order of each alternative by maximizing the group utility of the majority (i.e., the
weighted summed satisfaction) and minimizing the individual regrets (i.e., level of dissatisfactory of each goal)
(Suh et al., 2019). Its capability has been proven via various applications, e.g., debottlenecking strategies
selection in oil refinery (Teng et al., 2020), and eco-industrial park configuration evaluation (Teh et al., 2021).
To the best of the authors’ knowledge, none of the previous works has attempted to incorporate VIKOR
calculation into the P-graph framework.
In this work, a novel VIKOR - P-graph method was developed to optimally synthesize a rice-based sustainable
integrated biorefinery. The hybrid and simultaneous approach utilized the decision-making capabilities of VIKOR
and the efficient algorithms of the P-graph to achieve the economic and environmental goals of the SIBR.
2. Problem Statement
Given a set of biomass-processing units t which can be used to convert rice husk and rice straw into a set of
valuable products p. Suppose the material unit prices, the conversion rate, power consumption and carbon
emissions of each processing unit are known, an optimal rice-based SIBR is determined with the consideration
of both economic (i.e., total annual profit) and environmental (i.e., total emissions) benefits (indicators are
denoted as i). The list of feasible configurations of rice-based SIBR is denoted as j.
3. P-graph construction
This section demonstrates how VIKOR can be represented in the P-graph framework.
3.1 Normalization
The values of each indicator are usually expressed on a different scale. Therefore, in order to enable a fair
comparison between these indicators, data normalization is performed. The original data 𝑥𝑖𝑗 can be normalized
to 𝑦𝑖𝑗 via max-min aggregation method, where 𝑥𝑖𝑗 𝑏𝑒𝑠𝑡 and 𝑥𝑖𝑗 𝑤𝑜𝑟𝑠𝑡 refer to the best and the worst obtained value
of 𝑥𝑖𝑗 . As shown in Figure 1, the P-graph model is constructed differently depending on the type of the indicators
(benefit indicator or cost indicator). Following the red arrow, one can convert the original data to weighted
normalized data. For detailed description of this step, please refer to Aviso and Tan (2018).
Figure 1: P-graph representation for normalization and determination of Sj (red fonts indicates the flow
magnitude for the arrows)
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3.2 Determination of Sj
In VIKOR, the value of 𝑆𝑗 is minimized to ensure the obtained solution is with maximum group utility. It can be
determined by summing up all the weighted-normalized values as shown in Eq(1):
𝑆𝑗 = ∑ 𝑤𝑖
𝑥𝑖𝑗
𝑏𝑒𝑠𝑡−𝑥𝑖𝑗
𝑥𝑖𝑗
𝑏𝑒𝑠𝑡−𝑥𝑖𝑗
𝑤𝑜𝑟𝑠𝑡𝑖 = ∑ 𝑆𝑖,𝑗𝑖 ∀𝑗 ∈ 𝐽 (1)
where 𝑤𝑖 refers to the weightage assigned to each indicator. It can be determined through numerous
approaches (e.g., analytical hierarchy process (AHP) (Saaty, 1980)). For this work, the indicators are assumed
to be equally important. Note that Eq(1) has also been modelled in Figure 1. As shown the input and output ratio
across the “normalization” nodes is set as 1: 𝑤𝑖
𝐶𝑂𝑀
𝑥𝑖𝑗
𝑚𝑎𝑥−𝑥𝑖𝑗
𝑚𝑖𝑛
. Since the input is equal to 𝑥𝑖𝑗 𝑏𝑒𝑠𝑡 − 𝑥𝑖𝑗, the output will
therefore be 𝑤𝑖
𝑥𝑖𝑗
𝑏𝑒𝑠𝑡−𝑥𝑖𝑗
𝑥𝑖𝑗
𝑏𝑒𝑠𝑡−𝑥𝑖𝑗
𝑤𝑜𝑟𝑠𝑡
(or 𝑆𝑖,𝑗). Finally, the summed value is denoted as 𝑆𝑗.
3.3 Determination of Rj
𝑅𝑗 is the counterpart of 𝑆𝑗 which is minimised in VIKOR to ensure the obtained solution is with minimal individual
regrets. It is defined in Eq(2). Figure 2 demonstrates how such “MAX function” can be represented in P-graph
model. This is the first attempt of using P-graph to model “MAX function”.
