Journal of Cleaner Production

(1)

Journal of Cleaner Production 318 (2021) 128526

Available online 4 August 2021

Does age matter? A strategic planning model to optimise perennial crops based on cost and discounted carbon value

Jaya Prasanth Rajakal

^a

, Raymond R. Tan

^b

, Viknesh Andiappan

^c

, Yoke Kin Wan

^a^,^d^,^*

, Ming Meng Pang

^a

aSchool of Computer Science & Engineering, Taylor’s University, Lakeside Campus, No. 1 Jalan Taylor’s, 47500, Subang Jaya, Selangor, Malaysia

bChemical Engineering Department, De La Salle University, 2401 Taft Avenue, 0922, Manila, Philippines

cSchool of Engineering and Physical Sciences, Heriot-Watt University Malaysia, 62200, Putrajaya, Wilayah Persekutuan Putrajaya, Malaysia

dDepartment of Chemical and Environmental Engineering, University of Nottingham Malaysia, Broga Road, 43500, Semenyih, Selangor, Malaysia

A R T I C L E I N F O

Handling editor: Cecilia Maria Villas Bˆoas de Almeida

Keywords:

Perennial crops Yield profile Land use change Carbon emissions Mathematical optimisation Discounted carbon value

A B S T R A C T

Many perennial crops are cultivated in large plantation estates by agro-industrial companies. Some of the attributes of perennial crops, like annual variation in yields and time lag from planting to initial yield, create complex challenges in developing land utilisation strategies in plantations. This work develops a mathematical programming model to determine the optimal maturity (age) of the different plantations needed to meet the demand with reduced environmental impacts. The model also determines the corresponding planting period for new plantations, accounting for the yield profile of the perennial crops. Piecewise linearisation technique is used to model the yield profile, thus reducing the model to mixed integer linear programming. The optimisation is carried under two approaches – total cost and discounted carbon value (DCV). The total cost approach aims to determine the planting strategy that results in minimising the capital and operations cost at plantations. The DCV approach aims to delay the peak carbon emissions, thereby reducing the intensity of climate change effects and also buying time for mitigation and adaptive measures. The model developed in this work is illustrated with an oil palm plantation case study, which showed that though the total cost is the same for both the approaches, carbon emissions are 3.28% lower in the DCV result compared to the cost approach.

1. Introduction

Crops can be divided into two categories: Perennial and annual.

Perennial crops are those that live more than two years and are harvested multiple times in their lifespan without the need for replanting.

Some examples of perennial crops include rubber, oil palm, coconut, sago palm, coffee, tea, banana, etc. In contrast, annual crops have a life span of one year or one season before being harvested. Examples of annual crops include rice, wheat, soybean, corn, etc. Most of the perennial crops are high value cash crops (Abalu, 1975) predominantly grown in tropical regions (Monfreda et al., 2008). Also, perennial crops generally have higher productivity compared to their annual competi- tors, thereby requiring lesser land footprint to produce agro products (Tapia et al., 2021). However, unlike annual crops, most of the perennial crops have varying yield each year. Such variation is often dependent on age or maturity of the crop (Tregeagle, 2017). Furthermore, perennial

nature results in minimal disturbance to ecosystem due to reduced soil tillage and fertilisation. On the other hand, annual crops lead to soil erosion and soil carbon loss due to frequent tillage (DeHaan, 2015). The high application of fertilisers for annual crops leads to ground and sur- face water contamination from nutrient runoff (DeHaan, 2015); this excess nutrient is responsible for large nitrogen and phosphorus foot- prints (Cuˇ ˇcek et al., 2012). Hence, perennial crops act as a potential remedy for most of the limitations to sustainability and productivity in agriculture (DeHaan, 2015). Perennial crops may be a solution to address multiple issues of environmental conservation and food security amidst shrinking land resources (Zhang et al., 2011).

One of the key challenges in perennial crop expansion is management of land resources. Land resources have witnessed increased competition from population growth, urbanisation, and industrialisa- tion (Laskar, 2003). The food-energy-environment trilemma has called for sustainable allocation of land resources and cautioned about the risk

* Corresponding author. Department of Chemical and Environmental Engineering, University of Nottingham Malaysia, Broga Road, 43500, Semenyih, Selangor, Malaysia.

E-mail address: [email protected] (Y.K. Wan).

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/jclepro

https://doi.org/10.1016/j.jclepro.2021.128526

Received 30 January 2021; Received in revised form 18 July 2021; Accepted 2 August 2021

(2)

of increasing carbon footprint and loss of biodiversity (Tilman et al., 2009). This issue has more relevance to perennial crops which require large tracts of land for plantation development. Moreover, with most of these plantations being developed in tropics, it necessitates careful planning to minimise ecological and environmental disturbances (Pha- lan et al., 2013) Also, perennial crops are cultivated by agro companies with commercial interests. In many cases, economic interests and environmental protection are in conflict. Decision support tools are required for optimising land allocation and utilisation to achieve sustainable perennial crop expansion.

