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Cocoa processing and commercialization: Processing plant
feasibility study through the use of operation research techniques
Carlos Ardila*, María Cortés*, Daniela Rodríguez*, Ivan Mura* Andrés Medaglia* Sebastián
Escobar**, Jader Rodríguez**
*Departamento de Ingeniería Industrial, Universidad de los Andes
{ca.ardila11, mf. cortes10, ld.rodriguez20, i.mura, amedagli} @uniandes.edu.co
**Centro de investigación Tibatata, Agrosavia
[email protected], [email protected]
Abstract
Cocoa harvesting, processing, transformation and commercialization involves a large amount of processes and various
interactions among them. A poorly established value chain system leads to low quality cocoa that restrain the producer
from getting high revenues in a premium cocoa market. Systematization of the main stages of the cocoa value chain
lead to standard processes and better decisions in the overall cocoa transformation process, tending to generate higher
profit. To improve cocoa transformation process and generate high operation profits, we propose an end-to-end
solution involving operation research techniques and models, including parameter estimation, optimization models
for transport and commercialization, and a simulation of the post harvesting process inside a potential cocoa
processing plant. At the core of our approach lies a set of interconnected models that use optimization methods, and
simulation. These models cover operational (transport allocation), industrial (processing plant), and financial (market
dynamics) decisions. We present a robust analysis for the cocoa value chain, primarily focusing in the potential
constriction of a processing plant in Tame, Arauca, and the systematization of processes and decisions revolving
around it. The results show a strong potential for process standardization, leading to higher profits and optimal
operation decisions with full control of input parameters that may generate uncertainty to the operation.
Keywords: Transport Allocation – Discrete Event Simulation – Price Forecasting – Agricultural
Systems – Operations Research in Agriculture
1. Introduction
Cocoa (Theobroma cacao L.) is a native species from Central and South America tropical forests
(Mororó, 2012; Müller & Valle, 2012). It is cultivated in locations between 10°𝑁 and 10°𝑆 of the
Equator, and more than 90% of the production around the globe originates in small farms. The
major producing countries are Côte d'Ivoire, Ghana and Indonesia (International Cocoa
Organization, 2013). Colombia accounts for approximately 1% of the Cocoa production
worldwide; however, different efforts have been made by the government and the private sector
to increase the production and promote Colombia’s competitiveness internationally (Oxford
Business Group, 2014). Cocoa production in Colombia is concentrated in Santader, which
accounts for 25% of country’s production, and is followed by Nariño with 11%, Antioquia with
10% and Arauca with 9% (Gobierno Digital Colombia, 2017).
The varieties of Cocoa trees are classified in three broad categories: Criollo, Forastero and
Trinitario. The Forastero category produces the beans with strongest flavor and it accounts for
85% of the world’s production. The Criollo category usually produces very high-quality Cocoa
beans, which are aromatic and lack bitterness. This category represents less than 3% of the
world’s Cocoa production. Finally, the Trinitario trees are hybrids of the above-mentioned types,
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and represent about 12% of the world's production. They are mostly found in the Caribbean, in
Venezuela and in Colombia (The Chocolate Society, 2010).
Pods that contain Cocoa seeds grow in the branches of the trees. In Arauca, the farmers or
smallholders open the pods to extract the wet Cocoa seeds and, after this, they carry out the post-
harvest process in their terrains. First, the seeds are piled together in boxes for micro-organisms
to start the fermentation process, in which chemical reactions that cause the flavor and color to
develop take place. Afterwards, Cocoa beans are dried, either with sun drying or artificial drying,
in order to reduce the moisture content to about 7%. Then, Cocoa dry beans may be stored and
sold in the market (International Cocoa Organization, 2012).
The market classifies the dry beans of Cocoa into two categories: fine or flavor, and bulk Cocoa
beans. The difference between these market categories relies on the flavor and chemical
characteristics, color, degree of fermentation, drying and acidity (Internatonal Cocoa
Organization, 2017).
The fine or flavor Cocoa accounts for just 5% of the worldwide yearly production of Cocoa beans,
and Latin America and the Caribbean regions produce about 80% of the world fine or flavor
Cocoa. The main consumer market of fine or flavor Cocoa consists in the Western Europe
countries, where chocolate manufacturers have premium quality chocolate products that require
fine or flavor Cocoa (International Cocoa Organization, 2013). It is worth mentioning that the
price of fine or flavor Cocoa is higher than the one of bulk Cocoa, as the first one usually
commands a premium over London terminal markets. Fine or flavor Cocoa market has
experienced the greatest growth through years, being motivated by changing tendencies of
consumers’ behavior. Demand for healthier chocolate has been increasing, along with demand
for chocolate with particular organoleptic properties such as floral, fruity or caramel flavors. The
premium Cocoa market offers greater development opportunities and benefits, both in monetary
and non-monetary terms, compared to the bulk Cocoa market. Fine or flavor Cocoa market
prices are not affected by interactions in stock markets because they are determined by the result
of a bargaining process, making it highly variable and ranging to premium prices of over $1,000
USD per ton sold (Ríos, Ruiz, Lecaro, & Rehpani, 2017) (Internatonal Cocoa Organization, 2017)
Previously mentioned information suggests that post harvesting transformation should be
focused on fine flavor Cocoa processing, controlling conditions in concordance with quality
standards determined by the market. Consequently, a diverse variety of factors significantly
affect quality and homogeneity between processed batches.
Generally, fine or flavor Cocoa beans come from Criollo or Trinitario Cocoa-tree varieties, while
bulk Cocoa beans are produced by Forastero trees. However, flavor and quality are also
significantly related to other factors, such as the degree of fermentation, the acidity, the
percentage of impurities, and the degree of drying (Internatonal Cocoa Organization, 2017).
Industrial processing is also fundamental in the transformation from Cocoa beans to chocolate,
especially the roasting process where a vast majority of organoleptic features are developed
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(Lima, Almeida, Nout, & Zweitering, 2011). This combination of factors substantially depends on
the post-harvest processing of the Cocoa fresh fruits.
However, in Arauca, Colombia, smallholders are the ones in charge of the fermentation stage,
which is considered the main stage of flavor and scent development in the whole post harvesting
process. Due to the lack of adequate fermentation methods, the process is poorly made, without
any kind of control over external conditions. Therefore, Cocoa beans may have quality anomalies
caused by diseases, poor handling, bad fermentation or inadequate drying, among others. For
this reason, a particular concern to chocolate manufacturing companies is the decline in quality
of the Cocoa beans, due mainly to the imperfect post-harvesting procedures (International Cocoa
Organization, 2001), thus reducing the possibilities of participating in hi-quality market
segments (Beg, Ahmad, Jan, & Bashir, 2017).
It is important to note that post harvesting transformation has not been systematized in any
Cocoa producing country. The vast majority of processing countries produce hi quality Cocoa,
seeking new distinctive features due to the change in consumer preferences that are willing to
pay a higher price in return to the product’s unique flavor. However, commercialization
dynamics in Colombia are based on bulk Cocoa, mainly focusing on heterogeneous Cocoa
transactions. Therefore, differentiation value is lost, as well as the opportunity for smallholders
to participate in premium markets. The whole problem resides in the lack of incentives for
smallholders because there is no extra compensation for producing fine flavor Cocoa beans with
hi quality.
Owing to the previously mentioned information, a Cocoa producing region needs to be able to
regularly produce hi quality Cocoa, keeping an appropriate processing volume, especially fine
flavor Cocoa. Consequently, the construction of a processing center in Tame, Arauca is desirable,
to standardize and control the Cocoa post-harvest processing for producing dry Cocoa beans
with a more reliable and consistent quality. In fact, the construction or a processing plant will
allow a better management of environmental factors that affect fermentation and drying, and
will therefore improve the flavor profiles of beans.
For this reason, the objective of this work is to study the feasibility of constructing the proposed
Cocoa processing plant in the municipaly of Tame. We divided this study in three phases. First,
we developed a transport allocation model that established the daily routes for the collection of
Cocoa in the different villages of Tame, and determines the most favorable way of transporting
Cocoa (in the form of pods or seeds), in terms of logistic costs and quality aspects. Then, we built
a discrete-event simulation model (DES) for representing the post-harvest process inside the
plant, taking into account Cocoa seeds’ perishability. The simulation model allowed us to specify
the requirements for the plant design, for instance, the number of workers and machinery
maintenance frequency, but specially integrates processes related transformation from Cocoa
seeds to dry beans being strictly related to the efficiency of both bulk and fine flavor Cocoa….
The model is also useful to estimate the production yield of dry Cocoa beans and overall
performance metrics to analyze the viability of the project. Finally, we developed a Mixed Integer
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Lineal Programming (MINLP) to determine the best quantities and moments for selling bulk
Cocoa in order to cover the periodical expenses of the plant’s operation along with a
systematization of Cocoa selling process responding to market values and dynamics. Along with
a profitability analysis of Cocoa processing, the model incorporates building and operation
investment to guarantee a robust analysis. We estimated the parameters for the three stages with
data collected in Tame, Arauca, Colombia.
This paper is organized as follows: section 2 presents literature on previously developed models
in crop harvesting and agricultural processing planning. Section 3 briefly describes the proposed
methodology. Section 4 presents the parameter estimation, implementation steps and
summarizes our results. Section 5 specifies the information and parameters needed before using
our models as a decision-making tool. Concluding remarks and suggested future work are
presented on section 6.
2. Literature review
Agriculture has been a main focus area for operations research (OR) techniques (Higgins, et al.,
2010). According to Weintraub & Romero (2006), agriculture is considered one of the fields in
which OR was first applied. Since 1950, linear programming has been used to optimize the
complete agri-business supply chain in different fields and diverse crop varieties. Aside from the
wide use of linear programming, operations research provides other modeling paradigms
applicable to agriculture. Lately, as stated by Ahumada and Villalobos (2009), as well as Borodin
et. al. (2016), the supply chain of agricultural products has been drawing greater attention.
Operations Research methods commonly used in an agricultural context are linear programming
(LP), dynamic programming (DP), mixed-integer programming (MIP), stochastic programming
(SP), stochastic dynamic programming (SDP), simulation, metaheuristics, and forecasting (Plà-
Aragonés, 2015). LP and MIP have been extensively used in planning and transportation as stated
by Bjørndal et. al. (2012), Buchet (2017) and Plà-Aragonés (2015). For incorporating the
stochasticity of supply chains, simulation models have been applied in several agricultural
planning problems. For instance, discrete-event simulation (DES) was used to model rice-
harvesting process coordination (Busato, 2015) and a vegetable supply chain (Yates, 2014).
Nevertheless, few models have been developed to evaluate and represent the post-harvest
processing of agricultural products. Tsubone et al. (1983) developed a multipurpose
mathematical model to determine a production plan for a processing line in which a perishable
agriculture raw material was converted into a final product. The model aimed to minimize the
worker’s idle time and the inventory levels or raw and final products. For the specific case of
Cocoa, Mujica Mota, El Makhloufi, De Bock, and Scala (2018) developed a discrete event
simulation model to analyze the supply chain of Cocoa products in Côte d’Ivoire. The authors
simulated the transportation of Cocoa dry beans from the farmers or cooperatives to the grinders,
where beans are transformed into Cocoa butter. Afterwards, they simulated the posterior sea
transportation to the final center of shipment. However, to the best of our knowledge, no
previous model has been proposed to evaluate the post-harvest operation of Cocoa in processing
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centers, considering Cocoa seeds’ perishability and using parameters estimated with Colombian
data.
On the other hand, price forecast has been a recurrent topic for operational research techniques,
ranging from time series forecast of electricity prices (Nogales, Contreras, Conejo, & Espinola,
2002), going through financial forecasts using support vector machines (Kim, 2003) and reaching
high complexity predictions such as the stock price prediction model using neural networks that
Kazuhiro et. al. (1998) proposed. In the agricultural field, forecasting takes a predominant role in
every stage of the value chain, such as price information retrieving and analysis through data
mining techniques (Kaur, Heena, & Kundra, 2014). Moreover, Kantanantha et. al. (2010) did a
yield and price forecasting using predictive models and principal component analysis. However,
optimization models for determining the best strategic selling response to market price changes
applied to the agri-food value chain problems have not being developed. Studies of this type of
problems have been conducted in other fields like the electricity spot market and the optimal
reaction of a thermal unit to price changes (Arroyo & Conejo, 2000).
