001.docx


 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 83, 2021 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Jeng Shiun Lim, Nor Alafiza Yunus, Jiří Jaromír Klemeš 
Copyright © 2021, AIDIC Servizi S.r.l. 
ISBN 978-88-95608-81-5; ISSN 2283-9216 

Mathematical Approach to Forecast Oil Palm Plantation Yield 
under Climate Change Uncertainties 

Jaya Prasanth Rajakala, Viknesh Andiappanb, Yoke Kin Wana,* 
aSchool of Computer Science and Engineering, Faculty of Innovation and Technology, Taylor’s university, Lakeside  
 Campus, No. 1 Jalan Taylor’s, 47500 Subang Jaya, Selangor, Malaysia. 
bSchool of Engineering and Physical Sciences, Heriot-Watt University Malaysia, 62200, Putrajaya, Wilayah Persekutuan  
 Putrajaya, Malaysia 
 yokekin.wan@taylors.edu.my 

Climate change is affecting crop yields and disrupting the global food system. Oil palm is one of the important 
vegetable oil crops and is widely cultivated in the tropical belt. Accounting the climate change effects while 
forecasting the oil palm yield is critical in building a resilient palm supply chain and ensuring food security. 
Though the productivity of oil palm plantations depends on various agroclimatic conditions and agronomic 
practices, the palm age, rainfall, and temperature are critical variables determining the yield. However, most 
works have failed to account for the age of palms. This work aims to account for the age of palms and also the 
impact of changing rainfall patterns and rise in temperature in forecasting the yield. A simple but robust 
mathematical approach is proposed to forecast yield at plantation level by accounting for the above-mentioned 
factors. An illustrative case study is solved to demonstrate the model. The results show that climate change 
effects results in 33.31 % - 8.18 % reduction in FFB yield. The proposed model allows effective planning and 
management of activities at plantations and can offset the impact of fresh fruit bunch yield uncertainties due to 
climate change effects on the downstream units of the palm supply chain.  

1. Introduction 
Oil palm is a humid tropical crop that thrives well under high rainfall and moderate temperatures. Palm oil is 
produced from the fresh fruit bunches (FFB) harvested from oil palm plantations. Palm oil production has 
increased from a mere 1.8 Mt in 1968 to 65.15 Mt in 2018 and currently contributes around 35 % of global 
vegetable oil production. It also accounts about 40 % of edible oil exports (Chong et al., 2017) and unlike other 
vegetable oils which have only regional relevance, palm oil is widely traded at the international market. Oil 
palm has positioned itself as one of the major oil crops. It has emerged as a crucial commodity in meeting 
global vegetable oil demand where a large population, especially in the developing countries, rely on cheap 
and available cooking oil. Given the significance of palm oil, any disruption in its production will not only affect 
the palm supply chain but also have large implications on global food security. 
Climate change has negative impacts on oil palm plantations (Flesis et al., 2017). The major climate change 
effects at the tropics are erratic rainfall patterns resulting in floods or drought, rise in mean temperature, new 
pests and plant diseases, etc. It is expected that the frequency and intensity of such extreme events to 
increase in the coming years (Nelson et al., 2014). Under these circumstances, forecasting the FFB yield can 
help to improve the ability to respond to disruptions caused by climate change. Also, forecasting allows 
effective planning and management of activities at downstream units in the supply chain synchronising with 
the disruption in the yield at plantations (Feng, 2016).  However, any such attempt can be successful only with 
a reasonably accurate forecast of the yield accounting for the climate change effects.  
Most of the works in forecasting the FFB yields have used either statistical (Keong and Keng, 2012), artificial 
neural network (Kartika et al., 2016) or remote sensing (Carolita et al., 2017) methods. The statistical and 
artificial neural network methods require historical data while remote sensing requires high-level satellite 
imagery. Such requirements restrict the usage of these models by decision-makers at the plantation level. 
More often these models are used for forecasting at a regional or national level. Also, these works have not 

 
 
 
 
 
 
 
 
 
 
                                                                                                                                                                 DOI: 10.3303/CET2183020 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 29/06/2020; Revised: 04/08/2020; Accepted: 06/08/2020 
Please cite this article as: Rajakal J.P., Andiappan V., Wan Y.K., 2021, Mathematical Approach to Forecast Oil Palm Plantation Yield under 
Climate Change Uncertainties, Chemical Engineering Transactions, 83, 115-120  DOI:10.3303/CET2183020 
  