Mathematical programming is a useful method for addressing the land allocation and utilisation problems for sustainable perennial agriculture (Kaim et al., 2018). A mathematical programming model may be defined as set of equations and inequalities that represent the behaviour of the system (Andiappan, 2017). It involves finding the maxima or minima of a function, subject to constraints, for synthesis or operation of an efficient system. Otherwise, it can also be termed as selection of the best possible result under given constraints from a set of available al- ternatives. Mathematical programming models are capable of repre- senting the system interactions, solve large and complex problems, and effectively aid in decision-making. This work develops a mathematical programming model to optimise land utilisation for perennial crops with reduced environmental impacts. A brief account of the various mathematical models developed for optimising perennial crops is provided in the following sub-section.

1.1. Strategic planning models for perennial crops

Strategic planning models deal with decision variables that are to be determined for long term. These decisions need careful considerations as they are not easily reversible, as in the case of location and production capacity choices.

Perennial crops are mostly industrial crops and find applications in food, livestock (Ojeda et al., 2018) and biofuel (Fernando et al., 2018) industries. Generally, the harvested crop from the plantation is processed into value-added consumer products. For such crops, supply chain optimisation is important for efficient operation and economic performance (Papageorgiou, 2009). Mathematical models to determine the optimal supply chain network design for various perennial crops like oil palm (Rajakal et al., 2021), grape (Fragoso and Figueira, 2020), olive (Yurt et al., 2019), and sugarcane (Jonker et al., 2016) have been developed. Similar models have also been proposed for forest biomass in bioenergy systems (Dessbesell et al., 2017). Strategic decisions on the optimal location and capacity of processing units and storage facilities in the supply chain are also determined along with the choice of trans- portation options (Gonzalez et al., 2021). Typically, the optimisation is based on a single objective to minimise the cost or maximise the profit (Rajakal et al., 2019). However, sustainability indicators like carbon footrprint and water footprint have been considered in recent multi-objective models (Tapia et al., 2021). Uncertainties in yield, demand, and price are also accounted for in the supply chain optimisation (Shavazipour et al., 2020). More recently, the supply chain of coffee was optimised based on circular economy considerations (Baratsas et al., 2021).

Land allocation and utilisation often have a significant impact in the supply chain operations and ultimately on production. Land allocation refers to land assigned for a specific purpose (Sheth, 2018). For crops, it is based on biophysical, social, and economic factors (Bunning and De Pauw, 2017). Biophysical factors include soil, water, climate, and ecology; social factors include labour and public acceptability; and economic factors include cost, supply, and demand. In addition, land allocation for perennial crops has been optimised considering biodiversity (Kennedy et al., 2016), ecological stability (Zhang et al., 2014), and minimal forest disturbance (Rajakal et al., 2019). In the work of Tapia et al. (2021), spatial optimisation using geographic information system (GIS) was used in land allocation for perennial crops. Post land

allocation, various strategic decisions like cropping pattern, crop density, and planting period are to be taken for new plantation develomnet.

The economic potential of the perennial crops under various cropping pattern was analysed by Fradj and Jayet (2018). Nesterchuk et al.

(2016) optimised the composition of different perennial crops in a given area of land to realise maximum profit. Catala et al. (2013) optimised the composition of pome (apple and pears) in a given farm for a given time horizon under different financial scenarios. Ouattara et al. (2019) optimised the combination of annual and perennial crops based on production uncertainty. This was extended by Griffel et al. (2020) based on minimal operations cost and harvesting efficiency. Similarly, Fee- mena et al. (2018) determined the optimal cropping pattern with minimum nutrient delivery and minimum production cost. In addition, an optimal fertiliser strategy to improve the productivity of plantation crops was presented by Foong et al. (2019b). Solinas et al. (2021) studied the different fertilizer management strategies to optimise the production and carbon footprint in perennial energy crop system. Zhang et al. (2021) determined the optimal nitrogen fertilisation and cropping density to achieve sustainable production for perennial rice cropping system. An optimal replanting policy derived via dynamic programming was proposed for perennial plantation crops by Diban et al. (2016).

1.2. Identification of research gaps

Planting period is an important decision in perennial crops due to the maturity-dependent yields during their lifespan and a large lag time from planting to its first yield. Hence, failure to account for maturity may result in yields either less or more than the anticipated. Reduced yield will lead to demand-supply mismatch, while excess yield indicates a missed opportunity for efficient land utilisation. Furthermore, when land utilisation requires prior land use change (LUC), then optimisation provides opportunities for cost and emissions reductions, because a delay in LUC can lead to possible reductions in climatic impacts (Diban et al., 2016). Optimised planting periods hence play a crucial role in meeting the demand with supply with reduced environmental impacts.

However, the existing contributions have not accounted these factors.

The literature review above allowed the identification of the following research gaps.

• Important characteristics of perennial crops, like maturity dependent yield and time lag to maturity, have not been accounted in previous works. Previous works have used unrealistic assumptions of fixed and conservative yield values.

• Planting period, a key factor in management of plantation estates of perennial crops has not been addressed.

• The impact of the optimised planting period on the economic and environmental performance has not been studied.

• Previous works have not considered delaying a new plantation development and its environmental implications.

To address these research gaps, models considering the exclusive attributes of perennial crops are required. This paper develops a mathematical programming model to determine optimal maturity and corresponding planting periods for new plantations based on expected agro product demand. It also integrates yield profile of perennial crops into the model to account for the varying yield and time lag to maturity in optimisation. The optimisation is based on two approaches – cost approach and discounted carbon value approach (DCV). The cost approach aims to determine a plantation development strategy with minimum capital and operations cost. Land utilisation for additional crop capacity typically leads to LUC, resulting in carbon emissions from the conversion of pristine ecosystems. Therefore, the DCV approach aims to bring about a slow transition to peak carbon emissions due to LUC. This delay in peak emissions reduces the magnitude of global warming (Dornburg and Marland, 2008) and buys time for development of mitigation and adaptive measures (Marland et al., 2001).