3. Methodology
The proposed approach that deeply studies the feasibility of the construction of the processing
plant in Tame, Arauca, is comprised of three connected stages, as shown in Figure 1.
Figure 1. Three stage approach with interconnected models for the processing plant feasibility analysis.
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The first stage corresponds to the Cocoa transport model, which establishes the daily Cocoa
harvesting routes between the villages and the processing plant, in order to determine the best
way to transport the Cocoa (pods or seeds) according to transport costs. Knowing the best
transport policy, the next stage is to understand the process inside the plant, for which a discrete
event simulation was done. The simulation model takes the amount of Cocoa brought to the
plant as an input, simulates the whole production process and determines a feasible and tentative
number of workers, a production yield of processed Cocoa and overall performance metrics to
analyze the viability of the project. Finally, resides the financial feasibility stage, exhibiting a
mixed integer lineal optimization model which main purpose is to determine the selling times
and quantity for Bulk Cocoa, to cover the periodical expenses and maintain the plant operating
until a 25 ton batch of fine or flavor Cocoa can be completed, along with the minimum operating
capital needed to sustain the plant, and evaluating possible scenarios by varying parameters so a
policy recommendation can be made, for improving the operation and its profitability. Each of
the previously mentioned stages has an underlying parameter estimation process. The
interconnected model results provide a whole view of the feasibility of the project from different
perspectives.
4. Solution approaches, data processing and results
4.1. Transport Allocation Model
The Cocoa transport model establishes the daily Cocoa harvesting routes between the villages
and the processing plant, in order to establish which is the best way to transport Cocoa: in the
form of pods or seeds, according to transportation costs and quality.
The proposed approach that resolves the Transport Assignation Model consists of 3 phases. The
first phase consists in the identification, collection and/or estimation of required data such as
the geographic location of the villages, productivity, amount of vehicles needed, among others
(see section 4.1.1). In the second phase we develop linear optimization models aimed at finding
daily routes that minimize transportation costs, and we present an analysis of the results
obtained from these models (see section 4.1.2). The last phase consists in the development of a
tool that shows the transport costs associated with the daily Cocoa collection routes.
4.1.1. Parameter estimation
This section describes our methodology for collecting and estimating input parameters for the
Transport Assignation Model.
Time and spaces parameters
Taking into account the villages served in Fortul and Tame, we estimate the geographic location
of each village using information from Agustín Codazzi Geographic Institute (sp. IGAC)
(Instituto Geográfico Agustín Codazzi, n.d.) and the Geo-portal of the National Administrative
Department of Statistics (sp. DANE) (DANE, n.d.). With this information we were able to map
the estimated location of each village and of the processing plant. Figure 2 graphs the respective
polygon of each area.
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Figure 2. Geographic location of each village
The geographic location allows us to establish the distance and travel time among the villages,
and between them and the processing plant (“My Maps,” n.d.). It is important to emphasize that
it is not possible to estimate a constant speed due to the type of roads in this department;
secondary and tertiary, which makes the route depend directly on the conditions of each road.
Cocoa production
The production of Cocoa beans in Arauca corresponds to the number of tons that this
department produces annually. Two main factors affect this productivity: the yield of Cocoa per
plant depending on the seasonality of the harvest, and the presence of diseases in the pods. We
estimate Cocoa productivity for these municipalities according to information provided by the
Ministry of Information and Communication Technology (sp. MinTic) and its Open Data
program (“producion cacao por departamento | Datos Abiertos Colombia,” n.d.).
Graph 1. Annual production of Cocoa beans
In Graph 1 we can observe that, in average, 1640 tons of Cocoa beans are produced annually in
Tame, while in Fortul 610 tons are produced. The amount of produced Cocoa beans correspond
to 27 producers of Tame and 24 of Fortul. The producers, in this project will be grouped by
villages; small territorial groups that conform a municipality. This, due to their condition of
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active members of Coopcacao, cooperative involved in the development of this project.
Therefore, we obtain 17 producer groups (villages) in Tame and 12 in Fortul, for a total of 29
villages that we will be studied in this project.
Thus, to determine the amount of fresh Cocoa seeds produced by these two municipalities, we
assume that for each kilogram of Cocoa seeds, 0.3 kilograms of Cocoa beans are produced after
the post-harvest process (CNA, 2016). On the other hand, in order to determine the amount of
Cocoa produced in pods, we assume that for every 5.34 pods, one kilogram of Cocoa seeds is
produced (Caligiani et al., 2016). After obtaining the annual amount of Cocoa in seeds and pods
produced by these municipalities, we estimate the annual production of each village and then
the weekly production in kilograms of seeds and in number of pods.
Since the project for Arauca wishes to build a processing plant with a capacity of 6 tons per week,
we assume that it processes 4% of the Cocoa production in seeds and on the pods produced
weekly from each village. Therefore, the two factors that affect Cocoa productivity mentioned
above are not taken into account in this model, we assume that the amount of Cocoa entering
the plant has been selected to prevent the entry of unfit Cocoa, i.e. diseases.
Quality: maximum transportation time
This parameter corresponds to the maximum time that seeds and pods can last being transported
before the precursor agents of flavor and aroma change significantly due to the fermentation
process. Durán (2010) and Afoakwa et al., (2015) states that this time is appropriate up to four
hours for seeds and seven days for pods. However, for this model we use a time of 3 hours and 3
days respectively in order to give the plant some time to enlist the Cocoa.
4.1.2. Solution Approach
This section describes thoroughly the Transport Assignation Model we proposed for the
methodology described in Figure 1.
Transport assignation model
To begin with, we propose a linear optimization model in charge of routing Cocoa-producing
villages daily. To carry out this model, we generate two interconnected sub-models in charge of
distributing the villages between the working days and their daily routing according to
transportation costs, respectively.
Graph 2 and Graph 3 show the obtained results from the first sub-model. As we observe, the
amount of collected Cocoa, in pods and seeds, shows great variations between working days. In
Graph 2, the discontinuous line shows the average amount of Cocoa that must be collected daily,
and for example, we observe that on Thursdays and Saturdays, 45% more and 27% less pods are
collected, respectively. This behavior is similar for the case of seeds transportation.
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Graph 2. Number of pods picked up daily
Graph 3 Kilograms of seeds picked up daily
To reduce the difference between the maximum and minimum amount of daily collected Cocoa,
we added a sub-model that balances the amount of Cocoa collected and the number of villages
visited daily. Diagram 1 shows the three-step process to solve the Transport Assignation Model.
Diagram 1. Transport allocation model stages
Stage 1. Balance the amount of collected Cocoa and the number of daily visited villages
In the first stage, we developed a load balancing problem between the different collection days,
with the aim of reducing to the minimum the difference between the maximum and minimum
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load of Cocoa (pods and seeds) collected daily. We also seek to balance the number of visited
villages.
To carry out this model, we generate as many groups of villages as plant working days, in order
to group the villages in which the sum of their Cocoa supply is balanced. Each group has a main
village (centroid) which is supposed to collect all the Cocoa offered by the group, this ultimately
represents the villages and the amount of Cocoa collected each operational day of the plant.
Figure 3 shows an example of what was done by this model, being the blue box Tame processing
plant. The red triangles correspond to each group's centroids and the gray circles are the villages
attached to each group. In other words, each centroid corresponds to a working day of the plant
and the villages that must be visited that day.
Figure 3. Daily pick up balance
To develop this model, being 𝛿, 𝜗 the set of possible centroids of each group of villages denoted
by 𝑖 ∈ 𝛿 and the set of villages including the plant denoted by 𝑗 ∈ 𝜗, respectively. The 𝜇𝑗𝑘
parameter corresponds to the village's Cocoa production 𝑗 ∈ 𝜗; where k represents the way in
which it transports the Cocoa: pods or seeds. On the other hand, 𝜃𝑘 denotes the amount of
weekly processed Cocoa in the plant. The α parameter corresponds to the number of working
days in the processing plant. The binary variable 𝑥𝑖,𝑗 takes value of 1 if the 𝑗 ∈ 𝜗 village is visited
by the 𝑖 ∈ 𝛿 centroid; it takes value of 0, otherwise. The binary variable 𝑦𝑖 takes value of 1 if the
𝑖 ∈ 𝛿 centroid is activated; otherwise it takes value of 0. The 𝑟𝑖𝑘 variable represents the amount
of collected Cocoa in each 𝑖 ∈ 𝛿 centroid; the 𝑛𝑖 variable represents the amount of villages
attached to each 𝑖 ∈ 𝛿 centroid. Lastly, the auxiliary 𝑧𝑟 and 𝑧𝑛 variables allow the model to
balance the amount of Cocoa collected and the villages visited each day, respectively. The
components of the balance model are the following:
min 𝑧𝑟 + 𝑧𝑛, (1)
𝑠.𝑡.,
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∑ 𝑦𝑖
𝑖∈𝛿
= 𝛼, (2)
∑ 𝑥𝑖,𝑗
𝑖∈𝛿
= 1 ∀ 𝑗 ∈ 𝜗, (3)
𝑥𝑖,𝑗 ≤ 𝑦𝑖 ∀𝑖 ∈ 𝛿, ∀ 𝑗 ∈ 𝜗, (4)
∑𝜇𝑗
𝑘 ∗ 𝑥𝑖,𝑗
𝜃𝑘 = 𝑟𝑖𝑘
𝑗∈𝜗
∀𝑖 ∈ 𝛿, (5)
∑𝑥𝑖,𝑗
|𝜗|𝑗∈𝜗
= 𝑛𝑖 ∀𝑖 ∈ 𝛿, (6)
𝑧𝑟 ≥ 𝑟𝑖𝑘 ∀𝑖 ∈ 𝛿, (7)
𝑧𝑛 ≥ 𝑛𝑖 ∀𝑖 ∈ 𝛿, (8)
𝑥𝑖,𝑗 ∈ {0,1} ∀ 𝑖 ∈ 𝛿, ∀𝑗 ∈ 𝜗, (9)
𝑦𝑖 ∈ 0,1 ∀𝑖 ∈ 𝛿, ∀𝑗 ∈ 𝜗, (10)
𝑟𝑖𝑘 ∀𝑖 ∈ 𝛿, (11)
𝑛𝑖 ∀𝑖 ∈ 𝛿, (12)
𝑧𝑟 ≥ 0 (13)
𝑧𝑛 ≥ 0 (14)
Where the target function (1) minimizes the sum of the maximum load of collected Cocoa and
the maximum number of villages served daily. Constraint (2) forces to activate centroids
according to the working days in the plant. In a similar way, the set of constraints (3) guarantees
that all the villages must be visited. Constraints (4) guarantee that a village can be grouped to a
centroid only if it is activated. The sets of constraints (5) and (6) normalize the total amount of
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collected Cocoa in a centroid and the number of villages that are grouped to it, respectively.
Constraints (7) and (8) get the maximum total amount of collected Cocoa from all centroids and
the maximum number of villages grouped to them. Lastly, the set of constraints (9) to (14)
specify the nature of the decision variables.
Stage 2. Minimization of travel distances
In the second stage, in general, this model determines which villages should be visited daily
taking into account the balance considerations resolved by the previous model and the
minimization of distances. Therefore, it receives from the previous model the amount of Cocoa
expected to be collected daily; in kilograms of seeds and in number of pods, and the number of
villages expected to be visited daily. In this way, a variation of ± 15% of the expected amount of
Cocoa collected and ±1 village served daily is allowed.
