Agriculture has seen continuous expansion over centuries. It primarily involves activities that provide food for the world’s population. Rimando (2004) defines agriculture has systematic manner of crop production and livestock rearing for food, other human needs (i.e. wool, leather) or economic gain. In agriculture, crop production plays a significant role in producing the essential food supplies like cereals, oil, sugar, vegetables, and pulses required for mankind. The demand for these essentials is expected to increase up to 56% by 2050 due to population growth and increase in income level (van Dijk et al. 2021). This requires manifold increase in the supply to meet the demand, ensuring food security. Improvement in crop productivity is sought in order to increase the production. However, despite these efforts, expansion for crop production is inevitable considering the rate of increase in demand (FAO 2016). Therefore, there is growing concern that the increase in food production will intensify the competition for land, water and energy (Islam and Karim 2019).

As discussed above, land is one of the major resources necessary for crop production. With the increase in food demand, expansions are inevitable, and hence, more land is expected to be brought under crop production. However, this may lead to environmental impacts and act against the principles of sustainability. Moreover, land resource has witnessed increased competition from population growth, urbanisation and industrialisation (Laskar 2003). This calls for a systematic allocation of the available land resources and also explore opportunities for crop substitution with a low land footprint crop. Thus, it is imperative for policy-makers to plan for sufficient food stockpiles based on consumption requirements while ensuring lands are used in an accountable manner for a range of crops. This can be achieved using land-use planning (Andiappan et al. 2022).

Recently, there is a growing number of publications in land-use planning for crop production. Most of these previous works focus on developing mathematical models to optimise land use for a range of crops. However, these models often require expertise (i.e. mathematical optimisation and agriculture) that are not readily accessible to policymakers. In this respect, graphical methods can be used which may offer the simplification that policy-makers need when performing land-use planning (Andiappan et al. 2019). Pinch analysis is an example of a graphical method (Andiappan and Wan 2020). Pinch analysis was initially developed to identify the minimum external energy resources based on the energy recovery potential of a given process plant (Linnhoff et al. 1982). Since then, pinch analysis has seen its application extended to various fields. These fields include but not limited to water and wastewater recycle networks (Foo 2009), total sites (Dhole and Linnhoff 1993) and material integration (El-Halwagi and Manousiouthakis 1989). The following section presents a brief literature review on recent applications of pinch analysis.

Literature Review

State-of-the-art-reviews by Klemeš and Kravanja (2013) and Foo (2009) comprehensive present applications of pinch analysis for heat integration and water integration in industrial processes. In the recent decade, pinch analysis has been extended for novel applications (Klemes et al. 2018). For instance, pinch analysis has been used to determine the capacity of low carbon electricity generation required for meeting a given emission target. This extension of pinch analysis is known as carbon emission pinch analysis (CEPA) (Foo and Tan 2016). CEPA was proposed through the seminal work by Tan and Foo (2007). Since then, there has been a huge interest in applying CEPA to various emission targeting problems for regions such as (but not limited to) New Zealand (Atkins et al. 2010), China (Li et al. 2016), UK (Cossutta et al. 2021), Malaysia (Leong et al. 2019) and the Baltic States (i.e. Latvia, Estonia and Lithuania) (Baležentis et al. 2019). Aside from carbon constrained energy planning, pinch analysis has been applications in waste management (Ho et al. 2015), human resources management (Foo et al. 2010) and financial planning (Roychaudhuri et al. 2017), risk management (Tan et al. 2016) and economic planning (Tan et al. 2018a).

Based on the above review, it is evident that pinch analysis shows value of providing intuitive insights to stakeholders. Moreover, pinch analysis is able to present and communicate results visually, making it easily accessible to those with limited expertise on the subject matter. Despite such benefits, there exists a significant gap in using pinch analysis for land-constrained planning. To this extent, there is limited application of pinch analysis for land use planning for agriculture activities. The solitary contribution on pinch analysis related to agricultural planning was from Wong et al. (2011). However, the work utilised pinch analysis to determine a plantation schedule in order to reduce carbon emission levels over given time period.