(3)

The rest of this paper is organised as follows: - Section 2 defines the problem statement while the proposed methodology for addressing the problem is presented in Section 3. A palm case study is taken to illustrate the developed model in Section 4 with the corresponding discussion on the results in Section 5. Finally, Section 6 presents the conclusion with recommendations for future work.

2. Problem statement

Fig. 1 illustrates general problem addressed in this work. Appendix A presents an example scenario to support understanding of problem statement discussed in this section. The formal problem statement is defined as follows: Given,

•The perennial trees are planted as plantations g∈G of area, Ag (ha).

The set includes existing plantations and lands allocated for new plantation development.

•The planning horizon, T^Plan(years) for which decision maker intends to strategies plantation activities.

•The maturity or age of plantations at the start of T^Plan, M^IN_g. For new lands, value of M^IN_g is taken as 0.

•The plantations g∈G produce crops which is processed at processing facility to produce agro product.

•The total agro product demand during T^Plan, F^AP(tons).

Based on the above, a mathematical model is developed to determine,

•The maturity or age of the plantations required at the end of T^Plan, M^FN_g to meet total agro product demand (F^AP).

•The yield from the plantations, W^YLD_g during T^Plan. Subject to,

•The maturity dependent yield of the plantations

This work considers two approaches in determining optimal maturity required for the plantations, (M^FN_g ) – minimise cost and maximise discounted carbon value.

3. Methodology

This section presents mathematical formulations developed to

address the above-mentioned problem. As previously stated, yield from plantations is based on their maturity and it is an important factor to be considered in optimising land utilisation. A typical yield profile plots age of plantation to yield per hectare. This section takes example of oil palm plantation to illustrate the developed method. Fig. 2 presents yield profile of oil palm plantation of 1 ha in area (Tan, 2014). Typically, oil palm plantations are a few hundred to few thousand hectares in area.

Hence, Fig. 2 can be extended to forecast total crop yield from a particular plantation of given area against its age. This can be determined by multiplying yield per hectare values (presented in Fig. 2) with the area of plantation. An example of this can be seen in Fig. 3 which shows total fresh fruit bunch (FFB) yield against age of a plantation of 800 ha in area. From here, cumulative yield of plantations is developed as shown in Fig. 4. The cumulative representation shows the addition in yield that comes up with every successive year of plantation’s maturity.

This work uses the cumulative yield profile for modelling and optimisation.

As discussed in Section 2, the planting strategies are outlined by the agro companies for a planning horizon, T^Planwhich can range from 5 to 10 y. This T^Plancan be divided into shorter time intervals, tz where z=

0,1,2, ...,n. Typically, tz can represent each year in T^Plan. The time in-

terval t0 indicate the start of planning horizon T^Plan. The age of the

Fig. 1. Generic plantation planning diagram.

Fig. 2. Typical yield profile of perennial crops (oil palm plantations).

(4)

existing plantations at t0 is known while for new lands it is taken as “0” and is provided as user input to the model. Similarly, time interval tn

indicate the end of T^Plan. The age of the plantations required at tn to produce sufficient yield to meet the agro product demand is determined in this work. The initial and final state of plantations are compared to determine yield from the plantations. Thus, the initial and final state of plantations are modelled separately, where the age for initial state is provided as user input while the that of the final state is determined as shown in Fig. 5. The optimisation is carried under two approaches with different objective functions, i.e., minimising cost and maximising DCV.

The following discussion in this section on the mathematical modelling is arranged as follows,

• Initial state of plantations

• Final state of plantations

• Determining the maturity and yield of plantations

• Optimisation objectives

•Cost approach

•DCV approach

3.1. Initial state of plantation (t0)

This section describes how the initial state of plantations can be modelled. Note that cumulative yield profiles are often non-linear as shown in Fig. 4. Thus, this work employs a piecewise linearisation technique (Graves and Wolfe, 1963) to transform the non-linear profiles into a mixed integer liner program (MILP). This will make determining the global optimum solution easier. From Fig. 4, it is evident that yield of a plantation, w is a function of its age, m as shown in Equation (1).

w=f(m) (1)

For a given plantation g∈G with area Ag, a set of discrete age values, mg,i(y) are taken as points on cumulative yield profile graph, with mg,1

and mg,I as the lower and upper limits. The index i∈I represent the nth point on the cumulative yield profile graph of plantation g. On substituting these points (mg,i) in Equation (1), corresponding yield values obtained, form another set of discrete points referred as wg,i(t).

Thus, for every mg,i point taken, corresponding wg,i point is determined.

For example, Fig. 6 shows mg,i points (y) considered in yellow markings.

Fig. 3. Total yield from a plantation of 800 ha in area.

Fig. 4. Cumulative yield from a plantation of 800 ha in area.

Fig. 5. Initial and final state of plantations.