115

mailto:yokekin.wan@taylors.edu.my


explicitly considered the climate change effects in forecasting the FFB yield. Oil palm is a perennial crop with a 
lifespan of 25 y – 30 y and the FFB yield from the tree varies with its age. The above-mentioned works have 
also failed to account this varying yield due to maturity.  Apart from this, previous research works studied the 
impacts of climate change effects like rainfall (Christensen et al. 2013), temperature (Paterson et al. 2015), 
sea level rise (Siwar et al. 2013), increased atmospheric carbon concentration (Long et al. 2006), pests and 
diseases (Paterson et al. 2015) independently on the FFB yield. However, none of the works accounted for 
the cumulative impact of the different climate change effects on the FFB yield. The literature analysis has 
allowed to synthesis the following research gaps, 

 Very limited works are focused exclusively on forecasting yield at plantation level.  
 The previous works did not consider the varying yield due to maturity of the plantations in forecasting  
 A comprehensive tool accounting the cumulative impacts of the different climate change effects on oil 

palm yield has not been developed.   
To address the above discussed research gaps, this paper aims to develop a simple but robust mathematical 
approach to forecast the FFB yield of plantations accounting for the age of the plantation and climate change 
effects. This work restricts in considering water deficit and rise in temperature due to their significant impact on 
yield and availability of established data. This work intends to integrate the cumulative impacts from the 
physiological (oil palm maturity) and climate change factors (rainfall and temperature) in yield forecasting as 
shown in Figure 1a.  

2. Problem statement  
The formal problem definition is as follows: Given are a set of plantations 𝑔𝑔 ∈ 𝐺𝐺 with area A𝑔𝑔 producing fresh 
fruit bunches (FFB). The FFB production from the plantation g depends on its age or maturity (𝐹𝐹𝑔𝑔,𝑡𝑡MTY) at the 
period t. Also, climate change effects like water deficit (WD𝑔𝑔,𝑡𝑡−1) and rise in temperature (𝑇𝑇𝑔𝑔,𝑡𝑡−1) have a 
significant negative impact on the FFB yield. This work aims to account these factors in forecasting the FFB 
production (𝑋𝑋𝑔𝑔,𝑡𝑡FC) from the plantations 𝑔𝑔 ∈ 𝐺𝐺 during the year t. 

3. Mathematical formulation  
3.1 Modelling oil palm yield profile  

As discussed in Section 1, the yield of the oil palm depends on its age. Typically, the yield from an oil pam 
varies every year. A yield profile plots the age of the palm against its maximum yield under optimal agro 
climatic condition as shown in Figure 1b. This section presents the mathematical technique to model Figure 1b 
and is referred to as the yield profile model.  
(a)  

 

(b)  

 
Figure 1: Illustration of a) Overview of FFB forecasting and b) Typical yield profile of an oil palm tree (Tan, 
2014) 
 
The FFB yield of an oil palm tree (𝑤𝑤) is a function of its age (𝑚𝑚) as shown in Eq(1). It can be noted that age or 
maturity is the independent variable and yield is the dependent variable. 

𝑤𝑤 = 𝑓𝑓(𝑚𝑚)  (1) 

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A set of discrete points 𝑚𝑚𝑔𝑔,𝑖𝑖 (𝑖𝑖 = 1,2,3, . . . 𝐼𝐼) are identified with 𝑚𝑚𝑔𝑔,1and 𝑚𝑚𝑔𝑔,𝐼𝐼 as the lower and upper limits.  The 
points 𝑚𝑚𝑔𝑔,𝑖𝑖 are taken along the horizontal axis as shown in Figure 2. The points 𝑚𝑚𝑔𝑔,𝑖𝑖 are identified such that to 
segmentize each linear section of the curve. It can be noted that the oil palm yield profile curve has linear 
sections or approximate linear sections from age 0 - 2, 2 - 5, 5 - 7, 7 - 9, 9 - 11, 11 - 14, 14 - 19 and 19 - 26. 
Therefore, the points 𝑚𝑚𝑔𝑔,1, 𝑚𝑚𝑔𝑔,2, 𝑚𝑚𝑔𝑔,3, 𝑚𝑚𝑔𝑔,4, 𝑚𝑚𝑔𝑔,5, 𝑚𝑚𝑔𝑔,6, 𝑚𝑚𝑔𝑔,7, 𝑚𝑚𝑔𝑔,8 and 𝑚𝑚𝑔𝑔,9 are identified at age 0, 2, 5, 7, 9, 
11, 14, 19 and 26 as shown in Figure 2.  On substituting 𝑚𝑚𝑔𝑔,𝑖𝑖  in Eq(1), corresponding yield values for each 
point can be determined, obtaining another set of discrete points referred to as 𝑤𝑤𝑔𝑔,𝑖𝑖 (𝑖𝑖 = 1,2,3, . . . 𝐼𝐼) as shown in 
Figure 2.  

