Synthesis of Biomass Corridor in Peninsular Malaysia via Hybrid Mathematical and Graphical Framework

Abstract

The valorisation of biomass by synthesising a multi-biomass corridor can be an optimistic pathway to solving the growing waste management problem. However, the supply chain problem usually involves a massive number of variables, including the connectivity of the sink source and the selection of a technology pathway. In this work, a “Decomposition Approach” was utilised, wherein a P-graph was incorporated with a conventional mathematical model to reduce the number of variables. Although this type of approach is well established with respect to solving biomass supply chain problems, no previous works have comprehensively considered the effect of the maximum allowable travel distance (MATD) on a supply chain model. A case study in Peninsular Malaysia involving oil palm, paddy, and coconut biomass was conducted using the proposed approach. Moreover, a multiple linear regression (MLR) tool for formulating the cost-correlated function based on the best technology pathway obtained from a P-Graph was incorporated. As a result, the net profit of the biomass corridor was estimated to be USD 0.87 billion, with 1.45 × 10⁷ tonnes per year of biomass being sent to 39 processing hubs over a 20-year lifespan. Furthermore, a sensitivity analysis was also conducted to investigate the impact of several cost-related parameters on the net profit.

1. Introduction

It has been projected that there will be a significant increase in global energy consumption of approximately 50% between 2018 and 2050. This growth is primarily driven by non-Organisation for Economic Cooperation and Development (OECD) countries, particularly those in Asia [1,2]. This poses an urgent need to search for alternative energy sources that are renewable and sustainable. In the context of Malaysia, there are various types of renewable energy resources, namely, biomass, hydropower, and solar, that have a high potential to serve as an alternative source of power generation [3]. Recently, a great deal of research and development has focused on biomass, as it is a potentially valuable renewable energy resource [4]. Malaysia is one of the world’s leading agricultural countries; it mainly produces crops such as oil palms, paddy, coconuts, and rubber. After Indonesia, Malaysia is the next largest palm oil producer, accounting for 26% and 34% of the shares of global palm oil production and exportation, respectively [5]. In 2021, it was reported that 18.12 million tonnes of crude palm oil had been produced [6], which simultaneously resulted in the production of a substantial amount of palm oil biomass. In the palm oil industry, six different types of biomasses are produced, namely, empty fruit bunches (EFB), palm kernel shells (PKS), oil palm fronds (OPF), oil palm trunks (OPT), mesocarp fibre (MF), and palm oil mill effluent (POME) [7]. Due to the abundance of palm oil biomass, it is usually used as boiler fuel in palm oil mills to produce steam for electricity generation. Furthermore, the resulting wastes can be converted into pellets and organic compost. The biomass can also be transformed into higher-value products, such as bioethanol from EFB [8], activated carbon from PKS [9], and biogas from POME [10].

Paddy is also considered a major crop in Malaysia. It produces two types of biomasses, namely, paddy straw and rice husk [11]. In 2020, the total plantation area consisting of rice paddies across the whole country was estimated to be 644,854 ha, with an average yield of 4.01 tonnes of paddy per ha [12]. Paddy straw and rice husk are commonly combusted to generate energy, as both present HHV values ranging from 12.10 to 16.60 MJ/kg and 14.61 to 15.44 MJ/kg, respectively [13,14,15]. These lignocellulosic wastes can be utilised in applications in multiple sectors, including (but not limited to) as media for mushroom [16], ethanol, and biogas productions [17] and as adsorbents for the removal of pollutants from water [18]. Furthermore, based on statistics provided by the Department of Agriculture (DOA) [12], the total plantation area of coconut in Malaysia is 84,228 ha, yielding a production value of 0.57 million tonnes in 2021. Two of the major coconut biomasses are coconut shells and husks [19]. Coconut biomass can be transformed into electrical, thermal, or mechanical power via pyrolysis or gasification [20]. However, there is still minimal effort being exerted toward the utilisation of paddy and coconut biomass in Malaysia.

Hence, to foster the sustainable development in the renewable energy sector, it is imperative to establish a multi-biomass corridor that integrates underutilised biomass sources into the existing supply chain. The concept of a “biomass corridor” was first introduced by Ng et al. [21], defining it as an imaginary region that encompasses the facilities connecting biomass supply to product demand. In essence, the corridor encompasses a designated area with diverse, untapped biomass sources and processing hubs for the conversion of biomass into valuable products and the marketing of these products. Extending this concept to biomass supply chain management in Malaysia holds significant potential. However, designing an optimal structure for a biomass corridor poses a complex and challenging problem, involving activities such as biomass allocation, the application of technology, and transportation route design [22].

This challenge can be effectively addressed through the incorporation of process network synthesis (PNS) methodologies. PNS is an approach concerning the optimisation of material and energy flow systems. The goal of the approach is to identify the optimal configuration of processes and the corresponding network structure to achieve desired objectives, such as minimizing costs, maximizing resource utilization, and reducing environmental impacts [23]. To solve such complex combinatorial problems in a supply chain network, there are three major types of techniques that can be used, namely, mathematical modelling, multi-agent technology, and heuristic algorithms [24]. For the mathematical-modelling-based approach, the corresponding problem is structured in relation to linear programming (LP), mixed-integer programming (MIP), or mixed-integer linear programming (MILP). Numerous studies have been conducted to tackle the supply chain problem using traditional mathematical modelling due to its high capacity and affordability [25]. For instance, in one study, an automated targeting model (ATM) was modified for the supply chains of production and energy [26]. The results obtained showed that the utilisation of ATM is more advantageous than other common tools used in process integration due to its linearity. Another hybrid framework that comprises carbon emission pinch analysis and a superstructure-based optimisation technique was suggested by Leong et al. [27], with the corresponding study focusing on oil palm plantations in Selangor, Malaysia. The proposed framework optimised both CO₂ emission minimisation targets and the bioenergy supply chain network simultaneously. In fact, the usage of such mathematical modelling approaches has been applied to solve other biomass supply chain problems (e.g., a coconut residue-based supply chain in Brazil [28] and a rice-straw-derived pellet supply chain in Japan [29]) as well.

Along these lines, the P-graph framework, which consists of both combinatorial and mathematical programming components, can be utilised for process network synthesis problems, e.g., azeotropic distillation [30], heat-integrated water regeneration networks [31], aquaponic farm design [32], ensuring negative emissions for polygeneration plants [33], and solving the biomass supply chain problem [34]. Friedler et al. [35] developed the P-graph to illustrate the structure of a process system using a unique bipartite graph, rendering it unlike other mathematical programming approaches. A P-graph can generate n-best solutions easily, while conventional mathematical modelling merely determines a single best solution. In a P-graph, there are nodes for the representation of materials and operating units as well as arcs for connection between an input and an output. Briefly, there are three important algorithms in a P-graph, namely, a maximal structure generator (MSG), a solution structure generator (SSG), and an accelerated branch-and-bound (ABB) algorithm. An MSG represents the model’s maximal structure, whereas an SSG comprises each solution structure. On the other hand, an ABB algorithm identifies the optimal structure.

Since the P-graph’s development in the 1990s, it has been applied extensively in the network synthesis of multiple sectors such as logistics and supply chains, technology and plant selections, and the planning and management of carbon capture and storage [36]. For example, a robust debottlenecking approach that incorporates a sustainability index into the P-graph framework had been developed for a given biomass supply chain [37]. The framework demonstrated exceptional ability in identifying the bottlenecks of the corresponding research problem effectively. Additionally, the P-graph method was used by Éles et al. [38] in the design of an energy system based on biomass in a rural area. In the results, it was observed that profits increased by about 31% with the developed MILP model, which includes different renewable resources, fermenters, and combined heat and power (CHP) plants. Although these studies have shown that the P-graph framework is capable of solving binary-intensive problems, the requirement for long computational times has limited its scalability, especially when one is dealing with large-scale problems that involve numerous entities. Therefore, to minimise the size of the problem, reduction approaches [39] must be introduced. Notably, How et al. [24] have developed a decomposition method that can systematically reduce the active variables required in a model by manually neglecting the infeasible options.

However, there are a few limitations in the previous works: (i) they have not comprehensively studied the effect of the maximum allowable travel distance (MATD) on the biomass supply chain model, which is expected to be one of the important parameters in designing the optimum biomass allocation, and (ii) they have merely addressed single-state problems, whose scalability to larger-scale problems (e.g., nation-wide problems) is still uncertain. Hence, this work aimed to address these limitations in order to further improve the corresponding model by applying a multi-regression tool to formulate the correlated cost function. In general, we aimed to allocate a set of biomass sources $i\in I \left(Mills\right)$ from Peninsular Malaysia to different sinks $j\in J \left(Processing Hub\right)$. In the processing hubs, biomass (r) is utilised as a renewable energy source in the production of heat, power, and value-added products (p) via different technologies (t). The products (p) such as biochar, py-oil, pellets, etc., are then sold to customers (k). Despite the effectiveness of the hybrid P-graph and mathematical programming approach (developed by How et al. [24]), its capability in solving a problem of a larger scale (i.e., previous research has only focussed on a single state) has yet to be tested.