Like the previous model, we let 𝛿 be the set of possible centroids of each group of villages denoted
by 𝑖 ∈ 𝛿 and 𝜗 be the set of villages including the plant denoted by 𝑗 ∈ 𝜗. The parameters used
in this model are 𝜇𝑗𝑘 for each village 𝑗 ∈ 𝜗, α; previously described, ∆𝑘 which represents the
expected amount of Cocoa collected, ∇ which specifies the expected number of villages visited
daily; the last two are the result of the previous model. At last, the 𝛽𝑖,𝑗 parameter corresponds to
the distance between the 𝑖 ∈ 𝛿 centroid and the 𝑗 ∈ 𝜗 village. The binary variable 𝑥𝑖,𝑗 has a value
of 1 if the 𝑗 ∈ 𝜗 village is visited by the 𝑖 ∈ 𝛿 centroid; it has a value of 0, otherwise. The 𝑦𝑖 binary
variable takes the value of 1 if the 𝑖 ∈ 𝛿 centroid is activated; otherwise, it takes a value of 0. The
components of the distance minimization model are the following:
∑ ∑ 𝑥𝑖,𝑗 ∗ 𝑑𝑖,𝑗
𝑗∈𝜗𝑖∈𝛿
(15)
𝑠.𝑡.,
∑ 𝑦𝑖
𝑖∈𝛿
= 𝛼, (16)
∑ 𝑥𝑖,𝑗
𝑖∈𝛿
= 1 ∀ 𝑗 ∈ 𝜗, (17)
𝑥𝑖,𝑗 ≤ 𝑦𝑖 ∀𝑖 ∈ 𝛿, ∀ 𝑗 ∈ 𝜗, (18)
∆𝑘 ∗ 0.85 ∗ 𝑦𝑖 ≤ ∑ 𝑥𝑖,𝑗 ∗ 𝜇𝑗𝑘
𝑗∈𝜗
∀𝑖 ∈ 𝛿, (19)
∆𝑘 ∗ 1.15 ∗ 𝑦𝑖 ≥ ∑ 𝑥𝑖,𝑗 ∗ 𝜇𝑗𝑘
𝑗∈𝜗
∀𝑖 ∈ 𝛿, (20)
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𝛻 ∗ 𝑦𝑖 − 𝑦𝑖 ≤ ∑ 𝑥𝑖,𝑗
𝑗∈𝜗
∀𝑖 ∈ 𝛿, (21)
𝛻 ∗ 𝑦𝑖 + 𝑦𝑖 ≥ ∑ 𝑥𝑖,𝑗
𝑗∈𝜗
∀𝑖 ∈ 𝛿, (22)
𝑥𝑖, 𝑗 ∈ {0,1} ∀ 𝑖 ∈ 𝛿, ∀𝑗 ∈ 𝜗, (23)
𝑦𝑖 ∈ {0,1} ∀𝑖 ∈ 𝛿, ∀𝑗 ∈ 𝜗, (24)
Where the objective function (15) minimizes the distance traveled from each centroid to the
villages grouped together plus the distance between the plant and the activated centroids. The
group of constraints (16), (17) and (18) are identical to the constraints (2 to 4) of the previously
described model. Constraints (19) and (20) balance the total amount of Cocoa collected each
day, considering a variability of ±15% of the result of the previous model. In the same way, the
group of restrictions (21) and (22) balance the total number of villages visited daily allowing a
variability of ±1 village. Finally, the set of restrictions (23) and (24) specifies the nature of the
decision variables.
Stage 3. Vehicle routing problem (VRP) with time windows and capacity
The third stage generates the daily routes that must be carried out to collect all the Cocoa
produced by the villages of Fortul and Tame, this in function of the transportation costs. Once
the daily routes are established, we can determine the best way to transport the Cocoa; pods or
seeds depending on the objective function. This model is based on a typical vehicle routing
problem (VRP) with several vehicles with limited and constant capacity in charge of collecting
Cocoa from each served village; with the variation to be considered is a window of time to return
to the plant (VRPTW).
Like the previous models, we let 𝜗𝑑 be the set of villages including the plant denoted by 𝑖, 𝑗 ∈ 𝜗𝑑 ;
where d represents the day in which we will execute the model and 𝜕 the set of vehicles available
to perform the transport process, denoted by l∈∂. The parameters used in this model are 𝜇𝑖𝑘,𝛼,𝛽𝑖,𝑗
for each 𝑖, 𝑗 ∈ 𝜗𝑑 village described above. On the other hand, the 𝜏𝑖,𝑗parameter corresponds to
the travel time between the 𝑖 ∈ 𝜗𝑑 village and the 𝑗 ∈ 𝜗𝑑 village. The 𝛾𝑘parameter represents
the maximum time that the Cocoa can last being transported before reaching the plant again.
Likewise, the 𝜆𝑘 parameter corresponds to the limited capacity of the vehicles used for the
transport process; this is constant for all of them. In the same way, ԏ corresponds to the estimated
time it takes to load a package of Cocoa in the vehicle. The 𝜑𝑖𝑘 parameter corresponds to the
number of packages that must be collected in the 𝑖 ∈ 𝜗𝑑 village, we estimate this parameter as
in the following way:
14
𝜑𝑖𝑘 = ⌈
𝜇𝑖𝑘
𝑏⌉, (25)
Where 𝑏 corresponds to an estimated amount of pods and seeds within each sack. Lastly, the 𝜎
parameter corresponds to the cost per minute of using a vehicle for the route.
The binary variable 𝑥𝑖,𝑗,𝑙 has a value of 1 if the route between the 𝑖 ∈ 𝜗𝑑 village and the 𝑗 ∈ 𝜗𝑑
village belongs to the route formed by the 𝑙 ∈ 𝜕 vehicle; otherwise, it has a value of 0. The 𝑦𝑖,𝑙𝑘
variable represents the amount of Cocoa transported in the 𝑙 ∈ 𝜕 vehicle before reaching the 𝑖 ∈
𝜗𝑑 village. Lastly, the 𝑤𝑖,𝑙 variable corresponds to the time of arrival at the 𝑖 ∈ 𝜗𝑑 village using
the 𝑙 ∈ 𝜕 vehicle. The components of this model are the following:
min ∑ ∑ ∑ 𝑥𝑖,𝑗,𝑙 ∗ (𝜏𝑖,𝑗 + ԏ ∗ φ𝑗k
𝑙∈𝜕𝑗∈𝜗𝑑𝑖∈𝜗𝑑
) ∗ 𝜎
(26)
𝑠. 𝑡.,
∑ ∑ 𝑥𝑖,𝑗,𝑙
𝑙∈𝜕𝑗∈𝜗𝑑
= 1 ∀𝑖 ∈ 𝜗𝑑\{𝑃𝑙𝑎𝑛𝑡}, (27)
∑ ∑ 𝑥𝑖,𝑗,𝑙
𝑙∈𝜕𝑖∈𝜗𝑑
= 1 ∀𝑗 ∈ 𝜗𝑑\{𝑃𝑙𝑎𝑛𝑡𝑎} (28)
∑ 𝑥𝑃𝑙𝑎𝑛𝑡,𝑗,𝑙
𝑗∈𝜗𝑑
≤ 1 ∀𝑙 ∈ 𝜕, (29)
∑ 𝑥𝑖,𝑃𝑙𝑎𝑛𝑡,𝑙
𝑖∈𝜗𝑑
≤ 1 ∀𝑙 ∈ 𝜕, (30)
∑ 𝑥𝑖,𝑗,𝑙
𝑖∈𝜗𝑑
− ∑ 𝑥𝑗,𝑖,𝑙
𝑖∈𝜗𝑑
= 0 ∀𝑗 ∈ 𝜗𝑑 , ∀𝑙 ∈ 𝛿, (31)
𝑤𝑖,𝑙 ≤ 𝛾𝑘 ∀𝑖 ∈ 𝜗𝑑 , ∀ 𝑙 ∈ 𝜕 (32)
𝑦𝑖,𝑙𝑘 ≤ 𝜆𝑘 ∀𝑖 ∈ 𝜗𝑑 , ∀ 𝑙 ∈ 𝜕 (33)
𝑤𝑗,𝑙 ≥ 𝜏𝑃𝑙𝑎𝑛,𝑗 − 𝑀(1 − 𝑥𝑃𝑙𝑎𝑛𝑡,𝑗,𝑙) ∀𝑗 ∈ 𝜗𝑑 , 𝑙 ∈ 𝜕 (34)
𝑤𝑗,𝑙 ≥ 𝑤𝑖,𝑙 + ԏ ∗ φ𝑖k + 𝜏𝑖,𝑗 − 𝑀(1 − 𝑥𝑖,𝑗,𝑙) ∀𝑖 ∈ 𝜗𝑑 \{𝑃𝑙𝑎𝑛𝑡}, ∀𝑗 ∈ 𝜗𝑑 , ∀𝑙 ∈ 𝛿, (35)
15
Where the target function (26) minimizes the total daily transportation costs associated with
the time each vehicle uses. The set of constraints (27) and (28) forces the existence of an
entrance and an exit by some route in every village, respectively. Restrictions (29) and
(30) ensure that each route leaves the processing plant and re-enters at the end of its journey,
respectively. The set of constraints (31) shapes the equilibrium equations and force each route
into and out of the parcel (if visited). Restrictions (32) and (33) define the time limit and carrying
capacity in terms of the amount of transported Cocoa on each route, respectively. On the other
hand, the restrictions set (34) determines the accumulative transport time of each route from
the plant to the first village visited; while the restrictions set (35) accumulate the travel time of
each route to a particular village. In a similar way, restrictions (36) accumulate the amount of
Cocoa transported on each route from the plant to the first village visited, while restrictions
(37) accumulate this amount to any particular village. Lastly, restrictions (38), (39) and
(40) specify the variables' nature
4.1.3. Output analysis
Graph 4 allows us to compare the amount of Cocoa in pods that the plant receives daily when a
sub-model of balance (bars) is done and when not (continuous line) is done. In this way, we can
evidence that by performing a sub-model of balance we guarantee that the plant receives daily a
similar amount of Cocoa to be processed and therefore, its occupation will be homogeneous over
the course of the week. On the contrary, if we do not make a sub-model of balance, the amount
of Cocoa pods received daily the plant is unequal causing days with a greater occupation than
others.
𝑦𝑗,𝑙𝑘 ≥ 𝜇𝑃𝑙𝑎𝑛𝑡
𝑘 − 𝑀(1 − 𝑥𝑃𝑙𝑎𝑛𝑡,𝑗,𝑙) ∀𝑗 ∈ 𝜗𝑑 , 𝑙 ∈ 𝜕 (36)
𝑦𝑗,𝑙𝑘 ≥ 𝑦𝑖,𝑙
𝑘 + 𝜇𝑖𝑘 − 𝑀(1 − 𝑥𝑖,𝑗,𝑙) ∀𝑖 ∈ 𝜗𝑑 \{𝑃𝑙𝑎𝑛𝑡}, ∀𝑗 ∈ 𝜗𝑑 , ∀𝑙 ∈ 𝛿 (37)
𝑥𝑖,𝑗,𝑙 ∈ {0,1} ∀𝑖 ∈ 𝜗𝑑 , ∀𝑗 ∈ 𝜗𝑑 , ∀𝑙 ∈ 𝛿 (38)
𝑦𝑖,𝑙𝑘 ≥ 0 ∀𝑖 ∈ 𝜗𝑑 , ∀ 𝑙 ∈ 𝜕, (39)
𝑤𝑖,𝑙 ≥ 0 ∀𝑖 ∈ 𝜗𝑑 , ∀ 𝑙 ∈ 𝜕, (40)
16
Graph 4. Number of pods picked up daily
Also, Graph 5 allows us to compare the amount of Cocoa seeds that the plant receives daily when
a sub-model balance is made and when not. As we can see, when the amount of Cocoa that
reaches the plant is not balanced the difference between the maximum and minimum amount
of collected Cocoa is wide in comparison to a balanced condition. For example, on Thursday the
plant receives around 2400 kilograms of Cocoa seeds, while on Saturday it only receives around
380 kilograms; when the load is not balanced.
This not only causes the plant on certain days to have a higher occupation, but also generates
loss of Cocoa quality. As previously mentioned, Cocoa seeds only have one hour to be processed
once they reach the plant. Therefore, if a large quantity of Cocoa arrives that day, the seeds must
wait longer than allowed, thus compromising the quality of the Cocoa processed in the plant.
Graph 5 Kilograms of seeds picked up daily
17
On the other hand, Figure 4 allows us to visualize the villages that must be attended daily in
order to minimize the distances between them and the plant. As previously mentioned, this
grouping of villages was done allowing a variability of 15% of the expected amount of Cocoa
collected, in its two forms and more or less a village of the expected.
Figure 4. Daily visited villages map
Figure 5 and Figure 6 we can visualize the daily routes that must be made on Friday to transport
the Cocoa in seeds and pods, respectively, from each of the villages to the processing plant. These
daily routes minimize transportation costs and ensure that the quality of the Cocoa is not affected
by the time of exposure of the seeds to the environment.
These figures correspond only to one working day of the plant as an example.