 
Figure 2: Modelling oil palm yield profile 

𝑋𝑋𝑔𝑔,𝑡𝑡MTY (y) and 𝑋𝑋𝑔𝑔YLD (t) are the age and maximum FFB yield of the plantation 𝑔𝑔 ∈ 𝐺𝐺 with area 𝐴𝐴𝑔𝑔during the year 
t.  𝜌𝜌𝑔𝑔,𝑖𝑖,𝑡𝑡 is a set of variables that relates 𝑋𝑋𝑔𝑔,𝑡𝑡MTYand 𝐹𝐹𝑔𝑔,𝑡𝑡YLD as shown in Eq(2) and Eq(3). 

𝑋𝑋𝑔𝑔,𝑡𝑡MTY = �𝑚𝑚𝑔𝑔,𝑖𝑖

𝐼𝐼

𝑖𝑖=1

× 𝜌𝜌𝑔𝑔,𝑖𝑖,𝑡𝑡 ∀𝑔𝑔∀𝑡𝑡 (2) 

𝑋𝑋𝑔𝑔,𝑡𝑡YLD =  �𝑤𝑤𝑔𝑔,𝑖𝑖 × 𝜌𝜌𝑔𝑔,𝑖𝑖,𝑡𝑡

𝐼𝐼

𝑖𝑖=1

 ∀𝑔𝑔∀𝑡𝑡 (3) 

𝑋𝑋𝑔𝑔,𝑡𝑡MTY might not necessarily be amongst the selected discrete points 𝑚𝑚𝑔𝑔,𝑖𝑖. It can be any value in-between two 
adjacent 𝑚𝑚𝑔𝑔,𝑖𝑖points.  𝜌𝜌𝑔𝑔,𝑖𝑖 is constrained as shown in Eq(4) and Eq(5). 

�𝜌𝜌𝑔𝑔,𝑖𝑖,𝑡𝑡 = 1
𝐼𝐼

𝑖𝑖=1

 ∀𝑔𝑔∀𝑡𝑡 (4) 

𝜌𝜌𝑔𝑔,𝑖𝑖,𝑡𝑡 ≥ 0 ∀𝑔𝑔∀𝑡𝑡 (5) 

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However, not more than two adjacent 𝜌𝜌𝑔𝑔,𝑖𝑖,𝑡𝑡 values can be non-zero. This is achieved by introducing a new set 
of binary variables  𝜇𝜇𝑔𝑔,𝑖𝑖,𝑡𝑡 using the method previously discussed by Zhou et al. (2013) in optimising utility 
operations and is presented in Eqs(6) – (9).  

�𝜇𝜇𝑔𝑔,𝑖𝑖,𝑡𝑡 = 1
𝐼𝐼

𝑖𝑖=1

 ∀𝑔𝑔∀𝑡𝑡 (6) 

𝜌𝜌𝑔𝑔,𝑖𝑖,𝑡𝑡 − 𝜇𝜇𝑔𝑔,𝑖𝑖,𝑡𝑡 ≤ 0 ∀𝑔𝑔∀𝑡𝑡, 𝑖𝑖 = 1 (7) 

𝜌𝜌𝑔𝑔,𝑖𝑖,𝑡𝑡 − 𝜇𝜇𝑔𝑔,𝑖𝑖−1,𝑡𝑡 − 𝜇𝜇𝑔𝑔,𝑖𝑖,𝑡𝑡 ≤ 0 ∀𝑔𝑔∀𝑡𝑡, 𝑖𝑖 < 1 < 𝐼𝐼 (8) 

𝜌𝜌𝑔𝑔,𝑖𝑖,𝑡𝑡 − 𝜇𝜇𝑔𝑔,𝑖𝑖−1,𝑡𝑡 ≤ 0 ∀𝑔𝑔∀𝑡𝑡, 𝑖𝑖 = 𝐼𝐼 (9) 

The age or maturity, 𝑋𝑋𝑔𝑔,𝑡𝑡MTY is a parameter provided by the decision maker, based on which the corresponding 
maximum FFB yield 𝑋𝑋𝑔𝑔,𝑡𝑡YLD is determined. 