(5)

It can be noticed that 14 mg,i points are taken, (i.e., i =1,2, 3, …,14) with lower and upper limit being mg,1 and mg,14. On substituting mg,i values in Equation (1), corresponding yield values obtained, form a set wg,i, whose points are shown in red markings. The greater the number of mg,i points considered; higher will be the accuracy of modelling the cumulative yield profile graph.

Let MÎN_g (y) and WÎN_g (t) be age and cumulative yield of the plantation g∈G during the start of planning horizon T^Plan(i.e. t0). MÎN_g is a known value and is provided as an input to the model by decision maker. And let ρÎN_g,i(unitless) be a variable that relates MÎN_g and WÎN_g as shown in Equations (2) and (3). Based on the input value of MÎN_g , the WÎN_g is to be determined by assigning suitable values to ρÎN_g,i.

M^IN_g =∑^I

i=1

mg,i×ρ^IN_g,i⋅∀g (2)

W_g^IN=∑^I

i=1

wg,i×ρ^IN_g,i⋅∀g (3)

MÎN_g might not necessarily be amongst the selected discrete points mg,i. It can be any value in-between two adjacent mg,i points. This can lead to irrational assigning of values to ρÎN_g,i. To account for such cases, ρÎN_g,i

is constrained as shown in Equation (4).

∑^I

i=1

ρ^IN_g,i=1⋅∀g (4)

Also, not more than two adjacent ρ^IN_g,i values can be non-zero. This is achieved by introducing a set of binary variables μ^IN_g,i using the method previously used in Zhou et al. (2013) for optimising energy system operations, as shown in Equations (5) – (8).

∑^I

i=1

μ^IN_g,i=1⋅∀g (5)

ρ^IN_g,i− μ^IN_g,i≤0⋅∀g,i=1 (6)

ρÎN_g,i− μÎN_g,i−₁− μÎN_g,i≤0⋅∀g,1<i<I (7)

ρ^IN_g,i− μ^IN_g,i−₁≤0⋅∀g,i=I (8)

Therefore, age of the plantation at t0, M^IN_g is a parameter provided as an input to the model, based on which the corresponding cumulative yield W^IN_g is determined. The readers are directed to Appendix B for an example calculation. The discussion in the Appendix B section is merely an example calculation and not a result of optimisation.

3.2. Final state of plantation (tn)

The mathematical formulation for modelling final state of the plantation is similar to the initial state. Let M^FN_g and W_g^FNbe age and cumulative yield of plantation at end of planning horizon, T^Plan(i.e. tn).

Unlike initial state where M^IN_g is an input parameter, M^FN_g is a variable whose optimised value is to be determined by the model. M^FN_g and W^FN_g are related by ρ^FN_g,ias shown in Equations (9) and (10).

M^FN_g =∑^I

i=1

mg,i×ρ^FN_g,i⋅∀g (9)

W_g^FN=

∑^I

i=1

wg,i×ρ^FN_g,i⋅∀g (10)

Similar to discussion presented in Section 3.1., ρ^FN_g,i is constrained as shown in Equation (11) – (15).

∑^I

i=1

ρ^FN_g,i =1;⋅∀g (11)

∑^I

i=1

μ^FN_g,i =1⋅∀g (12)

ρ^FN_g,i− μ^FN_g,i ≤0⋅∀g,i=1 (13)

ρ^FN_g,i− μ^FN_g,i−₁− μ^FN_g,i ≤0⋅∀g,1<i<I (14)

ρ^FN_g,i− μ^FN_g,i−₁≤0⋅∀g,i=I (15)

where, μ^FN_g,iis a set of binary variables. The optimal M^FN_g and the corre- Fig. 6.Modelling the cumulative yield profile graph of a plantation.

(6)

sponding W_g^FNis determined based on agro product demand which is discussed in the following sub-section. The maximum possible maturity or age of plantation at final stage can be the sum of the age at initial state and planning horizon (i.e., M^FN_g =M^IN_g+T^Plan).

3.3. Determining the maturity and yield of plantations

As discussed, initial and final state of the plantations are compared to determine optimal maturity and yield. But first total yield, W^TOTAL(t) required from the plantations to meet agro product demand (F^AP) can be determined as shown in Equation (16).

W^TOTAL×C^PF=F^AP (16)

where, C^PFis conversion factor of crop to agro product at processing facility. This total yield, W^TOTALwill be aggregate of yields from all plantations as shown in Equation (17).

∑^G

g=1

W^YLD_g =W^TOTAL (17)

where, W^YLD_g (t) is yield from plantation g∈G during T^Plan. W_g^YLDcan be determined by deducing cumulative yield of final state from initial state as shown in Equation (18). The yield cannot be a negative value and hence W^YLD_g is constrained as shown in Equation (19).

W_g^YLD=W_g^FN− W_g^IN⋅∀g (18)

W_g^YLD≥0⋅∀g (19)

Finally, time interval in which new plantation g has to be planted to attain the optimised maturity (M^FN_g ), t^Plant_g can be determined as shown in Equation (20).

t^Plant_g =T^Plan− M_g^FN⋅∀g (20)

3.4. Optimisation objectives

The optimal maturity required for plantations at tn (M^FN_g ) is determined based on the optimisation objective. In this work, two approaches are used to determine optimal maturity of plantation as follows, 3.4.1. Cost optimisation approach

In this sub-section, the first approach based on cost is discussed. The maturity or age of plantations are optimised based on minimising the total costs at plantations. The total cost refers to the capital (only for new plantations) and operational expenditure at the plantations g∈G. The capital cost includes land cost, land clearing cost and planting cost. The operational cost includes harvesting cost, upkeeping cost, labour cost, and fertiliser cost at plantations. The total cost at all plantation g∈G during planning horizon T^Plan, Cost (USD) can be determined as shown in Equation (21). Equation (22) presents Big M formulation, for optimising the selection of lands for new plantation development.