To tackle these gaps, in this work, we aimed to extend the former P-graph-based hybrid to synthesize a biomass corridor across the entirety of Peninsular Malaysia, which contains a total of 11 states. The objectives of this work were as follows:

• Identify the optimal location in which to establish processing hubs (sinks) in Peninsular Malaysia;
• Evaluate the optimum allocation of various types of biomasses for valorisation;
• Evaluate the impact of the key parameters on the economic feasibility of the supply chain.

2. Methods

When multiple biomass sources across Peninsular Malaysia are considered, the result is a complex biomass supply chain problem. A decomposition algorithm was applied in this work, whereby the allocation and complex location were divided into smaller and simpler constituents [40]. As shown in Figure 1, there were 4 phases of this work. The first two phases concerned the identification of correlated cost functions by using the P-graph approach, while the last two phases concerned the optimisation of the model using a conventional mathematical model. The details of each phase are outlined in the following sections.

2.1. Phase I: Generation of MSG and SSG of Processing Hub

The combination of all viable process structures in a synthesis problem is known as maximal structure [41]. Prior to formulating the correlated cost function in Phase II, the P-graph framework proposed by Friedler et al. [41] was utilised to obtain the maximal structure of the processing hub. The information required by P-graph model comprises raw set (R), material set (M), product set (P), and operation unit (O). The cost-related variables, such as operating and capital costs, are pre-defined [42]. Figure 2 shows the maximal structure of a processing hub, where biomass (r) is turned into value-added products (p) via different technologies (t). Under certain pathways, intermediates (i) might be formed in between; therefore, another set of technologies (t′) is used to process them into the desired products (p). It should be noted that Figure 2 is just an illustrative example wherein there can be more than two technologies in between the raw material and final product.

2.2. Phase II: Formulation of Cost-Correlated Function

Since biomass sources are widely spread across Peninsular Malaysia, the supply chain model is generally complex and consists of a large number of “macro variables”. Moreover, a multi-biomass network must take a massive number of operational units, intermediates, and final products into account, resulting in many “micro variables”. It can be observed from Figure 3 that the term “macro variables” represents the flow variables between the supply chain entities and binary variables for hub selection, while the term “micro variables” refers to the internal flow variables between unit operations and binary variables for technology selection [24].

Additionally, to reduce the number of “micro variables”, the correlation between the amounts of raw material input to the hubs and gross profit is established by applying an ABB Algorithm in the P-graph framework. To obtain the n-best solutions, different amounts of raw materials are inputted into the model. There are different combinations of technology options in the processing hub for different solutions. Analysis of results is performed by establishing a correlation between the amount of raw materials input and maximal gross profit.

There are a few statistical models that can be used generally, namely, simple linear regression (SLR), multiple linear regression (MLR), and polynomial regression (PR). Three of these regression methods are designed to outline the correlation between a dependent variable and an independent variable(s). However, SLR is restricted to only a single independent variable that affects the dependent variable, which is not suitable in this case as this study involves various types of biomass feedstocks [43]. Moreover, the polynomial term in PR will alter the nature of the mathematical model such that is becomes a non-linear problem. This adds unnecessary complexity to the problem, and the optimality of the obtained solution is no longer guaranteed. On the other hand, MLR is an extension of SLR; it is a statistical method that involves several independent variables affecting the dependent variable [43]. The work performed by Thiangchanta and Chaichana [44] showed an example of utilising MLR to construct a mathematical model. In the same work, a heat load model was developed by the authors for an air-conditioned room. Ten independent thermodynamic parameters, including irradiation, temperature, and overall heat transfer, were considered to build the model. The heat load model was verified using a case study, and the error percentage was only 0.15%. Moreover, Rath et al. [45] built a prediction model to forecast the amount of new active cases of COVID-19 using MLR. The prediction model was constructed based on a case study in India, and it achieved a coefficient of determination (R²) value of 1. Moreover, Gowda et al. [46] developed a prediction model for diametrical deviations in machine components. The goal of the approach was to compensate for deviations due to thermal errors; hence, temperature(s) was employed as the independent variable(s). Several case studies were conducted, and the prediction model achieved an accuracy of 96.7%. Ottaviani and Marco [47] created an evaluation model to predict the total project cost required upon the completion of a project. This forecasting model was built by using 805 observed data from 29 completed real-life projects. The prediction model concluded that most of the projects would encounter cost overrun rather than be underbudgeted.

The amount of every biomass feedstock can serve as an independent variable that influences the maximal gross profit. Therefore, in this work, MLR model was utilised as the analytical tool to determine the correlation between the amount of raw materials input with maximal gross profit (i.e., the balanced cash flow between the revenue gained by selling the biomass-derived product and the cost associated with production). The Data Analysis tool in Microsoft Excel was used to carry out the MLR method [48]. The Data Analysis tool can be used after adding the ‘Analysis ToolPak’ application to the software through Excel Add-ins.

Gross profit ($C^{GP}$, USD) is a function of the amount of raw materials, and it was obtained using the MLR tool, as shown in Equation (1):

$$C^{GP}=F_1{C}_1+F_2{C}_2+\dots +F_r{C}_r$$

(1)

where $F_r$ denotes the amount of biomass r (ton), while $C_r$ refers to the respective cost constant for biomass r (USD/ton) obtained via the MLR model. Using this equation, the gross profit can be evaluated according to the number of feedstocks.

2.3. Phase III: Map Investigation

Map analysis was performed by conducting a site study of Peninsular Malaysia. Investigations of the locations of biomass sources and potential processing hubs were carried out in this phase to enable the synthesis of the supply chain model. There were three steps conducted in Phase III: regional division, elimination of infeasible area, and connectivity detachment. These steps were introduced to decrease the size of the model by removing the superfluous or infeasible “macro variables”.

2.3.1. Regional Division

It is necessary to selects sites for processing hubs in order to construct a supply chain model for a given case study. However, the area of a map to be investigated in a case study can be very large and complicated. Therefore, regional division was carried out by gridding the map to illustrate smaller zones. Each zone can be considered as a potential location at which to build a processing hub for the valorisation of biomasses. Figure 4a shows an example illustration of this step, where the grid lines divide the map area (Peninsular Malaysia) into smaller regions. The area enclosed by two pairs of adjacent horizontal and vertical grid lines constitutes a “zone”. An example of a “zone” is shown in Figure 4b. Similar step was carried out in the work performed by Lam et al. [49], where the study region was divided into a few supply and collections areas.

2.3.2. Elimination of Infeasible Zones

The zones that are unsuitable or not feasible for building a processing hub are known as “infeasible” zones. In particular, the “infeasible” zones include mountainous areas, reservoirs, reserve forests, lakes, residential areas, etc. Therefore, the “infeasible” zones can be removed from the model to reduce the burden on the solver, thus reducing the processing time of the solver. Figure 4b illustrates the infeasible zone elimination step, where the red shaded areas are the “infeasible” zones. Moreover, this step also eliminates the under-developed areas where there might not be consistent water or electricity supply.

2.3.3. Connectivity Detachment

Generally, in a supply chain problem, each source point i is connected to each possible processing hub j, while each processing hub j is connected to client k. The combinations of connectivity can produce a complex network with a large number of “macro variables”, leading to longer solving time. Since the efficiency of the model would be significantly reduced due to the large number of variables, the redundant “macro variables” were, therefore, removed [49]. Nevertheless, there is a limitation regarding the travelling distance in a real-world scenario, as the transportation costs of the raw material and product might exceed the profit generated. Hence, the maximum allowable travel distance (MATD, km) was considered for each biomass source. MATD can be calculated as the ratio of economic potential (EP, USD/ton) to the estimated transportation cost constant ($C^T$, USD/ton/km), as presented in Equation (2). Figure 5 provides a depiction of connectivity detachment for various biomasses.

$$MATD=\frac{C_r}{C^T}$$

(2)

2.4. Phase IV: Optimisation of Model

After the steps in Phase III have been applied, the remaining zones are the possible locations for constructing processing hubs. In Phase IV, a mathematical model is built to determine the optimal locations for processing hubs and an allocation pathway for biomass sources. The introduction of correlated cost function into the mathematical model can significantly reduce the number of variables. A description of the model’s formulation is outlined as follows:

Centralised hub j receives biomass r from source i to generate energy or to produce other valuable products. The amount of biomass r available in source i ($F_{i,r}$, ton) must always be larger than the total amount of biomass transported from source i to processing hub j (${{\displaystyle \sum }}_j{F}_{i,j,r}$, ton) at all times, as outlined in Equation (3):

$${\displaystyle \sum }_j{F}_{i,j,r}\le F_{i,r} \forall i\in I, \forall r\in R$$

(3)