Apart from the contribution from Wong et al. (2011), there were some contributions on pinch analysis within the agriculture sector but are very limited in number. These contributions mainly focused on conversion processes of agriculture wastes to value-added products. For example, Petersen et al. (2015) applied pinch analysis to maximise energy efficiency of separation and reaction processes within the production of biofuel from sugarcane bagasse. Likewise, Salina et al. (2021) applied pinch analysis to assess the feasibility of retrofitting a typical ethanol production process with fast pyrolysis of sugarcane straw. The results showed the heat integration can increase energy efficiency up to 46.4%. As shown, these research works were mainly focused on agriculture wastes, and they do not explicitly tackle land use as a criterion in pinch analysis.

Land use problems in agriculture systems have usually been addressed via mathematical models, spatial models or combination of both. For example, Biswas and Pal (2005) used fuzzy goal programming to solve land use planning problems in agriculture system. Besides, Qi et al. (2008) proposed a new approach to determine cost effective land use plans. This new approach integrated a modern heuristic optimisation technique with a computational modelling and a channel network model to optimise the land use. Later, this was extended to a conceptual framework for agricultural land use planning by Qi and Altinakar (2011) to address the water-land use problem. Similarly, Cao et al. (2012) developed a heuristic-based approach for sustainable land use optimisation. Recently, Diehl et al. (2020) used spatial analysis along with water and vegetation indices to determine land potential for agriculture use in Singapore. Meanwhile, in Malaysia, Rafaai et al. (2020) also used spatial analysis to identify future land-use change in agriculture. Rajakal et al. (2021a) developed a mathematical model for land use planning of plantation crops. This was later extended by accounting for optimal storage (Rajakal et al. 2021b) and optimal planting period (Rajakal et al. 2021c) in analysing its impact on land use.

Based on the above review, there is limited research work that use pinch analysis to tackle land use planning problem in agriculture. This is further evidenced based on a Scopus search conducted. This can be viewed from the Scopus search that around 9371 publications exist on keywords such as agriculture and land use planning. A refined Scopus search on agriculture, land use planning and pinch analysis led to only 6 publications by Foo et al. (2008), Tan and Foo (2013), Tan et al. (2018b), Baležentis et al. (2019), Jain et al. (2020) and Aviso et al. (2021). Distinctions can be made between these 6 publications. Firstly, Foo et al. (2008) presented a pinch analysis method aimed at energy planning based on carbon emission targets. The method focused on determining the minimum quantity of ethanol required from external sources, factoring the impact of energy planning on land footprint for bioenergy from sugarcane (Foo et al. 2008). Tan and Foo (2013) also developed a pinch analysis method for energy planning to evaluate the minimum external energy source required. However, Tan and Foo (2013) employed a quality index which integrates the consideration of land footprint, water footprint, carbon footprint, inoperability and energy. Tan et al. (2018a) then applied pinch analysis to biochar carbon management. The goal in that work was to determine the maximum biochar application in soil, where the contaminant limit for different land types were considered in developing the sink curve. Baležentis et al. (2019) on the other hand used pinch analysis to determine minimum quantity of renewable energy required to achieve carbon emission targets. Baležentis et al. (2019) essentially focused the energy planning based on land and water footprint. Similarly, Jain et al. (2020) proposed a pinch analysis method for energy sector planning. This method was used to determine the minimum capacity addition of new power plants using a sustainability indicator which aggregated land, water, carbon footprints, risk to humans and energy-return on investment (Jain et al. 2020). Lastly, Aviso et al. (2021) proposed a combined input-output modelling with pinch analysis to determine the optimal trade between economic sectors based on land requirements in each sector.