3.2 Modelling climate change effects on FFB yield  

As discussed in Section 1, this work accounts for two climate change induced events - water deficit and rise in 
temperature. The climate change effects usually have no immediate impact on the FFB yield. There exists a 
lag period between the period of climate change effect and the impact on the FFB yield. Typically, the lag 
period for rainfall is from 9 - 12 months while for temperature changes is 12 months (Shanmuganathan and 
Narayanan, 2012). Therefore, a lag period of 1 y is considered in this work.  
Figure 3a and Figure 3b presents the impact of water deficit (Carr, 2011) and temperature rise (Sarkar et al., 
2020) on the losses in FFB yield. Figure 3a is referred to as water deficit curve while Figure 3b as temperature 
rise curve. These relationships obtained from literature are based on experimental studies conducted on 
mature oil palms which have a potential FFB yield of 30 t/y under optimal agroclimatic conditions. This value is 
taken as the benchmark value or potential yield of oil palm and is denoted as 𝑋𝑋PL_YLD.  
The water deficit curve and temperature rise curve are modelled using the same technique presented in 
Section 3.1 and are referred to as water deficit model and temperature model. The water deficit (𝑊𝑊𝐷𝐷𝑔𝑔,𝑡𝑡−1) and 
rise in temperature (𝑇𝑇𝑔𝑔,𝑡𝑡−1) for the plantation 𝑔𝑔 ∈ 𝐺𝐺 for the year t-1 are provided as input to get the 
corresponding losses in yield,  𝑋𝑋𝑔𝑔,𝑡𝑡

LS_YLD_WDand 𝑋𝑋𝑔𝑔,𝑡𝑡
LS_YLD_T for the year t.  

(a)  

 

(b)  

 

Figure 3: Illustration on a) Impact of water deficit on FFB yield (Carr, 2011) and b) Impact of rise in 
temperature on FFB yield (Sarkar, 2020) 

3.3 FFB yield forecast  

The water deficit index (𝑊𝑊𝐷𝐷𝑔𝑔,𝑡𝑡INDEX) and temperature index (𝑇𝑇𝑔𝑔,𝑡𝑡INDEX) represent the percentage of the actual FFB 
yield with respect to the potential yield (𝑋𝑋PL_YLD). Based on the yield loss, the water deficit index and 
temperature index are estimated as shown in Eq(10) and Eq(11). 

𝑊𝑊𝐷𝐷𝑔𝑔,𝑡𝑡INDEX =
�𝑋𝑋PL_YLD−𝑋𝑋𝑔𝑔,𝑡𝑡

LS_YLD_WD�

𝑋𝑋PL_YLD
  ∀𝑔𝑔∀𝑡𝑡 (10) 

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𝑇𝑇𝑔𝑔,𝑡𝑡INDEX =
�𝑋𝑋PL_YLD − 𝑋𝑋𝑔𝑔,𝑡𝑡

LS_YLD_T�
𝑋𝑋PL_YLD

 ∀𝑔𝑔∀𝑡𝑡 (11) 

The maximum yield from the oil palm during the year t under optimal agro-climatic conditions is given by 𝑋𝑋𝑔𝑔,𝑡𝑡YLD. 
The impact of water deficit and temperature rise on the maximum yield is provided by the water deficit index 
(𝑊𝑊𝐷𝐷𝑔𝑔,𝑡𝑡INDEX) and temperature index (𝑇𝑇𝑔𝑔,𝑡𝑡INDEX). These indices are multiplied with the maximum yield to determine 
the actual yield. The forecast of the FFB production for the year t can be determined as shown in Eq(12).  