A binary number is defined as a numerical value containing only two numbers, where 0 represents absence and 1 indicates presence. Therefore, binary variables are commonly used in mathematical programming to denote the selection of objects (i.e., equipment, processing hubs, etc.). In this case, the total amount of biomass received in processing hub j from source i (${{\displaystyle \sum }}_r{F}_{i,j,r}$, ton/h) cannot exceed the hub’s capacity constraint (M, ton), while binary variable $B_j$ is introduced to denote the existence of a processing hub, as shown in Equation (4). It is worth mentioning that this is another key improvement on the former work [24], as the $C^{Hub}$ is now assigned based on the maximum hub capacity (a capacity constraint was not considered in the former work, which makes it less realistic). Accordingly, the value of binary variable is 1 if a processing hub is required; otherwise, the model will force the binary variable to be 0 to reduce investment costs.

$$\frac{{{\displaystyle \sum }}_i{{\displaystyle \sum }}_r{F}_{i,j,r}}{M}\le B_j \forall j\in J$$

(4)

The gross profit ($C^{GP}$, USD) can be calculated with the cost equation expressed previously, wherein it is a function of biomass amount, as presented in Equation (5):

$$C^{GP}={\displaystyle \sum }_j{\displaystyle \sum }_r{\displaystyle \sum }_i\left(F_{i,j,r}\times C_r\right)$$

(5)

The amount of final product p produced in processing hub j ($F_{j,p}$, ton) can be evaluated by multiplying the amount of biomass received in processing hub j from source i ($F_{i,j,r}$, ton) by the respective conversion factor for biomass r to be processed into final products p ($X_{r,t,p}$, %) for all sources i, as shown in Equation (6). Furthermore, the total number of products p generated from processing hub j that were being sent to all customers k (${{\displaystyle \sum }}_k{F}_{j,k,p}$, ton) cannot be more than the total amount of final product p produced in processing hub j ($F_{j,p}$, ton), as outlined in Equation (7).

$$F_{j,p}={\displaystyle \sum }_r{\displaystyle \sum }_i{\displaystyle \sum }_t\left(F_{i,j,r}\times X_{r,t,p}\right) \forall j\in J,\forall p\in P$$

(6)

$${\displaystyle \sum }_k{F}_{j,k,p}\le F_{j,p} \forall j\in J, \forall p\in P$$

(7)

Moreover, transportation cost ($C^{Tr}$, USD) is introduced into the system for the evaluation of economic performance. $C^{Tr}$ stems from the transportation cost of pre-processing, where biomass r is sent from source i to processing hub j ($C_{i,j,r}^{Tr}$, USD), and post-processing, in which product k is sent from processing hub j to client p ($C_{j,k,p}^{Tr}$, USD), as outlined in Equation (8). In particular, both of the transportation costs can be calculated via the multiplication of the material weights transported by the distance travelled ($d_{i,j}$, km; $d_{j,k}$, km) and the estimated transportation cost constant ($C^T$, USD/ton/km), as shown in Equations (9) and (10), respectively. In reality, the route from one location to another is not a straight line. However, the exact distance is challenging to calculate, and a displacement equation is normally used to calculate the distance. Therefore, a reality factor ($R_f$, km/km) of 1.2 is introduced into the displacement equation to account for the actual conditions of the road (e.g., crooked, bumpy, and/or curvy roads). Hence, the transportation distance between the source and destination, either to the processing hubs or the port ($d_{i,j}$, km; $d_{j,k}$, km), is determined by using displacement and reality factor, as shown in Equations (11) and (12):

$$C^{Tr}={\displaystyle \sum }_j{\displaystyle \sum }_r{\displaystyle \sum }_i{C}_{i,j,r}^{Tr}+{\displaystyle \sum }_k{\displaystyle \sum }_p{\displaystyle \sum }_j{C}_{j,k,p}^{Tr}$$

(8)

$$C_{i,j,r}^{Tr}=F_{i,j,r}\times d_{i,j}\times C^T \forall i\in I, \forall j\in J,\forall r\in R$$

(9)

$$C_{j,k,p}^{Tr}=F_{j,k,p}\times d_{j,k}\times C^T \forall j\in J, \forall k\in K,\forall p\in P$$

(10)

$$d_{i,j}=R_f\times \sqrt{{\left(X_i-X_j\right)}^2+{\left(Y_i-Y_j\right)}^2}$$

(11)

$$d_{j,k}=R_f\times \sqrt{{\left(X_j-X_k\right)}^2+{\left(Y_j-Y_k\right)}^2}$$

(12)

where $d_{i,j}$ and $d_{j,k}$ represent the travelling distance between source i and processing hub j and between processing hub j and client k. $X_i$, $X_j$, $X_k$, $Y_i$, $Y_j$, and $Y_k$ are the x and y coordinates of source i, processing hub j, and client k respectively.

Moreover, the total capital cost of constructing processing hubs ($C^{Inv}$, USD) can be calculated by implementing binary variable $B_j$ and the estimated investment cost for each hub ($C^{Hub}$, USD), as presented in Equation (13). Furthermore, the annualised capital cost ($C_{Annual}^{Inv}$, USD) can be determined via the application of capital recovery factor (CRF, %), as shown in Equation (14). Note that the CRF is computed using Equation (15):

$$C^{Inv}={\displaystyle \sum }_j{B}_j\times C^{Hub}$$

(13)

$$C_{Annual}^{Inv}=C^{Inv}\times CRF$$

(14)

$$CRF=\frac{Dr{\left(1+Dr\right)}^Y}{{\left(1+Dr\right)}^Y-1}$$

(15)

where lifespan is denoted as $Y$ (years), while the specified discounted rate is represented by $Dr$ (%). Note that readers can consider using other methods (e.g., the linear depreciation method) to annualise the capital cost depending on the nature of the problem. Lastly, the model was established to maximise the net profit ($C^{NP}$, USD), as shown in Equation (16).

$$max C^{NP}=C^{GP}-C^{Tr}-C_{Annual}^{Inv}$$

(16)

The model proposed is an MILP problem. Hence, it can be solved using a conventional mathematical model; the global solver in Lingo x19.0 was used in this work.

3. Case Study

To achieve a sustainable future for renewable energy development in Malaysia, it is important to establish a multi-biomass network that integrates unused biomasses. In this case study, coconut husk, shell, rice husk, paddy straw, empty fruit bunches (EFB), and palm kernel shells (PKS) were chosen as biomass sources. The technology pathways used in this case study, together with the raw materials and products employed, are depicted in Figure 6. Furthermore, the construction of the superstructure of the process flow for each biomass was represented using a P-graph (see Figure 7), where the circular nodes refer to materials (biomass and products), while the horizontal nodes represent the operating units included in the case study (note that readers can refer to Friedler et al. [36] for more information on the user manual for the P-graph software). In addition, the unit prices of the materials (note that the logistic costs such as transportation costs are counted separately in Equation (8)) involved are compiled in

Table 1. Material cost for biomass feedstocks, products, and utilities.

Item	Cost (USD)	References
EFB	3/ton	[50]
PKS	35/ton	[50]
Coconut Husk	150/ton	[51]
Coconut Shell	150/ton	[51]
Paddy Straw	16.25/ton	[50]
Rice Husk	25/ton	[50]
Fertiliser	260/ton	[50]
Pellet	140/ton	[50]
DLF	160/ton	[50]
Briquette	120/ton	[50]
Py-oil	100/ton	[24]
Biochar	350/ton	[50]
Syngas	0.12/L	[50]
MPS	22.6/ton	[50]
Electricity	0.14/kWh	[50]

.

Generally, coconut biomass, namely, coconut shells and husks, can be further processed into biochar, py-oil, and syngas via fast pyrolysis. Similarly, rice husk with a high energy content can be used to produce py-oil, syngas, and biomass via fast and slow pyrolysis [52]. On the contrary, dried long fibre (DLF; the dried form of wet long fibre (WLF)), pellets, electricity, and briquettes are the value-added products and resources produced using EFB and PKS from oil palm biomass. Briefly, EFB was processed into DLF via processes such as drying, sieving, and bailing. In addition, high-pressure steam (HPS) was generated from the boiler-based combustion of paddy straw, EFB, and PKS. HPS was then used for electricity and medium-pressure steam (MPS) generation. An intermediate product, short fibre (SF), was generated and used to produce briquettes, for which an additive was incorporated to enhance calorific value. Similarly, PKS was converted into briquettes and pellets [24]. The coconut shells and husks were processed into three final products, namely, biochar, py-oil, and syngas, which can be used for energy generation [53]. Paddy straw was also used to produce fertiliser via conditioning. The respective conversion ratios, capital, and operating costs are listed in

Table 2. Conversion ratios for each technology.