Figure 5. Daily routes for the transport of Cocoa seeds on Friday.
In Figure 5 we can visualize the two routes that must be carried out on Fridays if the Cocoa is
transported in seeds. Two routes are generated this day due to the window of time that the
Cocoa seeds have (3 hours).
18
Figure 6. Daily routes for transporting Cocoa in pods on Friday.
In the same way, in Figure 6 we can observe the three routes that must be carried out on Fridays
if the Cocoa is transported in pods. These three routes are generated due to the load capacity of
the vehicles used to transport Cocoa. One kilogram of pods yields approximately 0.20 kilograms
of Cocoa beans (Caligiani et al., 2016).Therefore, more vehicles are needed to transport Cocoa in
pods if the same type of vehicle is assumed to transport Cocoa; as is the case in this model.
Finally, we can compare the daily transport costs associated with harvesting Cocoa pods and
seeds, shown in the Graph 6 . As we can see, transporting Cocoa in pods incurs higher daily costs
compared to transporting Cocoa in seeds. In other words, the best way to transport Cocoa from
the villages to the plant is in seeds due to lower daily transport costs.
Graph 6. Daily cost of transportation
19
The behavior of this graph is determined by the amount of Cocoa that is collected daily in the
villages of Fortul and Tame. In Graph 4 and Graph 5 we can observe that the days that more
Cocoa is collected(in pods and seeds) are Wednesdays when the load is balanced. Therefore, the
greater the amount of Cocoa collected, the greater the number of routes. In this way, more
vehicles are used thus increase transportation costs.
Further, Graph 7 and Graph 8 allow us to visualize the number of vehicles required to transport
Cocoa in each of its two presentations and the percentage of occupation of these vehicles. This
information allows us to understand why the Cocoa transported in seeds has lower
transportationcosts.
Graph 7 Percentage of vehicle capacity occupied in seed transport.
Graph 8 Percentage of vehicle capacity occupied in pods transport.
20
As previously mentioned, it is necessary to have a greater number of vehicles when transporting
Cocoa in pods compared to Cocoa in seeds. This is due to the weight ratio of these two Cocoa
presentations.
On the other hand, the occupancy rate of vehicles used for transporting seeds is lower than for
transporting pods. This is due to the maximum time that the Cocoa seeds can last being
transported to maintain its quality. This is how the limited time window for the seeds forces the
vehicles used to not occupy the total of its load capacity, being underutilized. However, this
behavior does not generate the use of a greater number of vehicles compared to the transport of
pods. In this way, transporting Cocoa seeds incurs in less transport costs.
4.1.1. Results and scenario analysis
First, we assess how the transport allocation model behaves with changes in travel times between
villages and the plant. This, for example, could happen between April and October when the
probability of rain is greater than 39% (Weather Spark, n.d.), this would cause delays in the
transport process due to road congestion. Therefore, we want to assess whether it is still better
to transport Cocoa seeds while maintaining the quality of the seeds.
In graph 9 we can see that when Cocoa is transported in pods the number of vehicles used
remains constant. However, this behavior is not similar in transportation cost. This is since the
amount of Cocoa transported is not changing, this allows to control the number of vehicles used
without increase. However, the time of use of these vehicles does increase, and therefore also its
cost of transport.
On the other hand, when Cocoa is transported in seeds, the number of vehicles used and their
cost of transport increases as the travel time varies. Although the quantity of Cocoa transported
does not vary, the number of vehicles needed must increase to ensure that the Cocoa brought to
the plant meets the necessary quality, it needs to arrive without exceeding three hours of
transport. In this way, the transportation cost and the necessary routes are directly related to the
travel time.
Graph 9 Weekly transportation costs depending on the traveled distance
21
Otherwise, we proposed a test scenario in which the percentage of production served by the plant
increases. It is important to remember that to meet 4% of the production of each municipality,
the plant must have a capacity of six tons; likewise, for 8% the capacity must be around twelve
tons. As we can see in Graph 10, as the percentage of Cocoa collected increases, the costs of
transporting pods increase because a greater number of vehicles is required to collect that
amount, while the cost of transporting seeds decreases as the amount of Cocoa collected in each
villages increases, because the vehicles used increase their occupancy rate, making the number
of routes decrease.
Graph 10 Weekly transportation costs based on the percentage of Cocoa collected
Graph 11 Transport costs associated with stochastic production
Finally, we proposed a stage with 30 replicas in which the production of each village had a
stochastic component and not a deterministic one. We assumed that the production of each
22
village is distributed triangulated with a maximum and a minimum of ±30% of the expected
production. In Graph 11 we can visualize the random behavior of the weekly production in each
replica along with its transportation cost. As in the previous scenarios, we can conclude that it
is still cheaper to transport Cocoa beans in seeds based on the transportation costs associated
with the time required for each vehicle used.
With 95% confidence, we can conclude that the costs associated with transporting pods from
the villages to the plant will range from $1,234,910 to $1,257,430. Also, seeds transportation
costs will range from $890,293 to $923,721.
To conclude, the objective of the transport allocation model was to determine the best way to
transport Cocoa from the villages of Fortul and Tame to the processing plant based on the
transportation costs while maintaining Cocoa quality. Based on the results obtained, we can see
that the best way to transport the Cocoa is in seeds since the costs are minimized and it is
guaranteed that the Cocoa processed by the plant fulfills the restriction of time of 3 hours in the
journey until this one.
As previously mentioned, the cost of transporting Cocoa is determined by the number of vehicles
used and the time they are used, for this reason, transporting Cocoa in pods is more expensive
than in seeds. In this way, one way to reduce the number of vehicles used to transport Cocoa in
pods is to increase the vehicle's load capacity. That is to say, to count on vehicles with greater
capacity of load in comparison with those used for the transport of seeds.
For the transport allocation model, we assume that the vehicles used to transport seeds and pods
have a capacity of 1.8 tons. However, in order to evaluate how the results change by increasing
the capacity of vehicles used solely for the transport of pods, we assume that these have a capacity
of 2.2 tons.
In Table 2 we can see the costs associated with transporting Cocoa seeds and pods by increasing
only the carrying capacity of the vehicles used to transport the pods. For this, we assume that
these new vehicles have the same cost per minute as previously used vehicles. As we can see,
although the number of vehicles and the daily cost decreased for transporting the pods, it is still
less expensive to transport seeds. This is because the time needed to load a vehicle with pods is
longer than that used to load seeds, due to its volume.
Table 1 Costs of transporting Cocoa by increasing the carrying capacity
Seeds Vehicles
used (seeds) Pods
Vehicles
used (pods)
Monday $ 173,540 2 $ 189,380 2
Tuesday $ 128,040 2 $ 136,380 2
Wednesday $ 254,040 3 $ 221,640 2
Thursday $ 129,910 2 $ 168,120 2
Friday $ 128,540 2 $ 148,010 2
Saturday $ 127,910 2 $ 146,620 2
Total $ 941,980 13 $ 1,010,150 12
23
4.2. Process Analysis of the Postharvest Cocoa Plant
We used a discrete-event simulation approach for evaluating the post-harvest process that will
take place in the Cocoa plant at Tame, Arauca. We selected this approach as it enables us to
measure the system’s performance and analyze varied alternatives or scenarios.
The processing center in Tame will receive a daily amount of Cocoa produced by the smallholders
of the municipality. As mentioned before, Cocoa may be collected in two possible forms: pods or
fresh seeds. We developed simulation models for both alternatives a using the Simio simulation
software. In the following sections we describe the simulation models, we present the parameter
estimation and we analyze our main results.
4.2.1. DES model for the processing center when Cocoa is collected in pods
In this section we describe the simulation model that we built to represent the post-harvest
Cocoa processing that will take place in the potential plant of Tame, when whole pods are
collected and transported to the plant. We model the pod-opening, fermentation and drying
processes.
For the development of our model, we divided the Cocoa genetic varieties in two groups,
according to their quality: varieties from the Arauca Model, and bulk varieties. Moreover, we
divided the bulk varieties into two groups, according to their yield: high-yield bulk Cocoa
varieties, and low-yield bulk Cocoa varieties. The Arauca Model group includes the varieties
FEAR−5, TAME−2 and FSA−13, which are considered of high quality and yield, as they have
won several prizes at the “International Cocoa Awards” from the Salon du Chocolat in Paris
(Federación Nacional de Cacaoteros, 2017). Thus, we suppose that these varieties will certainly
produce fine of flavor Cocoa (FFC). On the other hand, the high-yield bulk Cocoa varieties
include FLE−3, FLE−2, FSA−11, FSA−12, CCN−51, ICS−60 and ICS−95, that require 20 or less
pods to produce one kilogram of dry Cocoa beans. Finally, low-yield bulk Cocoa varieties include
ICS−39, ICS−1, TSH−565 and others, that need more than 20 pods to produce a kilogram of dry
Cocoa (Proexport Colombia, 2012). We assume that the last two variety groups can only produce
bulk dry beans.
In the simulation model, entities represent packages of Cocoa pods with a capacity of 40
kilograms each. We defined three entity types for the three variety groups described previously,
and we performed interviews with different Cocoa producers from Tame in order to estimate the
proportion of Cocoa pods from each group: 36.29% for Arauca Model varieties, 20.56% for high-
yield bulk varieties and 43.15% for low-yield bulk varieties. For determining the amount of pods
that could be carried in a package, we estimated the mass of a single pod for each variety group
with the information of Proexport Colombia (2012). With this, we were able to calculate the
number of pods per package, depending on the variety group: 36 pods for the Arauca Model
varieties, 39 for the high-yield bulk varieties and 53 for low-yield bulk varieties.
24
The packages of pods arrive to the processing center in a daily basis, from Monday to Saturday,
according to quantities determined by the transport allocation model. The processing center
counts with a parking lot area, where the Cocoa is received by workers and transported into the
inside of the plant. We considered a stochastic walking velocity for workers, uniformly
distributed between 0.5 and 1 m/s (Sociedad de Ergonomistas de México, 2009). Moreover, we
supposed that the time required to unload a package that arrives to the plant is uniformly
distributed, between 11.03 and 13.48 seconds, based on our interviews with Cocoa farmers.
Then, pods must be classified according to their genetic variety using visual inspection, and
opened for removing the fresh Cocoa seeds. This process must be done by workers with pruning
hook tools. We estimated the time to perform this procedure with data from the pod-opening
competition done in Arauquita, Arauca. We performed a Kolmogorov-Smirnof goodness of fit
test and found that it follows a continuous uniform distribution between 5.19 and 15.87 seconds
for each pod. Hence, according to the Central Limit Theorem, the time to open a whole package
follows a normal distribution, with parameters that depend on the group of genetic varieties for,
as explained before, the packages of distinct group varieties contain different amounts of pods.
When the pods are opened, the mass of the seeds in each package is reduced to 20% of the
original mass (Schwan & Fleet, 2014); therefore, the entities are converted from packages with 40
kilograms of pods, to packages with 8 kilograms of fresh Cocoa seeds.
Subsequently, the fresh seeds pass through the fermentation process. In the processing center,
the seeds from varieties of the Arauca Model will be piled together in bioreactors with a capacity
of 400 kilograms each, while the rest of the varieties will be piled in wooden boxes of the same
capacity. The plant will include 5 bioreactors and 10 fermentation boxes. Bioreactors are
designed to mix their contents using renewable energy, while Cocoa seeds loaded in
fermentation boxes need to be mixed manually.
It is noteworthy remarking that, in the simulation model, packages of Arauca Model pods cannot
start to be opened until a group of 50 packages of this variety has been formed. This happens
since bioreactors have a 400 kilogram capacity; hence, this is the number of packages required
for them to start the fermentation process. We perform the same procedure for the combination
of high-yield and low-yield bulk packages of pods, as 50 packages are also required to fill a
fermentation box. We defined these decision rules to ensure that the fresh seeds, when removed
from their pods, will not wait too much time until the beginning of fermentation. Indeed,
according to agriculture specialists from Agrosavia, the Colombian corporation for agricultural
research and Durán (2010), the maximum waiting time is defined as 4 hours, to prevent quality
loss. When 50 packages are opened and fresh seeds are removed, the workers transport them
with the stochastic velocity mentioned before towards an available bioreactor or box, according
to the variety group. Then, the fermentation process takes place.