𝑋𝑋𝑡𝑡FC =  �𝑋𝑋𝑔𝑔,𝑡𝑡YLD × 𝑊𝑊𝐷𝐷𝑔𝑔,𝑡𝑡INDEX × 𝑇𝑇𝑔𝑔,𝑡𝑡INDEX
𝐺𝐺

𝑔𝑔=1

× 𝐴𝐴𝑔𝑔 ∀𝑡𝑡  (12) 

The developed mathematical model can be validated using historical data. The FFB forecast of a given year 
can be determined using the data on rainfall and temperature of the preceding year. The results from the 
model can be validated with the actual data. The accuracy of the model depends on factors like proximity of 
weather station to the plantation, accuracy of the climate variable readings, etc.  

4. Case study 
This section presents a case study to illustrate the proposed mathematical approach. It involves forecasting 
the total FFB production for a plantation company which owns plantation A, B and C for the year t. At first, the 
yield profile, water deficit curve and temperature rise curve are modelled as presented in Section 3.1 and 3.2. 
Later, the plantation age during t; water deficit and mean temperature rise values during t-1 are provided as 
input parameters. Table 1 presents the area, plantation maturity, water deficit and mean temperature rise.  
The maximum FFB yield from the plantations A, B and C are determined from the yield profile model.  
Similarly, the loss in FFB yield is determined from the water deficit and temperature rise model. Based on the 
FFB yield loss value, the water deficit index and temperature index are calculated using Eq(10) and Eq(11). 
Table 2 presents the maximum yield of the plantations at t; the water deficit and temperature index computed 
by the model. Finally, the forecast for FFB production is calculated using Eq(12). The case study which was 
solved in LINGO v18 contained 235 variables and 159 constraints with an elapsed run time less than 2 s. The 
solver was run-in a HP Pavilion x360 with Intel Core i5 8250 (1.80 GHz) processor and 8 GB RAM under a 64-
bit operating system. 

Table 1: Agroclimatic data of the plantation 

Plantation  
Area 
(ha) 

Maturity at t 
(y) 

Water deficit at t-1 
(mm) 

Temperature rise at t-1 
(℃) 

Plantation A 300 7 190 1 
Plantation B 300 16 70 0.5 
Plantation C 300 11 130 0.8 

Table 2: Yield, water deficit index and temperature rise index 

Plantation 
Potential Yield at t 
(t) 

Water deficit index Temperature rise index 

Plantation A 18 0.68 0.989 
Plantation B 23 0.93 0.999 
Plantation C 27 0.81 0.999 
 
The maximum FFB yield determined from the yield profile model for Plantation A, B and C are 5,400 t, 6,900 t 
and 8,100 t during t. Though the plantations are of the same size (300 ha), the variations in maximum possible 
yield is due to their different maturity levels. Plantation A and B with maturity of 7 and 16 y produce 33.33 % 
and 14.80 % less FFB compared to Plantation C of maturity 11 y, independent of the impact due to water 
deficit and temperature rise. The FFB forecast estimated at the Plantations A, B and C accounting for the 
climate change effects for the period t is 3,602.50 t, 6,379.02 t and 6,618.87 t. The cumulative impact of water 
deficit and temperature rise has resulted in yield drop of 33.31 %, 8.18 % and 18.29 % at plantations A, B and 
C from their maximum possible yield.  

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5. Conclusion 
This work presents a mathematical approach to forecast FFB production for plantation companies. This work 
has focused on discussing the mathematical technique to represent the relationship of plantation maturity and 
different climate change factors on FFB yield. The technique provides the flexibility to update data emerging 
from future studies. Also, other climate change effects like CO2 concentration, pest, diseases, etc can also be 
considered in forecasting by modelling their impacts using the same technique. The approach requires 
minimal data and user friendly to decision makers. The approach can aid in planning their activities like labour 
management, storage, marketing, etc. Unlike the other units in the palm supply chain, plantation is largely a 
biological unit which is highly vulnerable to disruption from climate change effects which are beyond 
management and operational intervention. This work can potentially improve the reliability and resilience of 
the palm supply change by mitigating the uncertainties in FFB production. Also, the current work can be 
extended to optimise the required plantation maturity based on the palm oil demand.  

Acknowledgment 
The authors acknowledge the academic support provided by Taylors Ph.D. Scholarship Programme 
(TUFR/2017/001/01) and technical support provided by LINDO systems. 

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