As shown, these 6 publications provided valuable extensions of pinch analysis by considering multiple quality measures, one of which was land footprint. In fact, some of these publications employed the use of composite or aggregated indices to incorporate various other footprint measures alongside land footprint. These publications signify an important step towards considering land use constraints in pinch analysis but they were mainly directed towards energy planning. In other words, these analyses were catered to address the usage of land for producing energy crops or deploying energy systems. However, none of these works has considered land use for crop allocation from food production planning perspective. Thus, this research gap serves as the motivation for this current work. The following describe the specific gaps identified:

  • Pinch analysis has been widely employed in tackling energy planning, finance management, waste management, emission reduction planning, human resource allocation and risk management. Nevertheless, there was no work that focused on targeting and allocating land for agriculture food products from a range of crops.

  • Previous work considered land footprint in targeting the minimum quantity of renewable energy required to ensure energy security. Moreover, these contributions considered the land footprint of several energy resources but none has looked into the land footprint of agriculture food products from a food security standpoint.

To address the abovementioned gaps, this work proposes a pinch analysis method to target the minimum amount of low land footprint crop required to meet the agro product demand. This extension of the pinch technique is termed as land-use pinch analysis (LUPA). LUPA offers visualisation of the agriculture planning problem and allows policymakers to determine strategies that limits expansion of lands to fulfil growing food demands of a given region.

The rest of this paper is organised based on the following sections: the “Problem Statement” section presents a formal statement of the problem addressed in this work. The “Methodology” section provides a detailed account on the methodology for LUPA. The “Case Study” section then presents a case study in which LUPA is demonstrated. The results obtained from the case study are also discussed in the “Case Study” section. The “Case Study (Revisited)” section revisits the case study to show other implications of the proposed methodology. Conclusions, limitations and future work are drawn in the final section of this paper.

Problem Statement

As discussed in the “Introduction” section, growing population and rise in income levels have resulted in continuous increase in the food demand. This requires expansions in crop production to increase the supply. However, land resource is limited, and witness increased competition from other economic activities. Hence, policymakers must prioritise land-use planning for efficient use of land. This may require determining a land allocation strategy for a range of crops to meet the demand within the available land resources, by introduction of low land footprint crop.

Thus, this work aims to address this problem by presenting a decision support tool known as land-use pinch analysis (LUPA). LUPA is a systematic tool that policymakers can use to identify the following,

  • Minimum area of low land footprint crop to be introduced to meet the demand within the land constraint.

  • Feasible land footprint value that can serve as guidelines for selection of low land footprint crops for planting.

  • The optimal land allocation strategy for a range of available crops to satisfy the demand within the specified land constraint.

LUPA is evaluated under the following two assumptions,

  • Land use is of high priority. Therefore, other resources requirements such as water, fertiliser and labour for each oil crop are not considered at this stage of planning. This stage focuses on setting targets for land use. Other resource requirements are assumed to be evaluated in the subsequent phase of planning.

  • Crops which produce similar food products can be substituted. For example, oil crops can be substituted for producing vegetable/cooking oil. This assumption is made provided that the calories are similar, putting aside the processing properties and taste. Such instances are possible in times of shortage and price hikes in other vegetable oils due to circumstances such as geopolitical issues (Southey 2022).


This section proposes the land use pinch analysis (LUPA) method to determine the minimum area of low land footprint crop required for land-constrained agriculture planning. Like other versions of pinch analysis (i.e. carbon emissions pinch analysis), LUPA uses pinch diagrams involving composite curves. It is worth noting that LUPA is a conceptual tool used to determine targets. These targets will then be used in the network design stage, where network optimisation is done considering detailed aspects such as costing, time of cultivation. This, however, is beyond the scope of this work. A block flowchart is presented in Fig. 1 to describe how these composite curves are plotted.