In the case of high and low-yield bulk Cocoa varieties, the seeds must remain inside the
fermentation boxes during two days without being mixed. Then, the seeds are manually mixed
25
every 24 hours during a period of three days with the aid of workers. According to Agrosavia
agriculture specialists, the mean time that a worker takes to mix a box is two hours. Arauca Model
seeds also need to remain unmoved during two days, inside the bioreactors. Then, they should
be mixed. As bioreactors operate with renewable energy, only one of them may be turned-on and
mixing at a time. Precisely, a bioreactor turns-on to mix its contents during 15 minutes, then, it
turns-off during 120 minutes to let the remaining bioreactors mix their contents. After
120 minutes have passed, the bioreactor turns-on again, and the process is repeated during a
two-day period. These processes are summarized in Figure 7.
Fermentation process in bioreactors
Fermentation process in boxes
Figure 7. Summary of fermentation processes
After the fermentation process is completed, the workers empty the contents of the boxes and
bioreactors, what takes a uniformly distributed time between 9.20 and 11.23 minutes, based on
our interviews with Cocoa farmers. It is worth mentioning that, during the fermentation process,
liquid sub products in the form of leachates are released. These leachates represent a loss of
around 25.38% in mass (Schwan & Fleet, 2014). Therefore, entities are converted from packages
with 8 kilograms of fresh Cocoa seeds, to packages with approximately 6 kilograms of fermented
seeds.
Finally, fermented seeds need to be dried. The plant includes two dryers and each of them can
be filled with 3 mobile carts. Each mobile cart is able to carry 7 trays full of 50 kilograms of
fermented seeds each. Therefore, each tray needs a batch of 8 packages of seeds to fill its capacity.
It is worth mentioning that bulk and Arauca Model seeds cannot be mixed in the same tray.
When the carts are filled, they are transported by workers to the drying zone of the plant, with
the stochastic velocity defined before. When a group of 3 full carts is ready, it is taken into an
available dryer to start the moisture reducing process.
The drying process is done in three consecutive stages. The seeds are firstly dried for 9 hours,
then, they rest during a term of 4 hours, and, to end, they are dried again for 4 hours. As a final
point, workers unload the contents of the dryer, what takes a uniformly distributed time between
6.17 and 7.55 minutes, based on our interviews with Cocoa farmers. When the drying process is
completed, the Cocoa beans reach about 7% of moisture and their mass is reduced in
approximately 59.80%, as stated by agriculture specialists from Agrosavia.
Workers are needed to perform certain tasks of the abovementioned processes. Specifically, they
should transport the pods from the parking lots into the plant, classify and open the pods,
transport the fresh seeds into the fermentation zone, mix the Cocoa seeds inside the boxes during
26
the fermentation process, empty the boxes and bioreactors, carry the fermented seeds into the
drying zones, and empty the dryers. In Colombia, a worker must not labor more than 8 hours a
day and 48 hours a week. Moreover, workers who labor on Sunday must receive an extra
premium of 75% of the daily basic income (Legis, 1950). Considering this information, in the
simulation model, we defined workweek employees with an eight-hour day schedule, from 8: 00
a.m. to 5: 00p.m., with a rest time from 1: 00 p.m. to 2: 00 p.m. Workweek employees labor from
Monday to Saturday. Additionally, we included Sunday workers with the same eight-hour
schedule. We defined diverse scenarios in order to determine the required number of workers to
ensure the stability of the system and to guarantee that the time that Cocoa seeds remain outside
the pods before being fermented does not surpass four hours. Then, we extended our model to
include machinery maintenance in the plant. We present our results in further sections.
The post-harvest process is summarized in Diagram 2. Moreover, the plan of the processing
center is presented in
Figure 8. The plan distances are measured in meters.
4.2.2. Output Analysis
We did an output analysis for a baseline scenario, including 4 employees who work from Monday
to Saturday, and 2 employees who work on Sunday. For this, we run 10 replications with a one-
month length. In order to determine the suggested simulation run length, we analyzed the
evolution of key performance metrics, such as the number of packages of bulk and Arauca Model
Cocoa in the system, during the simulation run. Graph 12 shows the evolution of the number of
packages of low-yield bulk Cocoa. We observe that the system starts empty, with no Cocoa
packages, and it reaches steady state after approximately 168 hours or seven days. Hence, we
determined a warm-up period of 7 days and 77-day run length.
Figure 8. Plan of the Cocoa processing plant
27
YesIs the raw
material pods?
Start
Pod-opening time and mass percentage of seeds from the total
pod
End
No
Fermentation in boxes
Arrival of Cocoa pods or fresh seeds to
parking lot
Daily amount of Cocoa collected,
proportion of variety groups, mass of a
pod by variety group
Input Data
Transport into the inside of the plant
No
Classification and opening of pods
No
Is it an Arauca Model variety?
Fermentation in bioreactors
Yes
Drying
Workers velocity and unload time,
processing plant area
Processing times, time to empty
container, mass percentage of
leachates, capacity of boxes and bioreactors
Transport to the drying zone
Transport to the fermentation zone
Workers velocity, processing plant area
Processing time, drying efficiency, time
to empty container, capacity of dryers
Diagram 2.Flow diagram of the Cocoa post-harvest process
Graph 12. Number of packages of low-yield bulk Cocoa during the simulation time
28
Furthermore, to determine the number of replications, we analyzed the half-width of certain key
metrics. We found that the must variable metric corresponds to the number of low-yield bulk
Cocoa packages in the system, with an average of 311.65 and a half-width of 2.93 packages. We
stablished 1 package as a desired error with 95% of confidence level, and we iterated with
increasing values of the number of replications (𝑅), until equation (1) was fulfilled (Banks, 2005).
𝑅 ≥ (𝑡(0.975, 𝑅−1) ∙ 𝑠
𝜖)
2
(41)
In this equation, 𝜖 corresponds to the desired error (1 package), and 𝑠 represents the standard
deviation of the number of low-yield bulk Cocoa packages in the system. We obtained that the
number of needed replications to achieve the desired error is 67.
4.2.3. Results and scenario analysis for the pods model
We run our model with the replications and run length specified above. For determining the
suggested number of workers needed in the system, we developed three distinct scenarios:
Table 2. Scenarios of different number of workers for the processing center
Scenario Workweek workers Workers on Sunday
1 4 2
2 4 1
3 5 1
We also analyzed scenarios with three workweek employees and one or two Sunday employees;
however, the system did not reach stability with these scenarios. In first place, we calculated the
scheduled utilization of the machinery and workers for the abovementioned scenarios, to verify
the system’s stability. We show these results with a 95% confidence level in Table 3.
Table 3. Scheduled utilization of resources by scenario
Resource Scenario 1 Scenario 2 Scenario 3
Fermentation Boxes 80.25% ± 0.52% 80.32% ± 0.51% 79.47% ± 0.33%
Bioreactors 86.33% ± 0.49% 86.32% ± 0.47% 86.52% ± 0.29%
Dryers 45.26% ± 0.32% 43.66% ± 0.35% 45.15% ± 0.19%
Workweek workers 87.48% ± 0.11% 87.49% ± 0.11% 71.3% ± 0.07%
Sunday workers 60.45% ± 1.06% 92.92% ± 1.28% 90.91% ± 0.94%
The average utilization of the Sunday worker for scenarios 2 and 3 surpasses 90%; in fact, the
maximum utilization reached by this worker during the simulation runs was 102.69% for
scenario 2 and 99.44% for scenario 3. Since for scenario 2 the maximum utilization value
29
surpasses 100%, and in scenario 3 the worker is almost fully utilized, scenario 1 is preferred.
Indeed, the maximum utilization reached during the simulation run for this scenario was 92.27%
for weekday workers, and 72.16% for weekday workers.
Furthermore, we need to guarantee that Cocoa fresh seeds do not remain more than four hours
outside of the pods, due to its perishability. We analyzed this waiting time for the three scenarios,
and we found that it does not surpass four hours in any case, as shown in Graph 13.
Graph 13. Time of fresh Cocoa seeds before fermenting
In addition, we compare these scenarios in terms of the time in system of a Cocoa package and of the weekly throughput of dry beans. These results are shown in Table 4 and Table 5.
Table 4. Time in system of a package of Cocoa by group variety (days)
Variety group Scenario 1 Scenario 2 Scenario 3
Bulk Cocoa 7.804±0.02 7.844±0.015 7.674±0.013
Fine or Flavor Cocoa 6.568±0.017 6.658±0.014 6.445±0.011
Table 5. Dry Cocoa beans throughput by week (kg)
Variety group Scenario 1 Scenario 2 Scenario 3
Bulk Cocoa 906.01±2.57 908.99±2.98 924.64±1.13
Fine of Flavor Cocoa 1200.26±2.28 1203.3±2.29 1211.12±0.57
We conclude that the time in system for the groups of Cocoa varieties is significantly lower in
scenario 1 than in scenario 3, with a 95% confidence level. On the other hand, the kilograms of
dry Cocoa beans produced by week are significantly higher for scenario 3 than for the remaining
scenarios. Nevertheless, the throughput differences between scenario 3 and scenarios 1 and 2 do
not surpass 14 kilograms of dry Cocoa beans per week.
30
After analyzing the key metrics presented before, we selected the alternative proposed in
scenario 1, for it guarantees stability, reduces the time in system and meets the waiting time
constraint for fresh seeds. For this scenario, the total weekly throughput of dry Cocoa beans is
about 2,106.27 kilograms, and the average mass of Cocoa-pod husks that are discarded every
week is 31,040 kilograms, which may be useful for composting. Besides, the weekly volume of
leachates produced in the fermentation process is approximately 1,838.67 liters
4.2.4. Pods model extension to include machinery maintenance
We did an extension to the model for including the maintenance of machinery, as it is imperative
for preventing failures and avoiding impurities, internal mould and off-flavors in Cocoa dry
beans. The maintenance procedures must be done periodically in bioreactors, fermentation
boxes and dryers. We consider a maintenance duration of four hours for bioreactors and one
hour for boxes and driers, as reported by Agrosavia agriculture specialists. The upkeep
procedures must be done by workers.
We tried different scenarios with distinct upkeep periodicities for each type of machine. Table 6
shows the number of batches that must be processed, before performing a maintenance.
Table 6. Number of batches to be processed on each type of machine, before
maintenance
Scenario Bioreactor Fermentation box Dryer
1 2 4 4
2 2 4 5
3 2 5 4
4 2 5 5
5 3 4 4
6 3 4 5
7 3 5 4
8 3 5 5
We run the simulation model with the specifications determined in prior sections, and we used
the number of employees determined previously: four employees during workdays, and two on
Sunday. We calculated the dry Cocoa beans throughput for these scenarios, as shown in Graph
14, where scenario 0 represents a case without maintenance. As expected, the throughput
increases with less frequent maintenance procedures; nevertheless, the difference among
scenarios is minor. In addition, Graph 15 presents the percentage of time that each type of
machine remains waiting for been maintained, or in maintenance procedures. As anticipated,
this percentage is greater for scenarios where the maintenance procedures are more frequent.
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Graph 14. Throughput of dry Cocoa beans for each scenario.
Graph 15. Percentage of time in maintenance for each type of machine and scenario.
As a final point, we compare the scheduled utilization for machines and workers in every scenario
in Graph 16 and Graph 17.
Graph 16. Utilization of the workers by scenario
32
Graph 17. Utilization of the machinery by scenario
The utilization for Sunday employees greatly increases when the upkeep of the bioreactors is
done more frequently. Indeed, the maximum utilization values reached during the simulation
run for scenarios 1 and 3 were 103.86%, and 107.31%, respectively. Therefore, we discard these
two scenarios for not guaranteeing workers’ stability. Moreover, in Graph 17 we observe that the
utilizations of dryers and boxes have minor changes among scenarios. On the contrary, the
utilization of bioreactors greatly increases when performing maintenance less frequently.
Therefore, for the sake of guaranteeing the system’s stability, increasing the throughput of dry
Cocoa beans, reducing the maintenance time and improving the machinery utilization, we
recommend the implementation of scenarios 5 to 8. For these scenarios, the maintenance of
bioreactors is done after processing three batches, and the upkeep of boxes and dryers is done
after processing four or five batches.