Cost=

∑^G

g=1

(

Ag×C^CAPEX_g ×Ig

) +

(

W_g^YLD×C^OPEX_g

) (21)

W_g^YLD≤Y×Ig⋅∀g (22)

where, C^CAPEX_g (USD/ha) is the capital expenditure involved for new plantation development. C^CAPEX_g is 0 for the exiting plantation while for the new plantations the cost depends on the type of LUC. C^OPEX_g (USD/t) is the operational cost at plantations. Ig is binary variable used for plantation selection and Y is a large arbitrary constant.

3.4.2. Discounted carbon value optimisation approach

Discounting is a financial mechanism normally used for adjusting for the time value of money (Walker and Kumaranayake, 2002). It is a method used to determine present value of the expected future cash flows. It is used in capital budgeting of companies to compare the profitability of different projects. Typically, project with highest net present value (NPV) will be considered for investment. NPV is a function of discount rate and time period. The time period considered is generally the expected operational lifetime of the project while discount rate is usually the prevailing inflation rate. The net cash flow for considered time period is the difference between total cash inflow (revenue) and total cash outflow (cost) in that time period. The cash inflows are considered as positive values while outflow as taken as negative values in financial analysis. When NPV is positive it means that cash inflows are greater than the outflows. Hence, projects yielding higher NPV have better financial viability.

Researchers have argued that carbon emissions can be measured on a similar principle to NPV (Meunier and Quinet, 2014). This argument is based on the climatic impact of carbon emissions being dependent on their timing (Asplund, 2017). In this case, the discounting principle applied for calculating NPV in financial analysis is used for carbon accounting. The impact associated with carbon emissions and carbon sequestration is taken analogous to cash outflow and cash inflow and can also be monetized through economic valuation methods. As previously discussed, LUC during new plantation development may result in carbon emissions. Carbon sequestration in perennial crops fluctuates cyclically with replanting cycles, but when averaged over multiple cycles, the figure is approximately constant per unit area, assuming that the crop variety used in future cycles remains the same.

In this work, the discounted net present value is termed as discounted carbon value (DCV). Positive NPV is generally desired in financial analysis. Similarly, in DCV, a positive value refers to carbon sequestration while a negative value refers to carbon emissions. Dis- counting accounts for the effect of timing, on the climate change mitigation potential of a given level of reduction of emissions. Hence the optimisation objective, in this case, is to maximise DCV. To begin with, the carbon value from plantation g∈G during planning horizon, T^Plan, Carbon^Value_g (USD) can be determined as shown in Equation (23).

Carbon^Value_g =Ag× (

C^SQT_g − C^LUC_g )

×M^FN_g ×C^Penalty_g ⋅∀g (23) where, C^LUC_g (tCO2/ha/y) is annual emissions from unit area of the plantation g due to LUC. C^LUC_g is 0 for existing plantations while for new plantations it depends on the type of LUC. C^SQT_g is the average value of annual carbon sequestered at plantation g. The total emissions from plantation g is function of its area (Ag) and the number of years since the plantation was developed. Concerning new plantations, the number of years is typically the age of the plantation which is represented by M^FN_g . C^Penalty_g (USD/tCO2) is penalty imposed on carbon emissions. This cost is a one-time upfront cost paid as a penalty for emitting one ton of CO2. The discounted carbon value for emissions from plantations g∈G at the end of time period T^Plan, DCVPlantation (USD) can be determined as shown in Equation (24).

DCV^Plantation=∑^G

g=1

Carbon^Value_g

(1+r)^T^Plan (24)

where, r is discount rate in percentage. This paper considers the discount rate to be 2.6% as suggested by Rennert and Kingdon (2019) for climate change policies. As shown in Equation (23), carbon value (Carbon^Value_g ) is a function of the maturity of the plantations (M^FN_g ). Also as discussed, maximising DCV would mean minimising the total carbon cost, which is achieved by determining least maturity required for new plantations to

(7)

meet the demand. The lower the maturity or age of the plantation the longer the delay in the planting period (t^Plant_g ) during planning horizon (T^Plan). Therefore, the DCV approach enables to identify permissible delay in expansion of new plantations thereby giving a reduction in carbon emissions during T^Plan.

The following section presents a case study to illustrate the proposed model in Section 3. The planting strategies are optimised for minimise total cost case and maximise DCV case and their results are presented for discussion.

4. Case study

Palm oil is one of the most important vegetable oils, accounting more than 30% of global vegetable oil production (USDA, 2021). The total crude palm oil (CPO) production during 2019–20 is more than 70

million metric tons (USDA, 2021). Indonesia and Malaysia are leading CPO producers while China, India and EU are leading CPO consumers (USDA, 2021). The demand for CPO has been rapidly increasing in past 5 - 6 decades due to its low cost of production and versatile applications in food, personal care, and biofuel industries. Recently, expansion of new oil palm plantation has become debatable due to LUC of ecologically sensitive tropical forests and peatlands. Hence, optimal land management of oil palm plantations is required to minimise LUC. Oil palm plantations are either owned as small holdings by independent farmers or as large plantation estates by palm oil mill companies. The fresh fruit bunch (FFB) is the primary product of harvest from oil palm plantation.