Biomass	Technology	Conversion	References
Palm Oil	Separation and Sieving	0.67 ton WLF/ton EFB 0.24 ton SF/ton EFB	[50]
	Drying and Sieving	0.56 ton DLF/ton WLF
	Pelletising	0.33 ton Pellet/ton Biomass
	Briquetting	0.33 ton Briquette/ton Biomass
	Combustion	2.59 ton HPS/ton EFB 3.96 ton HPS/ton PKS
Paddy	Fast Pyrolysis	0.53 ton Py-oil/ton Rice Husk 0.27 ton Biochar/ton Rice Husk 0.64 L Syngas/ton Rice Husk	[50]
	Slow Pyrolysis	0.36 ton Biochar/ton Rice Husk 0.21 L Syngas/ton Rice Husk
	Conditioning	0.7 ton Fertiliser/ton Paddy Straw
	Combustion (steam generation)	4.79 ton HPS/ton Paddy Straw
Coconut	Fast Pyrolysis	0.346 ton Biochar/ton Coconut Husk 0.173 ton Py-oil/ton Coconut Husk 0.269 L Syngas/ton Coconut Husk	[54]
		0.243 ton Biochar/ton Coconut Shell 0.255 ton Py-oil/ton Coconut Shell 0.263 L Syngas/ton Coconut Shell
All	Electricity Generation	0.91 ton MPS/ton HPS 0.58 kW/ton HPS	[50]

(note that the linear conversion rate is expressed with the functional unit of the mass of the biomass input) and

Table 3. Economic data for each technology (adapted with permission from Yeo et al. [50]).

Technology	Cap Cost (USD)	Operating Cost (USD)
DLF Production	9/ton/h	18.5/ton/h
Pelletising	5/ton/h	22/ton/h
Briquetting	4.5/ton/h	27/ton/h *
Slow Pyrolysis	48/ton	30/ton
Fast Pyrolysis	39.18/ton	47.6/ton
Boiler	2.6/ton HPS/h	-
Turbine	0.05/kW	0.05/kW

* Additional additive (e.g., oil) is injected to enhance calorific value.

(expressed in proportional forms, while maintenance costs are not considered explicitly in this work). It is worth noting that the technology pathways considered in this case study are based on the Malaysian context; this work, by no means, aims to cover all the potential technologies available on the market. Nevertheless, the proposed formulations can be easily adapted to other case studies that involve different sets of biomass and conversion technologies.

In this work, Peninsular Malaysia was chosen as the study area due to its extensive biomass availability and its more developed modes of transportation. Figure 8 illustrates the oil palm and coconut biomass plantations and the paddy fields in the study area, with the respective crops’ availability values tabulated in

Table A1. Locations and availability of biomass sources.

Source, i	Xi	Yi	Area (ha)	Availability (t/y)
i1	135.55	714.83	23,075.00	131,989.00
i2	166.00	624.80	25,417.00	145,385.24
i3	154.40	578.33	31,165.00	178,263.80
i4	218.19	572.52	29,477.00	168,608.44
i5	165.27	505.72	47,813.00	273,490.36
i6	221.09	503.79	49,706.00	284,318.32
i7	175.42	454.41	47,650.00	272,558.00
i8	204.42	466.03	64,413.00	368,442.36
i9	199.34	441.83	6649.00	25,801.44
i10	221.82	415.69	47,650.00	272,558.00
i11	339.97	766.14	5750.00	22,312.88
i12	279.81	626.73	24,895.00	142,399.40
i13	334.17	624.80	24,895.00	142,399.40
i14	265.31	568.65	24,895.00	142,399.40
i15	333.45	579.30	24,895.00	142,399.40
i16	377.67	578.33	24,895.00	142,399.40
i17	403.04	679.01	24,948.00	142,702.56
i18	432.03	678.04	20,794.00	118,941.68
i19	406.66	573.49	35,150.00	201,058.00
i20	453.78	505.72	36,169.00	206,886.68
i21	461.75	462.16	36,169.00	206,886.68
i22	276.91	502.82	14,333.75	81,989.05
i23	333.45	505.72	14,333.75	81,989.05
i24	390.72	504.76	26,381.00	150,899.32
i25	288.51	446.67	14,333.75	81,989.05
i26	334.90	444.73	14,333.75	81,989.05
i27	393.62	441.83	26,381.00	150,899.32
i28	445.81	437.96	90,324.00	516,653.28
i29	293.58	394.39	21,141.00	120,926.52
i30	334.90	384.71	38,456.00	219,968.32
i31	394.34	382.78	32,945.00	188,445.40
i32	453.78	382.78	102,010.00	583,497.20
i33	334.17	324.69	26,793.00	153,255.96
i34	392.89	324.69	32,945.00	188,445.40
i35	451.61	322.75	68,636.00	392,597.92
i36	403.04	268.54	95,287.00	545,041.64
i37	452.33	261.76	68,636.00	392,597.92
i38	452.33	218.20	68,636.00	392,597.92
i39	210.94	384.71	5047.00	19,584.88
i40	220.37	345.02	28,150.00	161,018.00
i41	263.14	379.87	23,255.00	133,018.60
i42	239.21	261.76	27,110.00	155,069.20
i43	293.58	216.26	29,049.00	166,160.28
i44	376.22	260.80	73,493.00	420,379.96
i45	372.59	205.61	29,262.00	167,378.64
i46	351.57	170.76	54,131.00	309,629.32
i47	406.66	194.97	108,043.00	618,005.96
i48	508.15	156.24	62,814.00	359,296.08
i49	466.10	141.72	181,738.00	1,039,541.36
i50	396.51	116.55	46,639.00	266,775.08
i51	437.11	90.41	58,695.00	335,735.40
i52	457.41	90.41	8624.00	33,465.43
i53	476.25	53.62	22,073.00	126,257.56
i54	535.69	92.35	146,250.00	836,550.00
i55	515.40	41.04	47,341.00	270,790.52
i56	93.41	853.40	50,326.50	185,571.92
i57	114.17	791.99	50,326.50	185,571.92
i58	115.11	746.60	50,326.50	185,571.92
i59	149.08	758.57	50,326.50	185,571.92
i60	347.22	738.21	17,591.06	64,864.57
i61	290.61	690.52	5552.06	20,472.44
i62	334.01	695.09	9510.77	35,069.63
i63	264.19	618.16	6692.85	24,678.95
i64	318.92	622.93	6398.98	23,595.34
i65	294.38	584.65	1211.45	4467.05
i66	151.91	619.90	20,949.00	77,246.50
i67	149.08	555.53	20,949.00	77,246.50
i68	231.17	464.96	27,735.00	102,268.93

in the Appendix A [12,55]. Note that in this case study, the biomass yields were assumed to have the following values: 0.22 tons of EFB and 0.055 tons of PKS are produced per ton of oil palm fresh fruit bunches, respectively [56]; 0.7 tons of paddy straw [57] and 0.22 tons of rice husks [58] are generated per ton of rice grain harvested, respectively; and 0.35 tons of coconut husks and 0.12 tons of coconut shells are generated per ton of coconut harvested [59].

In Peninsular Malaysia, there are a total of 51 major oil palm plantation areas, each of them being over 20,000 ha, and they are distributed in Johor, Malacca, Pahang, Negeri Sembilan, Selangor, Perak, Kedah, Kelantan, and Terengganu. Moreover, there are four main plantation areas for coconuts, which can be found in Johor, Selangor, Perak, and Kelantan. The top three most productive paddy fields in 2020, which are located in Kedah, Kelantan, and Perak, were taken into consideration in this study [12]. The five main ports in Peninsular Malaysia are Johor Port, the Port of Tanjung Pelepas, Kuantan Port, Port Klang, and Penang Port. Regarding the development of the biomass corridor, it should be noted that the “demand points” refer to the exporting ports (except for MPS and electricity, which are assumed to be sold in the nearby area instead of being delivered to ports). Furthermore, the potential processing hubs have to be constructed at strategic locations, for which the major concerns are the availability of main roads and the distance between biomass sources and hubs. This is important for the minimisation of biomass transportation costs. Nevertheless, the utility and workforce supply network must be well established in these “potential” locations to build the hubs (see

Table A2. Locations of processing hubs.

Sink, j	Xj	Yj
j1	150.55	588.98
j2	138.55	538.78
j3	154.91	491.02
j4	214.91	484.90
j5	163.64	437.14
j6	210.55	427.35
j7	163.64	384.49
j8	207.27	379.59
j9	266.18	487.35
j10	414.55	486.12
j11	457.09	439.59
j12	459.27	399.18
j13	276.00	433.47
j14	337.09	432.24
j15	391.64	435.92
j16	280.36	383.27
j17	333.82	382.04
j18	401.45	383.27
j19	341.45	335.51
j20	393.82	335.51
j21	447.27	324.49
j22	333.82	286.53
j23	390.55	282.86
j24	450.55	280.41
j25	402.55	242.45
j26	452.73	236.33
j27	456.00	194.69
j28	258.55	322.04
j29	225.82	293.88
j30	258.55	240.00
j31	225.82	219.18
j32	328.36	231.43
j33	288.00	187.35
j34	330.55	184.90
j35	370.91	184.90
j36	346.91	140.82
j37	409.09	172.65
j38	452.73	143.27
j39	519.27	143.27
j40	408.00	94.29
j41	447.27	77.14
j42	555.27	90.61
j43	507.27	41.63
j44	94.74	748.09
j45	140.00	699.57
j46	328.42	670.21
j47	331.58	557.87

in the Appendix A).

In the model, the processing hub’s capacity (M) was set to 5.00 × 10⁵ tons, with an investment cost of approximately USD 1 million. On the other hand, the transportation cost constant ($C^T$) was obtained from an external logistic company, which was set to USD 0.1/ton/km. The remaining parameters involved in the model are shown in

Table 4. Parameters involved in the network.