4.2.5. DES for the processing center when Cocoa fresh seeds are collected.
This model is similar to the one developed in section 4.2. In this case, entities represent packages
of eight kilograms of Cocoa fresh seeds, and the opening process is omitted. Thus, after being
transported into the plant, the seeds pass directly to the fermentation process, according to the
genetic variety group. We assume that the seeds’ variety has been previously determined by the
farmers.
The packages of fresh seeds arrive to the processing center in a daily basis, from Monday to
Saturday. The transport allocation model establishes that fresh seeds have a time limit of about
three hours to complete their route to the plant. In consequence, once the seeds have arrived to
the processing center, they can only wait one hour before starting the fermentation process. To
guarantee that this maximum time is not surpassed, we defined that the amount of seeds that
arrive to the plant each day must be multiple of 400 kilograms for both: Arauca Model and Bulk
Cocoa varieties. We defined this decision rule because if the amount of seeds is not multiple of
400 kilograms, the surplus amount of seeds would have to occupy a complete box or bioreactor
to be fermented, due to the fact that seeds cannot wait until the next day for more fresh seeds to
arrive and complete the required quantity, and that seeds with different fermentation start times
33
cannot be mixed in the same container. Consequently, the capacity of boxes and bioreactors
would not be fully utilized.
Accordingly, in our simulation model, the daily arrivals of packages of each variety group are
multiples of 400 kilograms, and are generated in such a way that it matches the amount of weekly
production determined by the transport allocation model. The remaining post-harvest
procedures work as defined in the previous model. We first considered a baseline case without
maintenance for the simulation, and we proposed varied scenarios for determining the number
of required workers. Then, we extended our model to include machinery maintenance. We
present our results in the following sections.
4.2.6. Results and scenario analysis for the seeds model
We proposed the following scenarios for the number of workers:
Table 7. Scenarios for the number of workers in the processing center
Scenario Workers on workweek Workers on Sunday
1 2 2
2 3 2
We run 67 replications for the proposed scenarios, with a length of 77 days and a warm-up period
of 7 days. We also tried a scenario with 3 workweek workers and 1 Sunday worker; however, the
system did not reach stability as the utilization of the Sunday worker surpassed 100%. We
calculated the utilization of the machinery and workers of the plant to verify the system’s
stability. We show these results with a 95% confidence level in Table 8. The difference between
the average utilization of all the types of machinery in both scenarios is minor. On the other
hand, in scenario 2 the utilization of the workday employees is significantly lower than that of
scenario 1. Therefore, for making a better use of the labor capacity, we suggest the
implementation of scenario 1.
Table 8. Scheduled utilization of resources by scenario
Resource Scenario 1 Scenario 2
Fermentation Boxes 74.912% ± 0.005% 74.798% ± 0.005%
Bioreactors 80.000% ± 0.014% 80.000% ± 0.024%
Dryers 44.762% ± 0.000% 44.762% ± 0%
Workday workers 56.519% ± 0.081% 37.693% ± 0.042%
Sunday workers 65.692% ± 0.014% 65.689% ± 0.012%
Moreover, in Table 9 we verify that the waiting time of the fresh seeds before being fermented
does not surpass one hour, due to their perishability.
34
Table 9. Time of fresh seeds before fermentation (hours)
Variety group Scenario 1 Scenario 2
Bulk Cocoa 0.127±0.002 0.085±0.001
Fine or Flavor Cocoa 0.141±0.002 0.094±0.001
In addition, we compared the scenarios in terms of the time in system of a Cocoa package. In
Table 10 we observe that the difference between the times in system of the variety groups in both
scenarios is minor. Besides, as expected, for each variety group and every scenario, the time in
system is significantly less when fresh seeds arrive to the plant, than when the whole Cocoa pods
are collected (Table 4).
Table 10. Time in system (days) of a package of Cocoa by group variety.
Variety group Scenario 1 Scenario 2
Bulk Cocoa 6.897±0.001 6.935±0.003
Fine or Flavor Cocoa 5.540±0.002 5.526±0.000
On the other hand, the throughput of dry Cocoa beans produced by week is the same for both
proposed scenarios: around 1,100.16 kilograms for bulk, and 875.52 for fine or flavor Cocoa.
After analyzing these key metrics, we selected the alternative proposed in scenario 1, for
improving the workers’ utilization. For this scenario, the weekly volume of leachates produced
in the fermentation process is about 1,695.05 liters.
4.2.7. Seeds model extension to include machinery maintenance
We present the results of the fresh seeds model, including the machinery maintenance. We
tested the eight upkeep scenarios presented previously in Table 6, and we included two
employees for workdays and two more for Sundays. We used the same running specifications
presented in previous sections.
Graph 18. Utilization of the workers by scenario
35
Graph 19. Utilization of the machinery by scenario
We first calculated the utilization of the workers and machines in all the scenarios, as shown in
Graph 18 and Graph 19. Scenario 0 represents a case without maintenance. The utilization of
workweek employees decreases when the upkeep of the bioreactors is done after processing three
batches (scenarios 5 to 8). Likewise, the utilization for bioreactors increases for these scenarios.
On the other hand, the utilizations of dryers and boxes have minor changes among the scenarios,
as well as the utilization of Sunday employees.
In addition, we analyzed the percentage of time that each type of machine remains waiting to be
maintained, or in maintenance procedures. As shown in Graph 20, the percentage of
maintenance time for bioreactors is greater in scenarios 1 to 4, where the upkeep procedures are
done more frequently. Similarly, dryers reduce their percentage time of maintenance in scenarios
3 and 4, where maintenance is done after processing 5 batches.
Graph 20. Percentage of time in maintenance for each scenario
In conclusion, for the sake of reducing the maintenance time and improving the machinery
utilization, we would also recommend the implementation of scenarios 5 to 8.
4.2.8. Comparison between seeds and pods models
For determining whether is more advantageous to collect Cocoa in the form of seeds or pods, we
36
performed a comparative analysis between both cases. First, we compared the dry beans
throughput for both alternatives, in a scenario without maintenance, and in the maintenance
scenario 5.
Scenario 𝟎. No maintenance
Scenario 5. Maintenance
Graph 21. Throughput comparison between pods and seeds alternatives
We observe that, for both scenarios, with a 95% confidence level, the throughputs for bulk and
fine or flavor Cocoa are higher for the alternative consisting in collecting pods. Besides, we
compared both scenarios in terms of monthly labor costs considering that, in Colombia, the basic
hourly wage of a worker is $ 26,041.40 and that workers who labor on Sunday must receive an
extra premium of 75% of the basic income (Legis, 1950). With the pods alternative, four workers
are needed during workweek days and two during Sundays. With the seeds alternative, two
workers are needed for both: workweek days and Sundays.
Graph 22. Comparison of monthly labor costs for pods and seeds alternatives
We observe that the labor costs for the seeds alternative are approximately 55% of the labor costs
for the pods alternative. This is explained as more workers are required for the pod-opening
process in the pods alternative. In addition, we compared both alternatives in terms of the time
that a package of Cocoa remains in the processing plant, in a scenario without maintenance, and
in the maintenance scenario 5. We observe that, for both group varieties, the time is system is
lower for the seeds alternative, as the pod-opening process is omitted.
37
Scenario 𝟎. No maintenance
Scenario 5. Maintenance
Graph 23. Time in system comparison for pods and seeds alternatives
To sum up, the seeds alternative is more favorable in terms of labor costs and time in system.
However, the throughput of dry Cocoa beans is larger for the pods alternative, as for this case
there is no constraint about the amount of pods that must arrive every day. On the contrary, for
the seeds model, the processing center must receive a mass of seeds that is multiple of
400 kilograms. Moreover, it is noteworthy remarking that, if the pods are opened by the farmers
and the fresh seeds of Cocoa are transported to the plant, it will be very difficult to determine
their genotype and quality. On the contrary, if Cocoa pods are collected before being opened,
the quality could be predicted by visual inspection. Therefore, the pods alternative could bring
about a benefit in terms of Cocoa quality and flavor. Besides, the Cocoa-pod husks that are
discarded in the pods model could be used for further composting. This could be an alternative
to generate additional value.
4.3. Profitability Analysis
The Cocoa commercial business, for both bulk and fine flavor Cocoa, depends on interactions
between suppliers and demanders, making it highly dependable on price changes. This project
seeks to establish a business model for producers and cooperatives in charge of Cocoa post-
harvesting processes that aids them on decisions concerning investment, processing capacities
and selling strategies. The model proposed revolves around fine flavor Cocoa sells, due to its high
price and selling ease. This grants a crucial importance to variables and parameters related to
fine flavor Cocoa market and processing dynamics.
4.3.1. Parameter estimation
The main financial parameters are the selling price of bulk Cocoa and the negotiation price of a
fine flavor Cocoa contract. Bulk Cocoa price is determined through supply and demand forces in
the international market. Specifically in Colombia, the selling price is calculated by considering
the Cocoa commodity price in the New York Stock Exchange (NYSE) and the London Stock
Exchange (LSE). Information about international bulk Cocoa price per ton was taken from
reports from The International Cocoa Organization (ICCO) bought by Agrosavia. However, the
only available reports of monthly prices were from dates previous to 2015 and could not be used
to forecast future price. As a proxy for the Cocoa commodity spot price, we proposed taking
38
prices of 1 month future Cocoa contracts from Quandt databases available online. Graph 24
shows both series in a monthly periodicity and shows that the chosen proxy is pretty close to the
actual data, with an estimated percentage error of 3.37%. It is important to note that the two
series were penalized by the inflationary rate, taken from (McMahon, 2018) to reflect constant
prices as of November 2018, instead of current prices so the inflationary effect over time was
mitigated.
Graph 24. Series comparison between Spot Prices and Future Contracts
Due to the need of determining an optimal selling policy for Cocoa stored in the processing plant
in a 17 week analysis horizon. We decided to establish the periodicity of the model as weekly,
which leads to the need of having weekly price information. Weekly averages for Cocoa futures
prices were calculated and represent the main parameter for the optimization model.
Estimating Bulk Cocoa price may be a tough process, due to its variability and unpredictability
through the past 30 years as seen in Graph 25. Conventional methods such as moving average or
exponential smoothing forecasting techniques may not be sufficient due to its simplicity, failing
to show significant changes through time and leading the model to ignore price variation and
just take decisions based on other factors (Brockwell, Davis, & Calder, 2002).
The chosen approach for price estimation was a Long-Short Term Memory Neural Network, due
to its capability of forecasting with precision and responding to historical variations. According
to (Ma, Tao, Wang, Yu, & Wang, 2015), LSTM neural networks “can overcome the issue of back-
propagated error decay through memory blocks, and thus exhibits the superior capability for
time series prediction with long temporal dependency”. As a backtesting method, a rolling origin
technique was applied, in which the series was split in 7 different subsamples, each one with a
training period of a year, and a test period of 17 weeks.
39
Graph 25. Future Cocoa Contract Price Series from 1990 to 2018
Forecasts were made for each of the splits, and the Mean Absolute Percentage Error (MAPE) was
computed. Equation (41) exhibits MAPE formula, where 𝑛 represents the number of observations
in a particular split, 𝑦𝑖 is the actual price value for week 𝑖, and �̂�𝑖 is the forecasted value for the
same week. As a precision metric, the mean of the 7 MAPE values was computed showing a value
of 2.12% which reflects a high precision on LSTM forecasts for the time series used. Forecasting
results are presented in Graph 26 where 17 weeks from November 2018 through February 2019
were predicted.
𝑀𝐴𝑃𝐸 = ∑|𝑦𝑖−�̂�𝑖|
𝑦𝑖
𝑛𝑖=1 (42)
Graph 26. 17 week forecast of Cocoa price, using LSTM neural networks
Fine Flavor Cocoa price is determined by a bargain between the two parts of the negotiation,
making it a somehow unpredictable parameter for conventional forecasting methods.
40
Information about 108 fine flavor Cocoa export contracts was gathered and analyzed from SICEX
database (2018) and as shown in Graph 27, the series show a stationary behavior, thus making it
predictable by adjusting a probability distribution to the data.
Graph 27. Fine Flavor Cocoa Price behavior
Plotting and histogram of the data gathered for Fine Flavor Cocoa contracts, we could determine
a tentative distribution to fit to the data. Specifically, due to the shape of the histogram and the
behavior of the series, the chosen distribution was a lognormal distribution. Graph 28 shows the
histogram and the theoretical density of a lognormal distribution, represented by the red line.