Unlike other oil crops, yield from plantations is not constant as it varies with crop maturity. Also, FFBs are harvested throughout the year when they ripen. The harvested FFBs are then transported to palm oil mills. A palm oil mill receives FFBs from multiple plantations. The FFBs are then

Fig. 7. Cumulative yield graph of plantations.

(8)

processed at mills to produce crude palm oil (CPO) as the main product and kernel palm oil, palm biomass and waste streams as by-products.

The palm oil mill companies are required to plan their expansions and operations to meet this growing demand (Foong et al., 2019a).

Unlike mills, expansion in plantations needs careful attention in planning, as capacity addition requires considerable time. Typically, it takes almost three years for new plantation to yield its first FFB harvest.

Hence, decision makers are required to make optimised plantation management strategies as it would impact the company’s bottom line for next few years to come. The proposed model aims to address this problem by providing optimised maturity of the plantations needed to meet the forecasted CPO demand. However, the impact of such optimisation on the expansions in palm oil mills and other downstream units in the palm oil supply chain is beyond the scope of this work. The capacity of the palm oil mill is assumed to be adequate to process the increased FFB production. Also, the new lands for which the planting periods are determined are pre-selected. The selection of lands for plantation expansion can be found in Rajakal et al. (2020).

This case study involves a palm oil mill company with existing plantations P1 and P2 with areas of 800 ha and 900 ha, respectively. The objective of palm oil mill company is to optimise the plantation management in meeting the expected increase in CPO demand. Apart from this P3, P4 and P5 are lands identified for new plantation development with areas of 630 ha, 750 ha and 590 ha, respectively. The cumulative yield graph of plantations P1 and P2 are presented in Fig. 7a and b.

Similarly, Fig. 7c, d and e presents the cumulative yield profile for to be plantations at lands P3, P4 and P5 respectively. Based on Fig. 7, cumulative yield profile of each plantation is modelled. The initial and final states of the plantations is modelled separately as discussed in Section 3.1 and Section 3.2, respectively.

Fig. 8 shows the diagrammatic representation of case study problem.

The planning horizon is the duration into future for which a company intends to make strategic decisions. Typically, plantation companies own multiple plantation estates in different locations. It is important for companies to strategies coordinated decision making of plantation activities to achieve synergies in production. Planting is one of the important strategic decision made by companies, generally for a planning horizon of 5–10 y. In this case study, planning horizon considered for devising planting strategies is 10 y, i.e., T^Plan=10 y. The T^Planis then divided into time intervals -t0, t1, t2, …, t10, where t0 marks the beginning while t10 the end of T^Plan. The time intervals in this case study represent each year within T^Plan. The CPO demand, F^APforecasted for the considered planning horizon, T^Planis 125,000 tons. The amount of FFB required, W^TOTALto meet the CPO demand is determined as shown in Equation (16), which is 625,000 t. As previously stated, P1 and P2 are

existing plantations with maturity of 9 y and 7 y at t0, i.e., M^IN₁ =9;

MÎN₂ =7. Since P3, P4 and P5 being virgin lands at t0, MÎN₃, MÎN₄ and MÎN₅ will take the value of 0. The total FFB that can be produced from P1 and P2 during T^Planis 208,000 t and 230,400 t (from Fig. 8a and b), sup- porting total CPO production of 87,680 t. A deficit of 37,320 t of CPO is observed, which corresponds to 186,600 t of FFB. Therefore, new lands P3, P4 and P5 have to be converted to oil palm plantations. The current land use type of P3, P4 and P5 is presented in Table 1. The case study is focused on optimising the planting strategies to highlight on the effect of the timing of LUC. Hence, this case study accounts only the carbon emissions from LUC and does not consider carbon sequestration. The LUC to oil palm plantation involves cost and carbon emissions. The data for these are presented in Table 1. Only degraded tropical forest is considered in this case study to clearly demonstrate the comparison in optimised maturity and their planting periods determined by the two objective functions – minimise total cost and maximise DCV. Since no carbon sequestration is considered, maximising DCV would effectively mean minimising carbon emissions. However, compared to the classical minimise carbon footprint optimisation method, DCV approach accounts the time value for carbon. The time value for carbon is important because it essentially represents that impact of carbon emission now is higher compared to the impact of the emission on a later period.

The optimal maturity, M^FN_g required at t10 for new plantations P3, P4 and P5 to meet the deficit in FFB production is to be determined. Based on this optimal maturity, planting period, t^Plant_g is estimated as shown in Equation (20). The yield (W^YLD_g ) from each plantation during T^Plan, can be determined from Equation (18). The total FFB yield from all plantations (P1, P2, …, P5) during T^Planshould meet FFB requirement, W^TOTALas shown in Equation (17). The maturity and their planting periods for new lands are optimised under two approaches - minimise total cost and maximise DCV, which is detailed in the following sub- sections. The case study is solved using LINGO v18.0 solver in a HP Pavilion x360 with Intel® Core™ i5 8250 (1.80 GHz) processor and 8 GB RAM under a 64-bit operating system. The processing time to obtain the global optimum solution is less than 2s. The model is of the class mixed integer linear programming (MILP).