Parameter	Value
Processing Hub’s Capacity (M)	5.00 × 105 ton
Investment Cost ($C^{Hub}$)	USD 1 million
Transportation Cost Constant ($C^T$) &	USD 0.1/ton/km
Discounted Rate (Dr) #	6%
Lifespan	20 years

^& Value estimated based on fuel consumption and hourly wages for drivers as per findings demonstrated in How et al. [37]. ^# Note that the discount rates of South-East Asian countries were between 2.5 and 7% as of May 2023.

.

4. Results and Discussions

A P-Graph was used to evaluate the optimal route for processing biomass. After this route was determined via the MSG and the SSG of the P-graph, the relevant biomass and products were utilised to construct a cost correlated function. Subsequently, the function was then incorporated into a mathematical model after an site investigation at Peninsular Malaysia.

4.1. Cost Correlated Function

Based on the results obtained using the P-Graph, the best pathways for processing rice husks and paddy straw are through fast pyrolysis and conditioning, respectively. Py-oil, biochar, and syngas were produced from the rapid pyrolysis of rice husks, while fertiliser was derived from paddy straw. On the other hand, pelletising and dehydration are the best pathways for EFB, in which pellets and DLF are produced, while the best pathway for PKS is through power generation to produce MPS and electricity. In this case, for the possible products, fertiliser, pellet, DLF, py-oil, biochar, and syngas were considered to be sent to the port for exportation, while MPS and electricity were considered to be sold to nearby plants or the grid. Subsequently, the formulated cost function for this case study could be obtained, as shown in Equation (17) (note that the coefficient constants in the cost function reflect the EP of the biomass):

$$f\left(r_1,r_2,r_3,r_4\right)=34.14r_1+36.28r_2+35.80r_3+165.75r_4$$

(17)

where $r_1, r_2, r_3$, and $r_4$ represent the quantities of EFB, PKS, rice husks, and paddy straw, respectively.

An optimisation model was formulated in LINGO x19.0 using the cost-correlated function obtained from the P-graph. Thus, the maximum profit gained, the number of hubs to establish, the respective strategic locations, and the optimal biomass allocation design could be obtained. As a result, it was determined that there were a total of 64 biomass sources being utilised. Coconut biomasses were not incorporated mainly because they have a negative EP, which indicates that they do not contribute any profits, even when utilised. This is because coconut biomasses have high raw material and technology costs of coconut biomasses but a relatively low product price when compared to oil palm and paddy biomasses. In particular, the cost of processing coconut biomasses is 38% higher than that of the revenue gained from selling coconut-derived products. Hence, based on the value of the EP of the biomasses, it can be concluded that paddy straw has the highest profit margin among the biomasses studied in this work.

4.2. Optimal Biomass Allocation Design

The optimal biomass allocation design is depicted in Figure 8, amounting to a total net profit of about USD 8.70 × 10⁸. It can be seen that 39 out of the 47 potential processing hubs should be constructed to achieve maximum profits. If fewer hubs were established, the transportation costs would be expected to increase since some of the biomass will be transported to another hub that is further away from the source. If more hubs were constructed, despite the decrease in transportation costs, the savings is insufficient to cover the further increased investment costs of developing these hubs. For instance, if the number of hubs was set to 40 while all the other parameters were kept fixed, a total of USD 55,900 could be saved in terms of transportation costs. However, this amount cannot compensate for the investment cost required for the new hub (i.e., USD 1 million). The detailed amounts of biomass allocated to the respective processing hubs are shown in

Table A3. Amount of biomass allocated to processing hubs (j1 to j12).

i/j	j1	j2	j3	j4	j5	j6	j7	j8	j9	j10	j11	j12
i1	0	0	0	0	0	0	0	0	0	0	0	0
i2	145,385	0	0	0	0	0	0	0	0	0	0	0
i3	170,451	7813	0	0	0	0	0	0	0	0	0	0
i4	0	168,608	0	0	0	0	0	0	0	0	0	0
i5	0	0	273,490	0	0	0	0	0	0	0	0	0
i6	0	0	0	284,318	0	0	0	0	0	0	0	0
i7	0	0	0	0	272,558	0	0	0	0	0	0	0
i8	0	0	226,510	137,868	0	4064	0	0	0	0	0	0
i9	0	0	0	0	0	0	0	0	0	0	0	0
i10	0	0	0	0	0	272,558	0	0	0	0	0	0
i11	0	0	0	0	0	0	0	0	0	0	0	0
i12	106,917	0	0	0	0	0	0	0	0	0	0	0
i13	0	0	0	0	0	0	0	0	0	0	0	0
i14	0	113,920	0	0	0	0	0	0	0	0	0	0
i15	0	0	0	0	0	0	0	0	0	0	0	0
i16	0	0	0	0	0	0	0	0	0	0	0	0
i17	0	0	0	0	0	0	0	0	0	0	0	0
i18	0	0	0	0	0	0	0	0	0	0	0	0
i19	0	0	0	0	0	0	0	0	0	142,214	0	0
i20	0	0	0	0	0	0	0	0	0	206,887	0	0
i21	0	0	0	0	0	0	0	0	0	0	206,887	0
i22	0	0	0	0	0	0	0	0	81,989	0	0	0
i23	0	0	0	0	0	0	0	0	0	0	0	0
i24	0	0	0	0	0	0	0	0	0	150,899	0	0
i25	0	0	0	0	0	0	0	0	0	0	0	0
i26	0	0	0	0	0	0	0	0	0	0	0	0
i27	0	0	0	0	0	0	0	0	0	0	0	0
i28	0	0	0	0	0	0	0	0	0	0	293,113	120,209
i29	0	0	0	0	0	0	0	0	0	0	0	0
i30	0	0	0	0	0	0	0	0	0	0	0	0
i31	0	0	0	0	0	0	0	0	0	0	0	0
i32	0	0	0	0	0	0	0	0	0	0	0	379,791
i33	0	0	0	0	0	0	0	0	0	0	0	0
i34	0	0	0	0	0	0	0	0	0	0	0	0
i35	0	0	0	0	0	0	0	0	0	0	0	0
i36	0	0	0	0	0	0	0	0	0	0	0	0
i37	0	0	0	0	0	0	0	0	0	0	0	0
i38	0	0	0	0	0	0	0	0	0	0	0	0
i39	0	0	0	0	0	0	0	0	0	0	0	0
i40	0	0	0	0	0	0	0	0	0	0	0	0
i41	0	0	0	0	0	0	0	0	0	0	0	0
i42	0	0	0	0	0	0	0	0	0	0	0	0
i43	0	0	0	0	0	0	0	0	0	0	0	0
i44	0	0	0	0	0	0	0	0	0	0	0	0
i45	0	0	0	0	0	0	0	0	0	0	0	0
i46	0	0	0	0	0	0	0	0	0	0	0	0
i47	0	0	0	0	0	0	0	0	0	0	0	0
i48	0	0	0	0	0	0	0	0	0	0	0	0
i49	0	0	0	0	0	0	0	0	0	0	0	0
i50	0	0	0	0	0	0	0	0	0	0	0	0
i51	0	0	0	0	0	0	0	0	0	0	0	0
i52	0	0	0	0	0	0	0	0	0	0	0	0
i53	0	0	0	0	0	0	0	0	0	0	0	0
i54	0	0	0	0	0	0	0	0	0	0	0	0
i55	0	0	0	0	0	0	0	0	0	0	0	0
i56	0	0	0	0	0	0	0	0	0	0	0	0
i57	0	0	0	0	0	0	0	0	0	0	0	0
i58	0	44,376	0	0	0	0	0	0	0	0	0	0
i59	0	0	0	0	0	0	0	0	0	0	0	0
i60	0	15,511	0	0	0	0	0	0	0	0	0	0
i61	0	4896	0	0	0	0	0	0	0	0	0	0
i62	0	8386	0	0	0	0	0	0	0	0	0	0
i63	0	24,679	0	0	0	0	0	0	0	0	0	0
i64	0	5642	0	0	0	0	0	0	0	0	0	0
i65	0	4467	0	0	0	0	0	0	0	0	0	0
i66	77,247	0	0	0	0	0	0	0	0	0	0	0
i67	0	77,247	0	0	0	0	0	0	0	0	0	0
i68	0	24,456	0	77,813	0	0	0	0	0	0	0	0
Sum	500,000	500,000	500,000	500,000	272,558	276,622	0	0	81,989	500,000	500,000	500,000

,

Table A4. Amount of biomass allocated to processing hubs (j13 to j23).