Graph 28. Fine Flavor Cocoa Price histogram and theoretical Lognormal distribution
In order to determine if the data statistically fits the aforementioned distribution a Chi-Squared
test was performed following the methodology presented by (Banks, 2005).
𝐻0: 𝐷𝑎𝑡𝑎 𝑓𝑖𝑡𝑠 𝑎 𝐿𝑜𝑔𝑛𝑜𝑟𝑚𝑎𝑙 𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
𝐻1: 𝐷𝑎𝑡𝑎 𝑑𝑜𝑒𝑠 𝑛𝑜𝑡 𝑓𝑖𝑡 𝑎 𝐿𝑜𝑔𝑛𝑜𝑟𝑚𝑎𝑙 𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛
41
Having a P.Value of nearly zero, we can conclude under a 5% level of significance that the data
fits a Lognormal distribution with 𝜇𝑙𝑜𝑔 = 0.831, 𝜎𝑙𝑜𝑔 = 0.132.
Information related to costs, both fixed and variable was provided by Agrosavia through an initial
financial analysis that was made previous to the planning and structuring of this project.
Bulk Cocoa and fine flavor Cocoa production yields were determined in the process analysis
stage, thus representing a main parameter for the profitability analysis model
4.3.2. Methodology
As previously stated, the objective of this analysis is to determine an optimal selling plan for
Cocoa transformed and stored in the processing plant, focusing on increasing fine flavor Cocoa
sells which will represent the main revenue stream for the project. Nonetheless, fine flavor Cocoa
is sold and exported in 25 ton containers, making it a hard product to sustain and sell due to the
cost associated to its accumulation. Therefore, the plant would need a stable cash flow to keep
its operation without needing to enter a debt, making necessary to establish a robust selling plan
for bulk Cocoa during the study period. For the aforementioned purpose, we proposed a linear
optimization model for deciding the optimal amount of bulk Cocoa to be sold, as well as the
minimum initial capital for the operation to be profitable. Due to the perishable nature of Cocoa
dried beans, the analysis horizon is of 17 weeks, representing the maximum time a batch of Cocoa
dried beans can be stored without losing its organoleptic features.
For the problem formulation, let T, P be the set of weeks in the analysis horizon and the set of
possible perish terms in the 17 week period of study. The vast majority of parameters in the model
are related to financial information of the operation, ranging from Cocoa price through the
different costs that the operation implies. Let 𝑝𝑟𝑡𝑐 and 𝑝𝑟𝑡
𝑓 the selling price in USD in week 𝑡 ∈ 𝑇
for bulk Cocoa and fine flavor Cocoa respectively. Considering that the model finds the minimum
operational capital needed to start production, the plant processing capacity in terms of tons of
raw Cocoa seeds is considered a parameter, represented by letter 𝑧. Let 𝑓𝑥 be the fixed expenses
for the plant operation in a week, and 𝑣𝑥 the variable expenses that depend on the chosen size
of the production plant. Let 𝑥𝑐, ℎ, 𝑐𝑠 the costs associated to the exportation of a 25 ton container
in USD, the weekly cost of storage of a ton of dried Cocoa (regardless of the variety of Cocoa)
and the cost related to selling bulk Cocoa. A parameter for including the equivalent amount of
Colombian pesos for 1 US dollar is included and represented by letter 𝑑, as well as the rate
representing the weekly cost of capital represented by 𝑟. Parameter 𝑙 represents the fixed weekly
fee necessary to pay the total amount of construction initial investment in an arbitrarily chosen
term. Lastly for the financial parameters, 𝑟𝑚 represents the minimum amount of money to have
at the end of each week as a preventive measure. The rest of parameters are associated to
inventory dynamics. Let 𝑣0𝑝 the amount of bulk Cocoa stored at the start of the model horizon
that perishes in week 𝑝 ∈ 𝑃 and 𝑐0 the total amount of bulk Cocoa stored at the start of the
operation, where 𝑐0 = ∑ 𝑣0𝑝𝑝∈𝑃 . The amount of fine flavor Cocoa at the start of the operation
horizon is represented by parameter 𝑓0. Maximum capacity for storage of mixed inventory is
represented by 𝑐𝑚. The plant transforms bulk and fine flavor Cocoa, and parameters 𝑐𝑝 and 𝑓𝑝
42
represent the percentage of the total plant yield that correspond to each type of Cocoa, with 𝑐𝑝 +
𝑓𝑝 = 1.
Variables 𝑦𝑡 , 𝑥𝑡 , 𝑎𝑡 represent if bulk Cocoa should be sold in week 𝑡 ∈ 𝑇, the amount of bulk Cocoa
to be sold and the number of 25 ton fine flavor Cocoa containers to be sold, respectively. The
final amount of bulk Cocoa and fine flavor Cocoa stored at the end of week 𝑡 ∈ 𝑇 is represented
by 𝑐𝑡 and 𝑓𝑡 respectively. For modelling the perishable nature of Cocoa dried beans, variables 𝑣𝑡𝑝
and 𝑠𝑡𝑝 were included, which represent the amount of bulk Cocoa stored at the end of week 𝑡 ∈
𝑇 that perishes in week 𝑝 ∈ 𝑃, and the amount of bulk Cocoa sold in week 𝑡 ∈ 𝑇 that perishes in
week 𝑝 ∈ 𝑃. As for the financial structure of the model, 𝑚𝑡 and 𝑢𝑡 represent the amount of money
at the end of week 𝑡 ∈ 𝑇 and the profit of the operation in a particular week. Lastly, 𝑘 represents
the minimum necessary amount of initial operation capital injection needed for operating the
plant. The optimization model follows:
max ∑𝑢𝑡
(1+𝑟)𝑡𝑡∈𝑇 − 𝑀1 ∗ 𝑘 (43)
s.t.,
𝑥𝑡 ≤ 𝑀2 ∗ 𝑦𝑡 ∀𝑡 ∈ 𝑇 (44)
𝑥𝑡 ≥ 𝑦𝑡 ∀𝑡 ∈ 𝑇 (45)
𝑐𝑡 = 𝑐𝑡−1 + 0.3 ∗ 𝑐𝑝 ∗ 𝑧 − 𝑥𝑡 ∀𝑡 ∈ 𝑇 (46)
𝑓𝑡 = 𝑓𝑡−1 + 0.3 ∗ 𝑓𝑝 ∗ 𝑧 − 25 ∗ 𝑎𝑡 ∀𝑡 ∈ 𝑇 (47)
𝑐𝑡 + 𝑓𝑡 ≤ 𝑐𝑚 ∀𝑡 ∈ 𝑇 (48)
𝑣𝑡𝑝 = 𝑣(𝑡−1)𝑝 − 𝑠𝑡𝑝 ∀𝑡 ∈ 𝑇, 𝑝 ∈ 𝑃 | 𝑝 < 𝑡 + 16 (49)
𝑣𝑡(𝑡+16) = 𝑣(𝑡−1)(𝑡+16) − 𝑠𝑡(𝑡+16) + 0.3 ∗ 𝑐𝑝 ∗ 𝑧 ∀𝑡 ∈ 𝑇 (50)
𝑥𝑡 = ∑ 𝑠𝑡𝑝𝑝∈𝑃 ∀𝑡 ∈ 𝑇 (51)
𝑐𝑡 = ∑ 𝑣𝑡𝑝𝑝∈𝑃 ∀𝑡 ∈ 𝑇 (52)
𝑠𝑡𝑡 = 𝑣(𝑡−1)𝑡 ∀𝑡 ∈ 𝑇 (53)
𝑢𝑡 = (𝑥𝑡 ∗ 𝑝𝑟𝑡𝑐 + 25 ∗ 𝑎𝑡 ∗ 𝑝𝑟𝑡
𝑓) ∗ 𝑑 − 𝑐𝑠 ∗ 𝑦𝑡 − ℎ ∗ (𝑐𝑡 + 𝑓𝑡) − 𝑐𝑥 ∗ 𝑎𝑡 ∗ 𝑑 − (𝑙 + 𝑣𝑥) ∗ 𝑧 − 𝑓𝑥
∀𝑡 ∈ 𝑇 (54)
𝑚𝑡 = 𝑚𝑡−1 + 𝑢𝑡 ∀𝑡 ∈ 𝑇 | 𝑡 > 1 (55)
𝑚1 = 𝑘 + 𝑢1 (56)
𝑚𝑡 ≥ 𝑟𝑚 ∀𝑡 ∈ 𝑇 (57)
𝑥𝑡 ∈ 𝑍+ ∪ {0} ∀𝑡 ∈ 𝑇 (58)
𝑦𝑡 ∈ {0,1} ∀𝑡 ∈ 𝑇 (59)
43
𝑐𝑡 , 𝑓𝑡 , 𝑚𝑡 ≥ 0 ∀𝑡 ∈ 𝑇 (60)
𝑠𝑡𝑝, 𝑣𝑡𝑝 ≥ 0 ∀𝑡 ∈ 𝑇, 𝑝 ∈ 𝑃 (61)
𝑢𝑡 ∈ 𝑅 ∀𝑡 ∈ 𝑇 (62)
𝑘 ≥ 0 (63)
Where objective (43) maximizes the present value of the operation profit with a penalization
term to guarantee that k takes the minimum possible value for operation. Note that maximizing
profit establishes the best possible balance between storage costs and sell revenues along the 17
week period. The set of constraints (44) and (45) guarantee the correct association between
variables 𝑥𝑡 and 𝑦𝑡. Sets (46) and (47) model the inventory trajectory through time, while set (48)
enforces the model to keep its total inventory under the maximum limit allowed. Constraints
grouped in (49) and (50) assure the trajectory of bulk Cocoa inventory in relation to their perish
time. Sets (51) and (52) enforce a connection between normal inventory trajectories and the
equations relating perish times, while set of constraints (53) enforces a sell in a particular period
if there is still existence of Cocoa that will perish in that week. Set (54) represent profit trajectory
and the factor influencing it, while constraints comprised in (55) and (56) model changes in the
amount of money through time, being forced to be over a minimum limit by constraints in (57).
Finally, sets of constraints (58) through (63) specify the nature of the decision variables.
4.3.3. Results
To evaluate the model performance, a baseline scenario is needed for comparison purposes to
determine if the optimization model properly reacts to price changes and if this reaction is
reflected in an increase in operation profit over the 17 weeks of study.
The baseline case we selected is the operation derived from immediately selling the batch of bulk
Cocoa produced in a particular week. The baseline case and its comparison with the optimal
solution will be shown under an arbitrary scenario in which the proportion of fine flavor Cocoa
processed by the plant is 28%, which leads to a proposed capacity for the plant of 18 tons.
Operation capital available at the start of the horizon is $150,000,000 COP. Graph 29 shows the
cash flows and selling times with their respective quantities for the scenario run through the
proposed optimization model. On the other hand, Graph 30 shows the same information for the
baseline case, assuming the same plant size and the initial investment decided by the model.
Comparing both models’ selling strategies under the same controlled arbitrary conditions, is
noticeable how the optimization model reacts to price changes, storing Cocoa in the second
weeks to sell it in the 2nd when price is predicted to be higher. Same behavior is exhibit in weeks
6 through 8 and 14 through 16. This optimized decision making leads to a huge increase in
revenue in some weeks, resulting in an increment on total profit. The main conclusion is that the
model performs better in terms of operation utility due to its reaction to forecasted price
changes, presenting an increase of operation utility of about 23%.
44
Graph 29 a. Optimization Model Selling Strategy for Bulk Cocoa.
Graph 29 b. Operation Utility and Cash Flow over the analysis horizon.
With results supporting the model performance, the complete model can be run, in which the
minimum operation capital is decided. In order to run the model and find an optimal solution
with its correspondent initial investment, a plant processing capacity is needed. Due to the need
of selling at least 1 container of fine flavor Cocoa before 17 weeks, to get high revenues and prevent
Cocoa perishing, plant size picking depends on the production proportion for fine flavor Cocoa
that the plant can handle. Given an arbitrary fine flavor Cocoa production rate, the plant size
chosen will be the minimum plant size that, in combination with the proportion given,
guarantees 25 tons of fine flavor Cocoa production before week 17.
45
Graph 30 a. Baseline Case Selling Strategy for Bulk Cocoa.
