cocoa processing and commercialization: processing plant

57
1 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° and 10° 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,

Upload: others

Post on 16-Oct-2021

9 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Cocoa processing and commercialization: Processing plant

1

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,

Page 2: Cocoa processing and commercialization: Processing plant

2

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

Page 3: Cocoa processing and commercialization: Processing plant

3

(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

Page 4: Cocoa processing and commercialization: Processing plant

4

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

Page 5: Cocoa processing and commercialization: Processing plant

5

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.

Page 6: Cocoa processing and commercialization: Processing plant

6

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.

Page 7: Cocoa processing and commercialization: Processing plant

7

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

Page 8: Cocoa processing and commercialization: Processing plant

8

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.

Page 9: Cocoa processing and commercialization: Processing plant

9

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

Page 10: Cocoa processing and commercialization: Processing plant

10

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.,

Page 11: Cocoa processing and commercialization: Processing plant

11

∑ 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

Page 12: Cocoa processing and commercialization: Processing plant

12

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)

Page 13: Cocoa processing and commercialization: Processing plant

13

𝛻 ∗ 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:

Page 14: Cocoa processing and commercialization: Processing plant

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)

Page 15: Cocoa processing and commercialization: Processing plant

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)

Page 16: Cocoa processing and commercialization: Processing plant

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

Page 17: Cocoa processing and commercialization: Processing plant

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).

Page 18: Cocoa processing and commercialization: Processing plant

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

Page 19: Cocoa processing and commercialization: Processing plant

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.

Page 20: Cocoa processing and commercialization: Processing plant

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

Page 21: Cocoa processing and commercialization: Processing plant

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

Page 22: Cocoa processing and commercialization: Processing plant

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

Page 23: Cocoa processing and commercialization: Processing plant

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.

Page 24: Cocoa processing and commercialization: Processing plant

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

Page 25: Cocoa processing and commercialization: Processing plant

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

Page 26: Cocoa processing and commercialization: Processing plant

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

Page 27: Cocoa processing and commercialization: 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

Page 28: Cocoa processing and commercialization: Processing plant

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

Page 29: Cocoa processing and commercialization: Processing plant

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.

Page 30: Cocoa processing and commercialization: Processing plant

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.

Page 31: Cocoa processing and commercialization: Processing plant

31

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

Page 32: Cocoa processing and commercialization: Processing plant

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

Page 33: Cocoa processing and commercialization: Processing plant

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.

Page 34: Cocoa processing and commercialization: Processing plant

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

Page 35: Cocoa processing and commercialization: Processing plant

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

Page 36: Cocoa processing and commercialization: Processing plant

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.

Page 37: Cocoa processing and commercialization: Processing plant

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

Page 38: Cocoa processing and commercialization: Processing plant

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.

Page 39: Cocoa processing and commercialization: Processing plant

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.

Page 40: Cocoa processing and commercialization: Processing plant

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

Page 41: Cocoa processing and commercialization: Processing plant

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

Page 42: Cocoa processing and commercialization: Processing plant

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)

Page 43: Cocoa processing and commercialization: Processing plant

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%.

Page 44: Cocoa processing and commercialization: Processing plant

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.

Page 45: Cocoa processing and commercialization: Processing plant

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.

Page 46: Cocoa processing and commercialization: Processing plant

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.

Page 47: Cocoa processing and commercialization: Processing plant

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

Page 48: Cocoa processing and commercialization: Processing plant

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.

Page 49: Cocoa processing and commercialization: Processing plant

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

Page 50: Cocoa processing and commercialization: Processing plant

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

Page 51: Cocoa processing and commercialization: Processing plant

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

Page 52: Cocoa processing and commercialization: Processing plant

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.

Page 53: Cocoa processing and commercialization: Processing plant

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.

Page 54: Cocoa processing and commercialization: Processing plant

54

References

Afoakwa, E.O., J. E. Kongor, A.S. Budu, H. Mensah-Brown, and J. F. Takrama. 2015. Changes in

Biochemical and Physico-Chemical Qualities during Drying of Pulp Preconditioned and

Fermented Cocoa (Theobroma Cacao) Beans. Afr. J. Food Agric. Nutr. Dev. 15 (1): 9651–

70. doi:http://dx.doi.org/10.15226/jnhfs.2014.00121.

Ahumada, O., & Villalobos, J. R. (2009). Application of planning models in the agri-food supply

chain: A review. European Journal of Operational Research, págs. 1-20.