i/j	j13	j14	j15	j16	j17	j18	j19	j20	j21	j22	j23
i1	0	0	0	0	0	0	0	0	0	0	0
i2	0	0	0	0	0	0	0	0	0	0	0
i3	0	0	0	0	0	0	0	0	0	0	0
i4	0	0	0	0	0	0	0	0	0	0	0
i5	0	0	0	0	0	0	0	0	0	0	0
i6	0	0	0	0	0	0	0	0	0	0	0
i7	0	0	0	0	0	0	0	0	0	0	0
i8	0	0	0	0	0	0	0	0	0	0	0
i9	0	0	0	0	0	0	0	0	0	0	0
i10	0	0	0	0	0	0	0	0	0	0	0
i11	0	0	0	0	0	0	0	0	0	0	0
i12	0	0	0	0	0	0	0	0	0	0	0
i13	0	0	0	0	0	0	0	0	0	0	0
i14	0	0	0	0	0	0	0	0	0	0	0
i15	0	0	0	0	0	0	0	0	0	0	0
i16	0	0	0	0	0	0	0	0	0	0	0
i17	0	0	0	0	0	0	0	0	0	0	0
i18	0	0	0	0	0	0	0	0	0	0	0
i19	0	0	0	0	0	0	0	0	0	0	0
i20	0	0	0	0	0	0	0	0	0	0	0
i21	0	0	0	0	0	0	0	0	0	0	0
i22	0	0	0	0	0	0	0	0	0	0	0
i23	0	0	65,591	0	0	0	0	0	0	0	0
i24	0	0	0	0	0	0	0	0	0	0	0
i25	81,989	0	0	0	0	0	0	0	0	0	0
i26	0	81,989	0	0	0	0	0	0	0	0	0
i27	0	0	150,899	0	0	0	0	0	0	0	0
i28	0	0	103,331	0	0	0	0	0	0	0	0
i29	0	0	0	120,927	0	0	0	0	0	0	0
i30	0	0	0	0	219,968	0	0	0	0	0	0
i31	0	0	0	0	0	188,445	0	0	0	0	0
i32	0	0	0	0	0	96,304	0	0	107,402	0	0
i33	0	0	0	0	0	0	153,256	0	0	0	0
i34	0	0	0	0	0	0	0	188,445	0	0	0
i35	0	0	0	0	0	0	0	0	392,598	0	0
i36	0	0	0	0	0	0	0	0	0	0	328,631
i37	0	0	0	0	0	0	0	0	0	0	0
i38	0	0	0	0	0	0	0	0	0	0	0
i39	0	0	0	0	0	0	0	0	0	0	0
i40	0	0	0	0	0	0	0	0	0	0	0
i41	0	0	0	133,019	0	0	0	0	0	0	0
i42	0	0	0	0	0	0	0	0	0	0	0
i43	0	0	0	0	0	0	0	0	0	0	0
i44	0	0	0	0	0	0	0	0	0	0	171,369
i45	0	0	0	0	0	0	0	0	0	0	0
i46	0	0	0	0	0	0	0	0	0	0	0
i47	0	0	0	0	0	0	0	0	0	0	0
i48	0	0	0	0	0	0	0	0	0	0	0
i49	0	0	0	0	0	0	0	0	0	0	0
i50	0	0	0	0	0	0	0	0	0	0	0
i51	0	0	0	0	0	0	0	0	0	0	0
i52	0	0	0	0	0	0	0	0	0	0	0
i53	0	0	0	0	0	0	0	0	0	0	0
i54	0	0	0	0	0	0	0	0	0	0	0
i55	0	0	0	0	0	0	0	0	0	0	0
i56	0	0	0	0	0	0	0	0	0	0	0
i57	0	0	0	0	0	0	0	0	0	0	0
i58	0	0	0	0	0	0	0	0	0	0	0
i59	0	0	0	0	0	0	0	0	0	0	0
i60	0	0	0	0	0	0	0	0	0	0	0
i61	0	0	0	0	0	0	0	0	0	0	0
i62	0	0	0	0	0	0	0	0	0	0	0
i63	0	0	0	0	0	0	0	0	0	0	0
i64	0	0	0	0	0	0	0	0	0	0	0
i65	0	0	0	0	0	0	0	0	0	0	0
i66	0	0	0	0	0	0	0	0	0	0	0
i67	0	0	0	0	0	0	0	0	0	0	0
i68	0	0	0	0	0	0	0	0	0	0	0
Sum	81,989	81,989	319,821	253,945	219,968	284,750	153,256	188,445	500,000	0	500,000

,

Table A5. Amount of biomass allocated to processing hubs (j24 to j35).

i/j	j24	j25	j26	j27	j28	j29	j30	j31	j32	j33	j34	j35
i1	0	0	0	0	0	0	0	0	0	0	0	0
i2	0	0	0	0	0	0	0	0	0	0	0	0
i3	0	0	0	0	0	0	0	0	0	0	0	0
i4	0	0	0	0	0	0	0	0	0	0	0	0
i5	0	0	0	0	0	0	0	0	0	0	0	0
i6	0	0	0	0	0	0	0	0	0	0	0	0
i7	0	0	0	0	0	0	0	0	0	0	0	0
i8	0	0	0	0	0	0	0	0	0	0	0	0
i9	0	0	0	0	0	0	0	0	0	0	0	0
i10	0	0	0	0	0	0	0	0	0	0	0	0
i11	0	0	0	0	0	0	0	0	0	0	0	0
i12	0	0	0	0	0	0	0	0	0	0	0	0
i13	0	0	0	0	0	0	0	0	0	0	0	0
i14	0	0	0	0	0	0	0	0	0	0	0	0
i15	0	0	0	0	0	0	0	0	0	0	0	0
i16	0	0	0	0	0	0	0	0	0	0	0	0
i17	0	0	0	0	0	0	0	0	0	0	0	0
i18	0	0	0	0	0	0	0	0	0	0	0	0
i19	0	0	0	0	0	0	0	0	0	0	0	0
i20	0	0	0	0	0	0	0	0	0	0	0	0
i21	0	0	0	0	0	0	0	0	0	0	0	0
i22	0	0	0	0	0	0	0	0	0	0	0	0
i23	0	0	0	0	0	0	0	0	0	0	0	0
i24	0	0	0	0	0	0	0	0	0	0	0	0
i25	0	0	0	0	0	0	0	0	0	0	0	0
i26	0	0	0	0	0	0	0	0	0	0	0	0
i27	0	0	0	0	0	0	0	0	0	0	0	0
i28	0	0	0	0	0	0	0	0	0	0	0	0
i29	0	0	0	0	0	0	0	0	0	0	0	0
i30	0	0	0	0	0	0	0	0	0	0	0	0
i31	0	0	0	0	0	0	0	0	0	0	0	0
i32	0	0	0	0	0	0	0	0	0	0	0	0
i33	0	0	0	0	0	0	0	0	0	0	0	0
i34	0	0	0	0	0	0	0	0	0	0	0	0
i35	0	0	0	0	0	0	0	0	0	0	0	0
i36	107,402	109,008	0	0	0	0	0	0	0	0	0	0
i37	392,598	0	0	0	0	0	0	0	0	0	0	0
i38	0	0	392,598	0	0	0	0	0	0	0	0	0
i39	0	0	0	0	0	0	0	0	0	0	0	0
i40	0	0	0	0	0	161,018	0	0	0	0	0	0
i41	0	0	0	0	0	0	0	0	0	0	0	0
i42	0	0	0	0	0	0	155,069	0	0	0	0	0
i43	0	0	0	0	0	0	166,160	0	0	0	0	0
i44	0	249,011	0	0	0	0	0	0	0	0	0	0
i45	0	0	0	0	0	0	0	0	0	0	0	167,379
i46	0	0	0	0	0	0	0	0	0	0	247,703	61,926
i47	0	141,980	0	0	0	0	0	0	0	0	0	0
i48	0	0	0	0	0	0	0	0	0	0	0	0
i49	0	0	0	401,024	0	0	0	0	0	0	0	0
i50	0	0	0	0	0	0	0	0	0	0	0	0
i51	0	0	0	0	0	0	0	0	0	0	0	0
i52	0	0	0	0	0	0	0	0	0	0	0	0
i53	0	0	0	0	0	0	0	0	0	0	0	0
i54	0	0	0	0	0	0	0	0	0	0	0	0
i55	0	0	0	0	0	0	0	0	0	0	0	0
i56	0	0	0	0	0	0	0	0	0	0	0	0
i57	0	0	0	0	0	0	0	0	0	0	0	0
i58	0	0	0	0	0	0	0	0	0	0	0	0
i59	0	0	0	0	0	0	0	0	0	0	0	0
i60	0	0	0	0	0	0	0	0	0	0	0	0
i61	0	0	0	0	0	0	0	0	0	0	0	0
i62	0	0	0	0	0	0	0	0	0	0	0	0
i63	0	0	0	0	0	0	0	0	0	0	0	0
i64	0	0	0	0	0	0	0	0	0	0	0	0
i65	0	0	0	0	0	0	0	0	0	0	0	0
i66	0	0	0	0	0	0	0	0	0	0	0	0
i67	0	0	0	0	0	0	0	0	0	0	0	0
i68	0	0	0	0	0	0	0	0	0	0	0	0
Sum	500,000	500,000	392,598	401,024	0	161,018	321,229	0	0	0	247,703	229,305

and

Table A6. Amount of biomass allocated to processing hubs (j36 to j47).