Graph 30 b. Baseline Case Operation utility and Cash Flow over the analysis horizon
Optimal size chosen would be the minimum size mentioned before, because initial investment
needed for building the plant increases linearly with the chosen size. Graph 31 shows all the
feasible combinations of Cocoa between fine flavor Cocoa proportion and plant capacity,
represented by the green colored area in the graph.
Taking the current estimated proportion of fine flavor Cocoa production of 36.29%, the
minimum plant capacity to achieve fine flavor Cocoa production over 25 tons in the 17 week
horizon is 14 tons of raw Cocoa seeds per week.
46
Graph 31. Feasible combinations of fine flavor Cocoa proportion and plant capacity
With a plant size being chosen, model can be run and gives robust and accurate results that aid
the decision makers in their analysis information. Graph 32a shows expected utility in the study
horizon, along with the available money flow through time, while Graph 32b exhibits inventory
dynamics for each variety of Cocoa and changes in total inventory. Lastly, Graph 32c presents the
bulk Cocoa selling strategy over the 17 weeks, were optimal decisions are made based on money
reserves, price changes and available inventory.
Graph 32 a. Operation Utility, Cash Flow and Money Reserve for the proposed scenario.
47
For this particular scenario, an investment of $122,264,065 COP is needed for operational
purposes, while the plant building estimated cost is $1,176,380,568 COP which will be paid as a
loan with an assumed term of 10 years. Nonetheless, this term of payment resides as a
parameter on the model and can be modified to get a more complete analysis on the sensitivity
of the results.
Graph 32 b. Inventory Dynamics of the selected scenario.
Graph 32 c. Selling Strategy for Bulk Cocoa under the specified conditions
The model result can be highly variable depending on the input parameters established. Some
input parameters are needed for the analysis to be robust and complete such the tentative
48
proportion of fine flavor Cocoa production, and the plant capacity selected (that, given a
proportion, guarantees 25 tons of Cocoa in less than 17 weeks). Graph 33 aids in the
understanding of this variability showing the utility path estimated by the model for 4 arbitrary
proportion values, over a range of different production capacities. As seen, there are some utility
spikes at capacity levels that coincide with multiples of the minimum capacity needed to
guarantee a fine flavor Cocoa batch processing. This finding follows the expected results, because
a combination of proportion and capacity that does not guarantee the production of a full 25 ton
batch in the analysis horizon will yield a loss in profit due to storage costs and the unavailability
to sell.
Graph 33. Utility behavior depending on Fine Flavor Cocoa proportion and plant
capacity
For analysis purposes and comparability, Table 11 shows the main results for 12 different scenarios
with combinations of fine flavor Cocoa proportions, and plant capacities equaling the minimum
capacity needed, twice and three times this value.
Building investment increases linearly as plant size varies. However, operation investment
increases as the fine flavor Cocoa production is made higher, but decreases with plant size.
Operation profit maximum is found at low levels of fine flavor Cocoa proportion, however these
low proportion values require big plants, which leads to higher building investments. The table
is meant to give the policy makers tools for making a decision about the sizing of the plant, and
the benefits and disadvantages of changing the proportion that arrives to the plant, because that
mix brought by Cocoa farmers is a crucial factor in the feasibility analysis.
Different input parameter values can be put into the model in order to see the model response
to its change, evaluate model sensitivity to these parameters and help giving broad
recommendations to the decision makers.
49
Table 11. Scenario Comparison with fixed Cocoa processing proportions and integer multiplications of minimum plant capacity per scenario.
Fine Flavor
Cocoa
Proportion
Plant Capacity
(tons of raw
seeds per
week)
Building
Investment
(COP)
Operation
Investment
(COP)
Operation
Profit (COP)
0.3
17 $ 1,428,462,119 $ 100,485,228 $ 90,135,335
34 $ 2,856,924,238 $ 86,725,614 $ 200,431,322
51 $ 4,285,386,357 $ 75,519,850 $ 309,578,598
0.4
13 $ 1,092,353,385 $ 129,893,352 $ 60,838,113
26 $ 2,184,706,770 $ 117,067,199 $ 142,060,490
39 $ 3,277,060,155 $ 102,227,316 $ 230,785,705
0.5
10 $ 840,271,834 $ 138,622,642 $ 51,307,600
20 $ 1,680,543,668 $ 125,662,357 $ 123,253,653
30 $ 2,520,815,502 $ 116,793,973 $ 171,094,413
0.6
9 $ 756,244,651 $ 149,489,707 $ 68,531,203
18 $ 1,512,489,302 $ 129,304,257 $ 101,841,323
27 $ 2,268,733,953 $ 134,190,159 $ 171,354,582
5. Implementation Requirements
5.1. Transport Allocation Model
The simulation stage is the one that requires more information, due to the amount of internal
processes that it considers. Data required basically resumes to processing times, processes’
efficiency, machinery capacity, available workers, and Cocoa specific features. Precisely, the
input parameters of the simulation model are presented in Table 13, along with their description
and the source we used to estimate them.
6. Table 12. Data required for the simulation model
Parameter Description
Proportion of variety groups
Proportion of Cocoa that arrives to the plant from each group: Arauca Model, high-yield bulk
varieties, low-yield bulk varieties
Geographical Location of the
Farms Actual location of Teme and Fortul farms
Cocoa production Production of cocoa beans from each farm
depending on the seasonality of the harvest.
Mass of pods by group
Mass of a single pod for each variety group: Arauca Model, high-yield bulk varieties, low-yield bulk
varieties
50
Classification and opening time
Time required to classify a pod by genetic variety, and to open it
Mass percentage of seeds
The mass percentage that fresh Cocoa seeds represent from the total fruit
6.1. Process Analysis of the Postharvest Cocoa Plant
The simulation stage is the one that requires more information, due to the amount of internal
processes that it considers. Data required basically resumes to processing times, processes’
efficiency, machinery capacity, available workers, and Cocoa specific features. Precisely, the
input parameters of the simulation model are presented in Table 13, along with their description
and the source we used to estimate them.
Table 13. Data required for the implementation of the simulation model
Parameter Description
Raw material arrivals
Amount of pods or seeds that will daily arrive to the processing plant
Proportion of variety groups
Proportion of Cocoa that arrives to the plant from each group: Arauca Model, high-yield bulk
varieties, low-yield bulk varieties
Mass of pods by group
Mass of a single pod for each variety group: Arauca Model, high-yield bulk varieties, low-yield bulk
varieties
Velocity Walking velocity for workers in the plant
Unload times Time required to unload a 40-kiogram package
that arrives to the plant
Classification and opening time
Time required to classify a pod by genetic variety, and to open it
Mass percentage of seeds
The mass percentage that fresh Cocoa seeds represent from the total fruit
Fermentation time for boxes
Length of time that high and low-yield bulk seeds must must be fermented.
Fermentation time for bioreactors
Length of time that Arauca Model seeds must be fermented.
Time to empty boxes and
bioreactors
Time required to empty the contents of one box or bioreactor (400 kilograms)
Capacity of bioreactors and
boxes
Number of available boxes and bioreactors, and their capacity (in mass units)
Mass percentage of leachates
Mass percentage loss during fermentation due to leachates releasing
Drying time Length of time that fermented seeds must be dried
Drying efficiency Mass percentage of dry Cocoa beans after the
drying process
51
Time to empty a dryer
Time required to empty the contents of one dryer
Capacity of dryers Number of available dryers and their capacity (in
mass units)
Workers’ work-schedule
Working time of an employee in a day
Workweek and Sunday workers
Amount of workweek and Sunday employees to be hired
Area of the processing plant
The area for the parking lot, classification and opening, fermentation, and drying zones of the
processing plant
Moreover, this model proposes scenarios for implementing the processing plant, considering the
number of workweek employees, Sunday employees, and the batches to process in each machine,
before performing maintenance procedures. With the model, it is possible to evaluate diverse
scenarios and select the one that generates more operational profitability, along with product
quality.
6.2. Profitability Analysis
The profitability analysis stage, due to its nature, does not need a lot of critical information in a
potential implementation scenario. Information related to actual yield of the production plant
and specifically the proportion between bulk Cocoa and fine flavor Cocoa, would be critical for
the implementation of this model. Also, because of its bargaining nature that makes it highly
variable and totally dependent on the seller, a detailed database on fine flavor Cocoa sells, their
size and price would lead the model to a more precise price series and, thus, an accurate
estimation of a probability distribution, causing predictions to be more robust and reliable.
Table 14. Data required for the implementation of the financial feasibility model
Parameter Description
Processing plant yield
Percentage equivalent between weight of war Cocoa seeds that enter the plant, and the processed
dry Cocoa beans
Proportion of variety groups
Proportion of processed Cocoa yielded by the plant from each group: Arauca Model, and bulk Cocoa
Fine flavor Cocoa contract prices
The price per ton of fine flavor Cocoa sells
Fine flavor Cocoa contract sizes
Size of fine flavor Cocoa contracts
Cocoa sells contract conditions
Specific information regarding costs, selling processes and overall conditions
Application financial results
Profit derived from following the optimal selling policy in order to compare and determining
accuracy of the model
52
Costs concerning operation and
commercialization Exportation costs, storage costs, selling costs
7. Conclusions and future work
In this paper we present a comprehensive analytical approach that is useful to assess the
feasibility of a post-harvest processing plant for Cocoa produced in the municipality of Tame in
Arauca, Colombia. The proposed solution divides the problem in three phases. In the first phase,
we developed a transport allocation model based on three linear optimization sub-models. These
sub-models allow to balance the amount of collected Cocoa, the number of visited villages and
minimize the daily traveled distance. This allows us to determine the daily routes from the
villages to the processing plant. With the aid of this model, we determined what the best way to
transport Cocoa is in the form of seeds, as transportation costs are minimized.
In the second phase, we proposed a discrete-event simulation approach to describe the dynamics
of a Cocoa processing center in Tame, Arauca, Colombia. This model takes into account the
perishability of Cocoa seeds, limiting the number of hours that they may wait before fermenting.
We first developed a model where whole Cocoa pods arrive to the plant and we compared it with
a model in which Cocoa arrives in the form of fresh seeds. For these two cases we determined
the number of required workers for achieving stability. In the case of receiving whole pods, the
plant needs four workweek employees and two Sunday employees for its operation. On the other
hand, if fresh seeds are received, the number of required employees is less: two during workweek
and two on Sunday. We then extended our models to include periodic machinery maintenance
procedures. We compared diverse maintenance scenarios in terms of the workers utilization, the
percentage of time that machines spend in maintenance, the throughput of dry Cocoa beans, and
the utilization of the machines in the plant. The main advantage of our model is that it may be
used as a decision-making tool in the process of specifying the requirements of the Cocoa
processing plant and evaluating different policies or alternatives.
Finally, we proposed a financial feasibility model that consists in a strong tool for decision makers
to rely on. With a set of input parameters, the model provides information of the operation utility
in a 17-week time horizon, the minimum initial operation investment, the optimal selling
periods and amounts for bulk Cocoa, the inventory dynamics for both: bulk and fine flavor Cocoa,
and the fixed weekly payment to cover the totality of the loan in the specified term. This model
is highly flexible, as different control variables can be entered as input parameters; hence, it can
be adapted to any scenario and help to lead decision makers to the best possible solution under
selected circumstances. If a policy based on incentives for producers can be establish in order to
increase fine flavor Cocoa processing proportion to 40%, we recommend to build a plant with a
13 ton capacity, due to its relatively low building cost. Profit made in 4 months is not very high
but operational investment can be covered in less than a year, making it an affordable alternative
with a middle term positive return. Nonetheless, if processing rate can be further increased to a
50%, a 20 ton plant would be ideal because operation investment can be covered in just a 4 month
period. A building investment of around 1,700 million COP would be needed, but with
operational investment of 125 million COP, the loan can be paid in 10 years of the optimal selling
strategy is followed.
53
Acknowledgements
We would like to thank Coopcacao and Agrosavia, especially in the problem identification and
data collection phases. We would also like to thank Simio, Gurobi and FICO Xpress for providing
licenses of their software under the academic agreements subscribed with Universidad de los
Andes. We would like to acknowledge the Research Office at Universidad de los Andes for
partially supporting us through the global initiative on agriculture which established links
between the Center for Optimization and Applied Probability (COPA) and Agrosavia at
Universidad de los Andes.
54
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