4.1. Strategy 1 - cost approach

In this approach, maturity and the corresponding planting periods of new plantations are determined to minimise the total costs, i.e. capital cost for new plantation development and operations cost at all plantations. The mathematical formulations presented in Section 3.4.1. is used in this approach. Fig. 9 presents diagrammatic result while Fig. 10 presents initial and optimal final state of plantations. The optimal

Fig. 8. Diagrammatic representation of the case study problem.

(9)

maturity (M^FN_g ) of new plantations, P3, P4 and P5 at t10 is 7 y, 9.7 y and 9 y. These results indicate that P3, P4 and P5 will need to be started 7 y, 9.7 y and 9 y, prior to the end of planning horizon. This means that P3, P4 and P5 must be planted by year 3, 0.3 and 1 from t0 respectively.

The total yield from P1, P2, P3, P4 and P5 during T^Planare 208,000 t, 231,300 t, 34,965 t, 90,500 t and 59,885 t. This amounts to the required FFB of 625,000 t. Fig. 11 present the FFB production from plantations during each time interval tz. The total cost estimated is USD 25.07 M while the net present carbon value is USD -4.81 M. As mentioned in Section 3.4.2, the negative value of DCV denotes net carbon emissions and the value USD 4.81 M is the discounted penalty of the carbon emissions.

4.2. Strategy 2 – discounted carbon value approach

This approach aims to maximise the DCV. Fig. 12 presents the diagrammatic result while Fig. 13 presents initial and optimised final state of plantations. The optimised maturity (M^FN_g ) of new plantations, P3, P4 and P5 at t10 is 10 y, 10 y and 4.5 y. These results mean P3 and P4 are to be planted at time interval t0 while P5 is to be planted at 5.5 y from t0. The total yield from P1, P2, P3, P4 and P5 during T^Planis 208,000 t, 231,300 t, 80,324 t, 95,625 t and 8,950 t; totalling to the required FFB of 625,000 t. Fig. 14 presents FFB production from plantations during each time interval tz. The net present carbon value is USD -4.64 M meaning net carbon emissions with discounted carbon cost of USD 4.64 M. The total cost estimated for new plantation development and operations is USD 25.07 M.

5. Discussion

This section analyses and compares the results generated from the two planting strategies (Strategy 1 – cost approach and Strategy 2 – DCV

approach). A distinctive difference can be observed in the planting strategies optimised by the two approaches. Table 2 compares optimised planting period (t^Plant_g ) of plantations determined by the two approaches.

The planting period represent time interval in which new plantation is to be planted during planning horizon T^Plan. In Strategy 2, P3 and P4 are to be developed at beginning of time period (i.e., at t0) while P5 is delayed by 5.5 y. Meanwhile, cost approach (Strategy 1) shows a different strategy, which in fact is sub-optimal in terms of DCV. Though planting strategies differ, the total cost for both strategies was noticed to be similar. This is due to all identified lands P3, P4 and P5 are selected by both strategies for new plantation development resulting in no difference in capital cost. The operations cost is a function of yield produced as shown in Equation (21). As the total FFB production is constrained to be equal to FFB requirement as shown in Equation (17), the total FFB produced in both strategies are 625,000 tons. However, the discounted carbon cost for Strategy 1 is 3.66% lesser than Strategy 2; meaning that cost approach resulted in higher impacts compared to DCV approach.

As discussed, the yield of a plantation depends on its maturity. The optimal maturity required of new plantations is different for two approaches. Therefore, the contribution of each plantation to total FFB requirement varies between two strategies which is presented in Fig. 15.

It can be noted that existing plantation P1 and P2 contribute to 70% of the FFB production in both strategies. However, remaining 30% is met by different plantation contributions between the two strategies. In cost approach P3, P4 and P5 contribute 6%, 14% and 10% of the total FFB production while in the case of DCV the contribution is 13%, 15% and 2%. Fig. 16 presents cumulative production of FFB along time intervals t0

to t10. The blue and red points refer to planting period of new plantations (P3, P4 and P5) in Strategy 1 and Strategy 2 respectively. It can be observed that in discounted carbon cost approach, there occurs marginally higher build-up of FFB production compared to cost Table 1

Plantations – Area, Maturity, Expansion cost and Carbon emissions.

Plantation Current land use Area (ha) Initial maturity (F^MTY_g,t0) (y) Capital cost (USD/ha) Operational cost (USD/t FFB) Carbon emissions (tCO2/ha)

P1 Oil palm plantation 800 9 0 315 0

P2 Oil palm plantation 900 7 0 315 0

P3 Degraded tropical forest 630 0 28,750 315 8.6

Fig. 9.Cost approach – Diagrammatic presentation of the result.

(10)

approach from t3 to t6. This is attributed to development of new plantations P3 and P4 at t0. However, in cost approach the production catches up from t6 by the development of P3 at t3. Though by the end of

t10 both the strategies produce the required FFB quantity of 625,000 t, the cumulative production data helps while considering the dynamics in CPO demand within the time intervals (tz) in T^Plan.