i/j	j36	j37	j38	j39	j40	j41	j42	j43	j44	j45	j46	j47
i1	0	0	0	0	0	0	0	0	0	131,989	0	0
i2	0	0	0	0	0	0	0	0	0	0	0	0
i3	0	0	0	0	0	0	0	0	0	0	0	0
i4	0	0	0	0	0	0	0	0	0	0	0	0
i5	0	0	0	0	0	0	0	0	0	0	0	0
i6	0	0	0	0	0	0	0	0	0	0	0	0
i7	0	0	0	0	0	0	0	0	0	0	0	0
i8	0	0	0	0	0	0	0	0	0	0	0	0
i9	0	0	0	0	0	0	0	0	0	0	0	0
i10	0	0	0	0	0	0	0	0	0	0	0	0
i11	0	0	0	0	0	0	0	0	0	0	0	0
i12	0	0	0	0	0	0	0	0	0	0	28,480	7002
i13	0	0	0	0	0	0	0	0	0	0	118,262	24,137
i14	0	0	0	0	0	0	0	0	0	0	0	28,480
i15	0	0	0	0	0	0	0	0	0	0	0	142,399
i16	0	0	0	0	0	0	0	0	0	0	0	142,399
i17	0	0	0	0	0	0	0	0	0	0	142,703	0
i18	0	0	0	0	0	0	0	0	0	0	118,942	0
i19	0	0	0	0	0	0	0	0	0	0	0	58,844
i20	0	0	0	0	0	0	0	0	0	0	0	0
i21	0	0	0	0	0	0	0	0	0	0	0	0
i22	0	0	0	0	0	0	0	0	0	0	0	0
i23	0	0	0	0	0	0	0	0	0	0	0	16,398
i24	0	0	0	0	0	0	0	0	0	0	0	0
i25	0	0	0	0	0	0	0	0	0	0	0	0
i26	0	0	0	0	0	0	0	0	0	0	0	0
i27	0	0	0	0	0	0	0	0	0	0	0	0
i28	0	0	0	0	0	0	0	0	0	0	0	0
i29	0	0	0	0	0	0	0	0	0	0	0	0
i30	0	0	0	0	0	0	0	0	0	0	0	0
i31	0	0	0	0	0	0	0	0	0	0	0	0
i32	0	0	0	0	0	0	0	0	0	0	0	0
i33	0	0	0	0	0	0	0	0	0	0	0	0
i34	0	0	0	0	0	0	0	0	0	0	0	0
i35	0	0	0	0	0	0	0	0	0	0	0	0
i36	0	0	0	0	0	0	0	0	0	0	0	0
i37	0	0	0	0	0	0	0	0	0	0	0	0
i38	0	0	0	0	0	0	0	0	0	0	0	0
i39	0	0	0	0	0	0	0	0	0	0	0	0
i40	0	0	0	0	0	0	0	0	0	0	0	0
i41	0	0	0	0	0	0	0	0	0	0	0	0
i42	0	0	0	0	0	0	0	0	0	0	0	0
i43	0	0	0	0	0	0	0	0	0	0	0	0
i44	0	0	0	0	0	0	0	0	0	0	0	0
i45	0	0	0	0	0	0	0	0	0	0	0	0
i46	0	0	0	0	0	0	0	0	0	0	0	0
i47	0	476,025	0	0	0	0	0	0	0	0	0	0
i48	0	0	0	359,296	0	0	0	0	0	0	0	0
i49	0	0	500,000	0	0	138,518	0	0	0	0	0	0
i50	0	0	0	0	266,775	0	0	0	0	0	0	0
i51	0	0	0	0	67,147	268,588	0	0	0	0	0	0
i52	0	0	0	0	0	0	0	0	0	0	0	0
i53	0	0	0	0	0	92,894	0	33,363	0	0	0	0
i54	0	0	0	140,704	0	0	500,000	195,846	0	0	0	0
i55	0	0	0	0	0	0	0	270,791	0	0	0	0
i56	0	0	0	0	0	0	0	0	141,196	44,376	0	0
i57	0	0	0	0	0	0	0	0	141,196	44,376	0	0
i58	0	0	0	0	0	0	0	0	141,196	0	0	0
i59	0	0	0	0	0	0	0	0	0	185,572	0	0
i60	0	0	0	0	0	0	0	0	0	0	49,353	0
i61	0	0	0	0	0	0	0	0	0	0	15,577	0
i62	0	0	0	0	0	0	0	0	0	0	26,683	0
i63	0	0	0	0	0	0	0	0	0	0	0	0
i64	0	0	0	0	0	0	0	0	0	0	0	17,953
i65	0	0	0	0	0	0	0	0	0	0	0	0
i66	0	0	0	0	0	0	0	0	0	0	0	0
i67	0	0	0	0	0	0	0	0	0	0	0	0
i68	0	0	0	0	0	0	0	0	0	0	0	0
Sum	0	476,025	500,000	500,000	333,922	500,000	500,000	500,000	423,588	406,313	500,000	437,613

in Appendix A.

As a result, there were a total of 5.86 × 10⁶ tons of products (excluding MPS and electricity) being produced from all the processing hubs (see Figure 9), which were exported to the different ports (i.e., the customers in this case). The respective numbers of products transported to the port are presented in Figure 10.

By referring to Figure 9, it can be seen that DLF is used to produce the most products, while biochar is used to produce the fewest. This is collectively due to (i) a relatively decent unit price of DLF and (ii) the cheaper cost of EFB compared to the other biomasses. In addition, a higher wt% of EFB can be obtained from oil palm fresh fruit bunches compared to PKS. On the other hand, most of the pellets and DLF are exported to Kuantan Port due to the massive amount of oil palm plantations in Pahang state, as shown in Figure 10. The remaining products are mainly exported to Penang Port, as paddy plantations in Malaysia are mainly concentrated in the northern part of Peninsular Malaysia.

4.3. Sensitivity Analysis

In this section, a sensitivity analysis was performed to illustrate how one can determine the impact of several parameters on net profit $(C^{NP})$. The selected parameters, including the maximum capacity of the processing hub $(M)$, the transportation cost constant $(C^T)$, the investment cost of the processing hub $(C^{Hub})$, and the unit price of the biomass, were varied. To ensure that the impact of each parameter was clearly captured, the one-parameter-at-a-time (OPAT) method was adopted (i.e., when one of the parameters varied, the remaining parameters were maintained at the same value, as depicted in the base case scenario).

Table 5. Sensitivity analysis on the capacity of processing hub.

Maximum Processing Capacity, $\mathit{M}$ (ton)	Net Profit, ${\mathit{C}}^{\mathit{N}\mathit{P}}$ (USD)	No. of Biomass Sources Utilised, $\mathit{i}$	No. of Processing Hubs Utilised, $\mathit{j}$	Amount of Biomass Utilised, ${{\displaystyle \sum }}_{\mathit{j}}{\mathit{F}}_{\mathit{i},\mathit{j},\mathit{r}}$ (ton)
3.00 × 105	8.10 × 108	64	47	1.41 × 107
5.00 × 105	8.70 × 108	64	39	1.45 × 107
7.50 × 105	8.76 × 108	64	39	1.45 × 107
1.00 × 106	8.77 × 108	64	38	1.45 × 107
5.00 × 106	8.77 × 108	64	38	1.45 × 107
1.00 × 107	8.77 × 108	64	38	1.45 × 107

shows an example of the variables in the sensitivity analysis of the maximum processing capacity of each hub. Figure 11, Figure 12, Figure 13 and Figure 14 illustrate the sensitivity analyses of the selected parameters, respectively.

By referring to Table 5 and Figure 11, it can be observed that the net profit increases when the maximum capacity of the processing hub increases. This is mainly because a greater extent of biomass allocation can be more cost-effective when the capacity constraint of a plant is increased (i.e., biomass can be sent to the nearby processing hub instead of being sent to other hubs due to capacity constraints). As a result, fewer processing hubs are required in the supply chain. This aligns with the concluding remarks provided in the study by Zhu et al. [60], revealing the positive impact of maximum capacity on the feasibility of a supply chain. Nevertheless, it should be noted that further increasing the capacity constraint from 1,000,000 tonnes/hub will not improve the overall profit any further (i.e., maintain a maximum value of USD 0.87 billion) given that the optimal number of hubs remains 38 after this point.

Based on

Table 6. Sensitivity analysis variables of transportation cost constant.