Fig. 1
figure 1

Block flowchart of LUPA

The following procedures are described based on Fig. 1:

  • Collect data for the source (given by source i ∈ I) and the demand (given by region j ∈ J) for the food products. The source data indicate the current production of food product from each of the available crops (expressed by Si) while the demand data indicate the demand for the food product in the considered regions (expressed by Dj). In addition, the land footprint of each crop to produce the food product is also provided in the data table (\({\textrm{L}}_i^{\textrm{Out}}\)).

  • Arrange the crops in increasing order of their \({\textrm{L}}_i^{\textrm{Out}}\) values.

  • Calculate the total land used by each of the crops for producing the food product (\({\textrm{S}}_i{\textrm{L}}_i^{\textrm{Out}}\)).

  • Plot the demand composite curve by plotting the food product demand value on the x-axis and land constraint value (\({\textrm{L}}_j^{\textrm{In}}\)) on the y-axis (see Fig. 2a).

  • Plot the source composite curve by plotting the supply of food product derived from each crop (Si) on the x-axis while their corresponding total land used (\({\textrm{S}}_i{\textrm{L}}_i^{\textrm{Out}}\)) on the y-axis (see Fig. 2a).

  • Introduce the low land footprint crop by plotting its locus. The gradient of the locus represents the land needed for the low land footprint crop to produce unit quantity of food product.

  • The source composite curve is shifted to the right along the locus of the low land footprint crop until the source composite curve meets the demand composite curve as shown in Fig. 2b. It can be noted that the two curves meet each other tangentially. This contact point would be the pinch point.

  • The minimum low land footprint crop needed can be determined by identifying the contact point of the shifted source composite curve on the locus (see Fig. 3). Perpendicular dropped from this contact point on the y-axis provides the minimum area of low land footprint crop needed (Fj) to meet the food product demand within the specified land footprint. This also means that the remaining part of the source curve after the pinch point is deemed as being replaced and is no longer required (Qi).

  • In the case where to determine the land area that could be offset due to the introduction of pre-determined land area of low land footprint crop, procedures shown in Fig. 4a to be followed. It can be noted that the introduction of pre-determined low land footprint crop could result in a gap between the source and demand composite curves. To address this, the demand composite curve can be lowered as shown in Fig. 4b. Therefore, the same food product demand is now achieved with a lower land footprint. The remaining part of the source composite curve that has been replaced can be seen via Qi in Fig. 4b.

Fig. 2
figure 2

a Construction of composite curves. b Shifting of source composite curve

Fig. 3
figure 3

Minimum low land footprint crop from pinch diagram

Fig. 4
figure 4

a Gap between source and demand composite curves. b Lowering of demand composite curve

Alternatively, the above procedure can be formulated as a simple linear mathematical model. The formulation shown below represents the mathematical equivalent of the graphical method shown in Fig. 2. This is consistent with Bandyopadhyay (2015)’s fundamental derivation of the graphical pinch analysis.

This will be particularly useful when policymakers would like to implement LUPA in spreadsheet calculations. The linear model begins with constraints related to the food product supply from various crops (Si). As shown in Eq. (1), Si can be distributed to meet the demands at regions j ∈ J (Xij) and the portion of sources that might be replaced (Qi).

$${\textrm{S}}_i=\sum_j^J{X}_{ij}+{Q}_i\kern0.5em \forall i$$

The constraint that describes the supply of food product to demands is given Eq. (2).

$${\displaystyle \begin{array}{cc}{\textrm{D}}_j=\sum \limits_i^I{X}_{ij}+{F}_j& \forall j\end{array}}$$

where Fj is the amount of low land footprint crop to be introduced to replace the portion of existing crop (i.e. Qi). Fj can be determined when a given land constraint value and \({\textrm{L}}_j^{\textrm{In}}\) is set. This can be done using Eq. (3).

$${\displaystyle \begin{array}{cc}\sum \limits_i^I{X}_{ij}{\textrm{L}}_i^{\textrm{Out}}\le {\textrm{L}}_j^{\textrm{In}}& \forall j\end{array}}$$