𝑅𝑗 = 𝑀𝑎𝑥
𝑖∈𝐼 {𝑤𝑖
𝑥𝑖𝑗
𝑏𝑒𝑠𝑡−𝑥𝑖𝑗
𝑥𝑖𝑗
𝑏𝑒𝑠𝑡−𝑥𝑖𝑗
𝑤𝑜𝑟𝑠𝑡
} = 𝑀𝑎𝑥𝑖∈𝐼 {𝑆𝑖,𝑗 } ∀𝑗 ∈ 𝐽 (2)
Figure 2: P-graph representation for determination of Rj (red fonts indicates the flow magnitude for the arrows)
In the first two steps, an arbitrarily large number, “M” is introduced, such that the resulting product will be 𝑀 −
𝑆𝑖.𝑗 . Then, the remainders are “mixed” with an input flow ratio of 1:1:1 and an output ratio of 1. As a result, the
minimum value among the remainders will therefore become the maximum possible value for the output. Finally,
to convert back to its original form ((𝑆𝑖,𝑗 )
𝑚𝑎𝑥
), the same arbitrary large number is subtracted from the resulting
number (𝑀 − (𝑀 − 𝑆𝑖,𝑗 )
𝑚𝑖𝑛
). Note that the M-vertex which is labelled as “max”, represents the value of 𝑅𝑗.
3.4 Ranking of alternatives
Conventionally, the objective function for VIKOR method is expressed as Eq(3), where the superscriptions of
“max” and “min” indicate its upper and lower limits respectively. It integrates both 𝑆𝑗 and 𝑅𝑗 by using a pre-
defined constant, 𝑣 (takes as 0.5 in this work) which represents the weight of strategy of maximum group utility
57
(Shemshadi et al., 2011). In this VIKOR - P-graph method, a reversed function, 𝑄′𝑗 is used instead (Eq(4)). With
this expression, alternative with larger 𝑄′𝑗 is more preferable. By assigning a unit price (e.g., 1 $/t) to the 𝑄′𝑗,
the model will rank all the alternative according to the 𝑄′𝑗 value (Figure 3).
𝑄𝑗 = 𝑣
𝑆𝑗 −𝑆𝑗
𝑚𝑖𝑛
𝑆𝑗
𝑚𝑎𝑥−𝑆𝑗
𝑚𝑖𝑛 + (1 − 𝑣)
𝑅𝑗 −𝑅𝑗
𝑚𝑖𝑛
𝑅𝑗
𝑚𝑎𝑥−𝑅𝑗
𝑚𝑖𝑛 ∀𝑗 ∈ 𝐽 (3)
𝑄′𝑗 = 𝑣
𝑆𝑗
𝑚𝑎𝑥−𝑆𝑗
𝑆𝑗
𝑚𝑎𝑥−𝑆𝑗
𝑚𝑖𝑛 + (1 − 𝑣)
𝑅𝑗
𝑚𝑎𝑥−𝑅𝑗
𝑅𝑗
𝑚𝑎𝑥−𝑅𝑗
𝑚𝑖𝑛 ∀𝑗 ∈ 𝐽 (4)
Figure 3: Ranking of alternative using Q’j (red fonts indicates the flow magnitude for the arrows)
4. Case study demonstration
In this hypothetical case study, three conversion units, i.e., fermentation, combustion and carbonization units
are considered to convert rice straw (5.0 t/h) and rice husk (0.8 t/h) into valuable products (i.e., bioethanol,
electricity, and solid fuel). Table 1 tabulates the process and material cost data for each considered unit; while
the operating cost and fixed investment cost for each unit are shown in Table 2. Note that the electricity
generated from combustion unit can be sold to the grid (0.1458 USD/kWh) or supplied to other units. In addition,
the power requirement can also be supplied by the imported electricity (assumed import prize as 0.176 $/kWh
with 0.000691 tCO2-eq CO2/kWh of emissions (Climate Transparency Report 2020)).