Transportation Cost Constant, ${\mathit{C}}^{\mathit{T}}$ (USD/ton/km)	Net Profit, ${\mathit{C}}^{\mathit{N}\mathit{P}}$ (USD)	No. of Biomass Sources Utilised, $\mathit{i}$	No. of Processing Hubs Utilised, $\mathit{j}$	Amount of Biomass Utilised, ${{\displaystyle \sum }}_{\mathit{j}}{\mathit{F}}_{\mathit{i},\mathit{j},\mathit{r}}$ (ton)
0.08	8.97 × 108	64	39	1.45 × 107
0.1	8.70 × 108	64	39	1.45 × 107
0.2	7.32 × 108	64	41	1.45 × 107
0.3	5.94 × 108	64	41	1.45 × 107
0.5	3.19 × 108	63	41	1.44 × 107
0.7	5.02 × 107	63	41	1.41 × 107

and Figure 12, the net profit decreases when the transportation cost constant increases, as a higher transportation cost constant indicates a higher transportation cost for both pre-processing and post-processing. The transportation cost constant is significantly correlated with the price of diesel. Hence, a higher transportation cost constant is imposed when the diesel price increases, and vice versa. Based on this result, it can be clearly seen that the optimal number of processing hubs has increased from 39 to 41 along with the transportation cost. More processing hubs were included to enable shorter total travel distances in order to combat the higher transportation cost constant [37]. Nevertheless, the number of hubs does not continuously elevate despite the fact that the cost constant increased 6.85-fold. This indicates that the cost savings in terms of transportation costs cannot compensate for the cost required for an additional processing hub [61]. Additionally, when the transportation cost constantly increases, the amount of biomass sent from the plantation areas to processing hubs decreases. This is because the $C^T$ value will affect the value of $MATD,$ as shown in Equation (2); thus, some biomass sources were not selected because they were not feasible. Figure 13 displays the $MATD$ value for each type of biomass along with the $C^T$ value.

By referring to Figure 13, it can be seen that as the $C^T$ value increases, the $MATD$ value for each biomass decreases. The changes in the $C^T$ value have the most significant impact on RH, as RH has the lowest EP among the four selected biomasses. When the $MATD$ value deviates, the optimal allocation of one biomass source to a hub will be affected. As a result, it is to be noted that the number of processing hubs being utilised will increase with the $C^T$ value, as shown in

Table 7. Sensitivity analysis variables of hub investment costs.

Hub’s Investment Cost, ${\mathit{C}}^{\mathit{H}\mathit{u}\mathit{b}}$ (USD)	Net Profit, ${\mathit{C}}^{\mathit{N}\mathit{P}}$ (USD)	No. of Biomass Sources Utilised, $\mathit{i}$	No. of Processing Hubs Utilised, $\mathit{j}$	Amount of Biomass Utilised, ${{\displaystyle \sum }}_{\mathit{j}}{\mathit{F}}_{\mathit{i},\mathit{j},\mathit{r}}$ (ton)
1.00 × 106	8.70 × 108	64	39	1.45 × 107
5.00 × 106	8.57 × 108	64	35	1.45 × 107
1.00 × 107	8.42 × 108	64	31	1.45 × 107
5.00 × 107	7.39 × 108	64	29	1.45 × 107

. This is simply due to two reasons: (i) the larger $C^T$ leads to a smaller $MATD$, which reduces connection flexibility, and (ii) the $C_{Annual}^{Inv}$ becomes less dominant.

According to Table 7 and Figure 14, the net profit decreases when the investment cost of the hubs increases. However, it should be noted that the value of a hub’s investment cost used in this study is based on a rough assumption. Thus, a more accurate investment cost can be incorporated if a detailed economic analysis is conducted. In addition, when a hub’s investment cost increases, the number of hubs utilised decreases markedly. It was noticed that the amount of biomass processed remains constant despite the changes in the hub investment costs and the number of hubs being utilised. This is because in the base case scenario, the 39 hubs being utilised were not operating at their maximum capacities. Therefore, when the number of hubs decreases and the other parameters remain constant, the same amount of biomass can be delivered to another hub for processing.

In the conducted sensitivity analysis, the transportation cost constant $(C^T)$ was found to be the most significant parameter with respect to affecting the net profit. To further verify the results from the sensitivity analysis, the constraints used for the investigated parameters were monitored using dual price values (obtained from LINGO) to ensure that there were no constraints that were too strict. Dual price denotes the amount that an objective would improve by if the constant term of the constraint increased by one unit.

Table 8. Dual price value.

Parameter	Unit	Dual Price Value
Processing Hub’s Capacity ($M)$	ton	49.190
Transportation Cost Constant $(C^T)$	USD/ton/km	−0.138 × 1010
Processing hub’s investment cost $(C^{Hub})$	USD	−3.393

summarises the dual price value for the constant term of the capacity of a processing hub $(M)$, the transportation cost constant $(C^T),$ and a processing hub’s investment cost $(C^{Hub})$ in the base case scenario.

Referring to Table 8, the transportation cost constant $(C^T)$ shows a dual price value of −0.318 × 10¹⁰, which can be interpreted as follows: an increase of one unit in the $C^T$ value will cause a decrease of USD 0.138 × 10¹⁰ in the net profit. The dual price values for the remaining two parameters can be interpreted in a similar manner. Therefore, the transportation cost constant is the most sensitive parameter, followed by a processing hub’s capacity and then the investment cost. However, the impact of the transportation cost constant could be minimised if the processing hub in question is located near the biomass sources. Thus, the processing hubs must be established at strategic locations near both biomass sources and a ports. Proper planning and careful consideration must be ensured before building a processing hub, as the price of diesel currently remains volatile. Moreover, other transportation modes such as railways and waterways can be considered to reflect real-life conditions. Nevertheless, it was found that a hub’s capacity $(M)$ and investment cost $(C^{Hub})$ are interrelated. Therefore, sensitivity analyses can be performed to identify their relationship, where investment cost is expressed as a function of capacity in order to yield a more accurate result. To improve accuracy, a more detailed economic analysis to evaluate the investment costs can also be performed.

Lastly, as the downstream usage of biomass gains more popularity, the market price will increase due to the higher demand compared to that in the past. This would affect the economic attractiveness of the biomass conversion pathways. In other words, it is important for decision makers to understand the threshold limit of the price of biomass (i.e., the maximum biomass cost at which the pathway can still break even).

Table 9. Threshold unit price to break even.

Biomass	Targeted Technology	Threshold Unit Price (USD/ton)
EFB	DLF and pellet production	37.14
PKS	Power generation	71.28
Paddy Straw	Fertiliser production	182.00
Rice Husk	Fast pyrolysis	60.80
Coconut Husk	Fast pyrolysis	51.65
Coconut Shell	Fast pyrolysis	23.80

shows the respective threshold unit price of each biomass, including coconut husks and coconut shells, which were not recommended by the model. Based on the analysis, it can be gleaned that the coconut-biomass-based pyrolysis considered in this work can only be economically feasible if the unit prices of coconut husks and coconut shells were reduced by 65.5% and 84.13%, respectively. On the other hand, the other selected technologies would not be feasible if the unit prices of biomass were not controlled below the threshold limits (e.g., the rapid pyrolysis of rice husk will not be attractive if the rice husk price increases 2.4 fold compared to the unit cost stated in this case study). Such impacts align with the findings reported by Lo et al. [62], who commented that the acquisition price is one of the key factors that affect the overall feasibility of the biomass industry.

5. Conclusions

A hybrid method that incorporates both a P-graph and a mathematical modelling approach has been successfully applied to synthesise a multiple-biomass corridor for a large-scale problem in Peninsular Malaysia. The technologies available for processing empty fruit bunches, palm kernel shells, rice husks, paddy straw, coconut shells, and coconut husks were presented in this work, along with their associated conversion. Furthermore, the correlated cost function for oil palm and paddy biomass was developed using a P-graph. Subsequently, area fragmentation was carried out to determine the distance from each biomass source to each potential processing hub and the distance from the processing hubs to the ports. By adopting the proposed method, decision makers can obtain important insights into the feasibility of each biomass technology alongside strategies regarding the number and locations of processing hubs. In the base case scenario, 99.31% of the oil palm and paddy biomass available in Peninsular Malaysia was converted into valuable products, with an annual net profit of USD 0.87 billion. Additionally, a comprehensive sensitivity analysis was performed to investigate the impact of four parameters, namely, the capacity of a processing hub $(M)$, the transportation cost constant $(C^T)$, a processing hub’s investment cost $(C^T)$, and the unit price of biomass, on the economic performance of the supply chain. This allows policymakers and process engineers to understand the bottlenecks of biomass conversion technologies and, therefore, attempt to tackle the problems effectively.

In terms of future extensions, to improve the robustness of the framework, sensitivity analysis on the degree of area fragmentation can be performed. Theoretically, more fragmentised zones will result in a solution that is closer to the actual global optimum but with the trade-off of greater computational time. Additionally, the model can be extended into stochastic programming to incorporate supply chain uncertainties, including (but not limited to) biomass availability, material unit costs, fuel prices, etc., so that one can understand the overall risk profile of the proposed supply chain [62]. With the aid of probabilistic data regarding each type of uncertainty, detailed plant design and a more comprehensive economic evaluation can be performed. To achieve this, collaborative research between process systems engineering and economic disciplines is highly recommended. With further regard to enhancing the model’s reliability, detailed transportation and logistics design can also be carried out to incorporate the additional costs required (e.g., considerations made for syngas transportation were not accounted for in the current work), the efficiency of the storage units, and time-sliced optimisation for effective scheduling into the current model. Moreover, it is worth considering the synergetic integration, or interaction between different entities or stakeholders competing for the same biomass resources using game theory approaches [63].