Finally, the objective function of this model is to minimise the area of the low land footprint crop required. This will essentially allow the model to determine the minimum Fj subject to the land constraint in Eq. (3) and the supply constraint in Eq. (1). Note that this will subsequently determine the portion of existing crop that can be replaced (Qi) by Fj. The goal here is to minimise the land area used for crop production by doing two essential things: (1) introducing low land footprint crops and (2) minimising new lands required for agriculture expansion.

$$\min \sum_j^J{F}_j$$

The model presented above offers the same intention indicated in the graphical approach. In fact, LUPA can be extended to consider other problems that were considered for previous pinch-related problems. This may include application of LUPA to multiple zones, multiple time periods and parametric uncertainties.

In the next section, LUPA is demonstrated using a case study. The case study highlights the features in LUPA that enable policymakers to draw useful insights.

Case Study

This case study presents a land use planning for different oil crops based on the edible oil demand of a given region. The oil crops available in this region are as shown in Table 1, which are used for edible oil production. Aside from this, Table 1 also shows the edible oil demand of the aforementioned region. The land use planning problem is to determine the minimum area of low land footprint oil crop required to fulfil the edible oil demand within the prescribed land use limits for cropping purpose. This land use limits are set under scenario that land resources are limited and have competing interests from other sectors in the economy. Land use pinch analysis (LUPA) is used to address this problem. It is worth nothing that there are several options of low land footprint oil crops available. An oil crop can be deemed as low land footprint when it requires significantly lower land to produce unit quantity of edible oil compared to those currently planted. This case study considers oil palm as the low land footprint oil crop.

Table 1 Oil crop data considered for case study


The data presented in Table 1 is used to generate the source and demand composite curves. The composite curves generated for this case study are shown in Fig. 5 (i.e. red curve referring to demand composite curve while blue curve is the supply composite curve). Vertical and horizontal axes of the plot represent land area (in million hectares) and edible oil (in million tons) respectively. Figure 7 shows the introduction of oil palm locus that essentially represents the land footprint gradient of oil palm crop.

Fig. 5
figure 5

Introduction of oil palm locus

The source composite curve is shifted along the oil palm locus until it meets the demand composite curve tangentially as shown in Fig. 6. Observations from Fig. 8 show that a minimum of 1 million hectares of oil palm crop required to meet the edible oil demand of 10.6 million tons within the prescribed land limit of 15 million hectares. The edible oil production from 1 million hectares of oil palm crop is about 3.25 million tons. The introduction of oil palm has allowed to replace 2.5 million tons and 0.25 million tons of production from high land footprint crops, rapeseed and soybean respectively. Therefore, a reduction in total land footprint from 22.6 million hectares to 15 million hectares is achieved to meet the same edible oil demand. Figure 7 presents the resultant cumulative curves after performing the steps discussed in the “Methodology” section.

Fig. 6
figure 6

Shifting of the source composite curve

Fig. 7
figure 7

Resultant composite curves

This case study evidently shows that LUPA can be used as a means for policymakers to strategise land allocation for a range of oil crops in meeting edible oil demands. Further implications of LUPA are discussed in the next section.


As mentioned previously, LUPA has advantageous features to aid policymakers. The simplicity of LUPA makes it a user-friendly tool, as terms used in its figures can be easily understood by policymakers and government officials. This is an important prerequisite for making policy in land use related matters. In addition, it is worth noting that this tool is positioned for use at the preliminary stage where targets need to be set for plans on how to use limited resources like land. It offers important insights on croplands can be utilised efficiently with low land footprint. Such insights will allow policymakers to efficiently determine potential subsidies to promote investment in low land footprint crops. However, LUPA offers several other implications on policy development. The following is a summary of several policy implications:

  • Increased land use efficiency: The direct implication of LUPA is the fact that low land footprint crops can be easily assessed and integrated into the overall planning. Policymakers can use LUPA to evaluate how much low land footprint crops can be used to meet growing edible oil demands.