Table 1: Process input-output data of each conversion unit and respective material costs
Material Fermentation Combustion Carbonization Cost ($/unit)
Bioethanol (L/h) 1.0000 0.0000 0.0000 1.1861 L-1
Solid fuel (kW) 0.0000 0.0000 1.0000 0.065 kWh-1
Electricity (kW) -1.6074 1.0000 -0.7380 0.1458 kWh-1
Rice straw (t/h) -0.0036 -0.0019 0.0000 27.5 t-1
Rice husk (t/h) 0.0000 0.0000 -0.00043 37.5 t-1
Emission (tCO2-eq/unit) 0.0030 L-1 0.000067 kWh-1 0.00045 kWh-1 -
References Sreekumar et al. (2020) Unrean et al. (2018) Aberilla et al. (2019) Market data
Table 2: Operational and investment cost for each conversion unit
Cost Fermentation Combustion Carbonization
Fixed investment cost ($/h) 157.92 168.45 278.27
Operating cost ($/unit) 0.3987 L-1 0.0050 kWh-1 0.0468 kWh-1
References Tefwik et al. (2015) Unrean et al. (2018) IRENA (2012)
The constructed VIKOR – P-graph model is presented in Figure 4. The model generated seven feasible
configurations for the proposed case study (Table 3). Carbonization unit was not selected in any of the generated
solutions. This is mainly due to the high investment cost which causes it to be economically-infeasible. It is worth
noting the best solution at 1st rank is neither the solutions with the highest profit (ranked 5th at 405.271 $/h) nor
the lowest carbon emission (ranked 4th at 0.176 tCO2-eq/h). This was due to the fact that the counter-part
consideration in those solutions is the worst-case scenario, highest carbon emission at 5.709 tCO2-eq/h and
58
lowest profit at 0.000 $/h respectively. In contrast, the optimal solution suggested to partially consume the rice
straw in both combustion unit (~30 % of the total feed) and fermentation unit (~70 % of the total feed). With this
configuration, compromised sustainability performance in terms of both economic and environmental aspects
can, therefore, be obtained (emissions reduced about 40 % with a reasonable profit margin). The results also
reveal that having a mixed power supply is more favourable than having only combustion unit as the sole power
supply despite that the cost of imported power is higher. This is due to the economic-competitiveness nature of
a limited resource system, where the balanced amount of biomass should be used to generate power for local
consumption and to be utilized in a more profitable process for bioethanol production.
Table 3: Solutions generated from P-graph model
Rank Bioethanol
(L/h)
Solid fuel
(kW)
Import Power
(kW)
Generated Power
to recycle (kW)
Generated Power
to be sold (kW)
Profit
($/h)
CO2
(tCO2-eq/h)
Q’
1st 972.179 0.000 773.124 789.556 0.000 161.606 3.504 1.11
2nd 751.421 0.000 0.000 1,207.83 0.000 121.76 2.335 0.99
3rd 941.753 0.000 1,513.77 0.000 847.205 130.529 3.928 0.92
4th 0.000 0.000 0.000 0.000 2,631.58 64.5763 0.176 0.87
5th 1,388.89 0.000 2,232.5 0.000 0.000 405.271 5.709 0.53
6th 326.078 0.000 0.000 524.137 1,489.61 0.000 1.113 0.46
7th 392.665 0.000 631.169 0.000 1,887.58 0.000 1.741 0.38
Figure 4: Representation of VIKOR - P-graph model for rice-based SIBR synthesis
5. Conclusions
A novel VIKOR – P-graph framework that can simultaneously yield feasible solutions and rank them based on
VIKOR calculation, has been proposed in this work. In other words, one does not need to pre-determine a list
of feasible solutions prior to the VIKOR optimization, which therefore can avoid the reliability issues of sequential
59
model. In this work, the effectiveness of the proposed VIKOR – P-graph model is demonstrated using a rice-
based SIBR case study. Overall, the model is proven capable of generating optimal compromised solution (not
over-prioritizing any objective) where both economic and environmental goals are considered. A SIBR that
encompasses fermentation and combustion technologies (which offers a profit of 161.6 $/h and emissions rate
of 3.504 tCO2-eq/h) has been synthesized. Future works include (i) extending the model in a complex system
or other scale and (ii) incorporating grey relational analysis (GRA) with the current VIKOR – P-graph framework;
this is to have better estimation of the closeness between each feasible solution with the ideal solution.
Acknowledgements
Authors would like to acknowledge the financial support from Swinburne University of Technology Sarawak
Campus via Research Supervision Grant [2-5545 RSG].
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