The total FFB production from all plantations during each time interval tz is presented in Fig. 17. In both the strategies, the FFB production increases over every preceding time interval. The average percentage of increase in FFB production for every time interval in cost and DCV approach is 8.4% and 7.5%.

Fig. 18 shows the cumulative carbon emissions due to LUC for new plantation development along time intervals t0 to t10. It can be observed that carbon emissions have an increasing trend due to addition of new plantations along the time intervals. However, slope of the DCV curve is lower compared to cost approach, meaning a delay in reaching peak carbon emissions. Also, total emission from DCV approach is 141,513 tCO2 while from that of cost approach is 146,157 tCO2 which is higher by 3.28% but with no additional cost compared to DCV approach during T^Plan.

The above discussion showed the difference between conventional total cost approach and DCV approach. The DCV approach allowed to determine a planting strategy that could reduce the carbon emission, which the total cost approach could not. The following are the summary of key outputs from the developed model.

Fig. 10.Cost approach – Initial and final state of plantations.

Fig. 11.Cost approach – Total FFB production during each time interval.

(11)

Fig. 12.DCV approach – Diagrammatic presentation of the result.

Fig. 13.DCV approach – Initial and final state of plantations.

(12)

•The model addresses two main questions – which land and what time period to go for new plantation development that can result in reduced carbon emissions per unit crop output.

•Create opportunity to get better prepared with mitigation and adaptive measures to address climatic impacts.

•Aid plantation companies to plan for harvesting at plantations and production at processing facilities.

6. Conclusion

A mathematical programming model was developed to determine optimal maturity required for perennial crops (plantations), to meet the expected agro product demand. The corresponding planting period for new plantations were also determined, enabling optimal utilisation of land resources, resulting in reduced environmental impacts. The complex attributes of perennial agriculture like varying yield, time lag to maturity were modelled using yield profile of perennial crops, aiding more accurate decision making. The model was illustrated using an oil palm plantation case study. The results of the case study showed marked difference between the two optimisation objectives – minimise total cost and maximise DCV. Though both same lands were selected in both objectives, but the key differences were observed in the planting periods.

The cost approach showed better financial management in land utilisation while DCV approach exhibited slower transition to peak emissions levels and reduced carbon emissions within the planning horizon.

The carbon emissions from cost approach is 0.2339 tCO2/t of FFB and that from DCV approach is 0.2264 tCO2/t of FFB; which is a reduction of 0.0075 tCO2/t of FFB. The model can be used by decision makers in agro companies in optimum utilisation of their land pool. The DCV approach also provides scope for evaluating carbon capturing or sequestration methods for carbon management strategies. However, exclusion of Fig. 14.DCV approach - Total FFB production during each time interval.

Table 2

Optimised planting periods of new plantations.

Plantation Cost approach DCV approach

P1 Existing plantation Existing plantation

P2 Existing plantation Existing plantation

P3 3rd year 0 (i.e. at t0)

P4 0.3 year (4th month) 0 (i.e. at t0)

P5 1st year 5.5th year

Fig. 15.Contribution of plantations to the FFB requirement.

Fig. 16.Comparison of the cumulative FFB produced.

Fig. 17.Comparison of FFB production during each time interval.

(13)

carbon sequestration is a significant limitation of this work which can considered in future works. In addition to land, water resources can also be considered in optimising land utilisation for perennial crops.

CRediT authorship contribution statement

Jaya Prasanth Rajakal: Conceptualization, Methodology, Software, Writing – original draft, Writing – review & editing. Raymond R. Tan:

Validation, Writing – review & editing. Viknesh Andiappan: Concep- tualization, Methodology, Writing – original draft, Writing – review &

editing. Yoke Kin Wan: Conceptualization, Methodology, Writing – original draft, Writing – review & editing. Ming Meng Pang: Writing – review & editing, Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The authors would like to acknowledge the financial support by Taylor’s University through its grant in Taylor’s Ph.D. Scholarship Programme (TUFR/2017/001/01) and also LINDO Systems for providing academic licenses to conduct this research.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jclepro.2021.128526.

Nomenclature Abbreviation

LUC Land Use Change DCV Discounted Carbon Value NPV Net Present Value USD United States Dollar FFB Fresh Fruit Bunches CPO Crude Palm Oil

MILP Mixed Integer Linear Programming Sets

g Index for plantations

z Index for time interval within the planning horizon

i Index for the selected discrete points in yield profile of the perennial crop Parameter

Ag Area of the plantation g in hectares

T^Plan Planning horizon for which the decision maker intends to strategies planting activities tz Time intervals selected within the planning horizon

M^IN_g Maturity or age of plantation g at the initial state F^AP ’Demand for the agro product

mg,i Set of discrete points selected along the axis of abscissas on the yield profile of plantation g C^PF Conversion factor of crop to agro product in the processing facility

C^CAPEX_g Capital expenditure involved for new plantation development in USD/ha C^OPEX_g Operational cost at the plantations in USD/ha

Y Large arbitrary constant

C^LUC_g Annual emissions from unit area of the plantation gdue to LUC in tCO2/ha/year C^SC_g Social cost of carbon emissions from plantation g in USD/t CO₂

Variable

wg,i Set of discrete points generated along the axis of ordinates on the yield profile of plantation g W^IN_g Cumulative yield of plantation g at the initial state

Fig. 18.Comparison of the cumulative carbon emissions.