  • Focused aids, resources and delegation: With systematic planning of crops, policymakers would be able to objectively determine where resources such as subsidies and funding aid can be delegated to. In fact, these support mechanisms would not only be in terms of aiding plantation operations but also upskilling the workforce in some segments of the agriculture sector. When certain crops are deemed to be important to reduce land footprint, resources can be mobilised to encourage more workers to join the workforce of that supply chain.

  • Reduced risks and oversight: As LUPA facilitates systematic planning of crop lands, it mitigates risks of farmers experiencing losses due to an oversight. By doing this, small-scale or large-scale farmers would be able to venture into low land footprint crop plantations with the support of strong risk mitigations systems which was efficiently allocated through planning.

  • Facilitates focused technology advancement: Although LUPA indicates how much of low land footprint is required to achieve edible oil demands, it also suggests the area for improvement in other crop yields. Such improvement can be in the form of technological advancement in other crop cultivation and harvesting activities. For instance, insights from LUPA can inform policymakers to consider offering grants and initiatives to improve oil content in other crops and to improve crop yields per hectare of plantation. Aside from this, support could be provided to improve oil extraction rates in crop milling processes. Figure 8 conceptually shows how yield improvement can be factored into LUPA to obtain useful insights. This will allow policymakers to plan targets for future innovations or lab studies to achieve. A numerical demonstration of this is shown in Section 6.

Fig. 8
figure 8

a Change in supply curve when yield per hectare of a crop is improved. b Reduction achieved from yield improvement

Case Study (Revisited)

The case study in the “Case Study” section is revisited to analyse the impact of crop yield on the planning of land use. Figure 9 shows that when the yield of mustard oil is improved through technology advancement, the gradient of its line will reduce. The decrease in gradient signifies that it will require less land for produce a given amount of product. The new gradient of the mustard crop line is found to be lower than soybean crop. Since the supply composite curve is arranged based on the order of increasing gradient or slope, the mustard crop line will now be moved below the soybean crop line as shown in Fig. 10. This new change has resulted in additional room for land use reduction and a new pinch point. This is indicated in the new position of the demand curve in Fig. 10. The shift in the demand curve indicates that about 1.5 million ha of land can be reduced further as a result of yield improvement in a given crop.

Fig. 9
figure 9

Change in supply curve due to yield improvement in mustard crop

Fig. 10
figure 10

Reduction achieved from yield improvement

The revised LUPA shows that the improvement in yield can further reduce the land use. Policymakers can use this a basis to strategise crop yield improvement targets in the future. By doing this, policymakers can prioritise projects and funding support to research that can meet these crop yield improvement targets.


This work presented a graphical method called land use pinch analysis (LUPA). LUPA was developed for planning and allocating low land footprint crop to achieve land footprint reductions. A numerical case study was demonstrated to display the advantages and features for the method. The case study yielded results that recommend 1 million hectares of low land footprint oil crop be used to replace 8 million hectares of a higher land footprint oil crop to meet the specified edible oil demand. This will allow policymakers to effectively reduce the overall land footprint for agricultural planning. From the case study, it is evident that LUPA provides insights on the minimum amount of low land footprint crop required to achieve reductions in land usage and to meet food product demands. The visualisation offered by LUPA allows easy access of information to policymakers and/or decision-makers to make informed decisions. Policymakers can use LUPA to increase land use efficiency, plan resources, reduce risk and oversight during planning and formulate policy for improving other crop yield factors. However, LUPA is limited to identifying targets for land use. These targets can serve as a basis to do detailed network optimisation based on aspects such as costing and time of cultivation. Thus, future works can be directed towards linking LUPA within a mathematical programming framework to consider these aspects. LUPA can be also extended to consider aspects that were previously developed for past variations of pinch analysis such as multiple zones, multiple time periods and parametric uncertainties. Aside from this, land use planning is also influenced by other factors such as carbon and water footprints. Thus, future work will be focused on considering these factors simultaneously in LUPA.