Arroyo, J. M., & Conejo, A. J. (August de 2000). Optimal Response of a thermal unit to an

electricity spot market. IEEE Transactions on Power Systems, págs. 1098-1104.

Banks, J. (2005). Discrete-Event System Simulation. Upper Saddle River, New Jersey: Prentice-

Hall.

Beg, M. S., Ahmad, S., Jan, K., & Bashir, K. (2017). Status, supply chain and processing of cocoa -

A review. Trends in Food Science & Technology, págs. 108-116.

Bjørndal, T., Herrero, L., Newman, A., Romero, C., & Weintrauh, A. (2012). Operation research

in the natural resource industry. International Transactions in Operational Research,

págs. 39-62.

Borodin, V., Bourtembourg, J., Hnaien, F., & Labadie, N. (2016). Handling uncertainty in

agricultural supply chain management: A state of the art. European Journal of

Operational Research, págs. 348-359.

Brockwell, P. J., Davis, R. A., & Calder, M. V. (2002). introduction to Time Series and

Forecasting. New York: Springer.

Buchet, S. (2017). Operation research for agriculture.

Busato, P. (2015). A simulation model for a rice-harvesting chain. Biosystems Engineering, págs.

149-159.

DANE. (n.d.). Weblet Importer. Retrieved November 29, 2018, from https://geoportal.dane.gov.co/veredas/

Durán, F. 2010. Cultivo y explotación del Cacao. Primera Edición. Colombia, Grupo Latino Eds,

pp. 40-46.

Federación Nacional de Cacaoteros. (10 de October de 2017). Noticias. Obtenido de Federación

Nacional de Cacaoteros: http://www.fedecacao.com.co/portal/index.php/es/2015-04-23-

20-00-33/494-sabe-usted-que-es-el-salon-del-chocolate-de-paris

Gobierno Digital Colombia. (2017). Agricultura y Desarrollo Rural. Obtenido de Datos Abiertos

de Colombia: https://www.datos.gov.co/Agricultura-y-Desarrollo-Rural/producion-

cacao-por-departamento/97ki-syuv

Page 55: Cocoa processing and commercialization: Processing plant

55

Higgins, A. J., Miller, C. J., Archer, A. A., Ton, T., Fletcher, C. S., & McAllister, R. J. (2010).

Challenges of operations research practice in agricultural value chains. Journal of the

Operational Research Society, pp. 964-973.

IGAC. (n.d.). ¿Qué estamos haciendo? | Instituto Geográfico Agustín Codazzi. Retrieved November 29, 2018, from https://www.igac.gov.co/es/contenido/areas-estrategicas/catastro/que-estamos-haciendo

International Cocoa Organization. (31 de January de 2001). About Us: Projects . Obtenido de

International Cocoa Organization: https://www.icco.org/about-us/international-Cocoa-

agreements/cat_view/50-projects.html

International Cocoa Organization. (2012, April 3). Harvesting and post-harvest processing.

Retrieved from International Cocoa Organization: https://www.icco.org/about-

Cocoa/harvesting-and-post-harvest.html

International Cocoa Organization. (26 de March de 2013). About Cocoa: Growing Cocoa.

Obtenido de International Cocoa Organization: International Cocoa Organization

Internatonal Cocoa Organization. (3 de January de 2017). About Cocoa: Fine or Flavor Cocoa.

Obtenido de Internatonal Cocoa Organization: https://www.icco.org/about-Cocoa/fine-

or-flavour-Cocoa.html

Instituto Geográfico Agustín Codazzi. (n.d.). Mapas Departamentales Físicos. Retrieved November 29, 2018, from https://geoportal.igac.gov.co/en/node/324

Kantanantha, N., Serban, N., & Griffin, P. (September de 2010). Yield and Price Forecasting for

Stochastic Crop Decision Planning. Journal of Agricultural, Biological and Environmental

Statistics, págs. 362-380.

Kaur, M., Heena, G., & Kundra, H. (12 de August de 2014). Data Mining in Agriculture Crop

Price Prediction; Techniques and Applications. International Journal of Computer

Applications.

Kazuhiro, K., Ishikawa, T., Fukuhara, Y., & Nakamura, Y. (1998). Stock Price Prediction Using

Prior Knowledge and Neural Networks.

Kim, K. J. (September de 2003). Financial time series forecasting using support vector

machines . Neurocomputing, págs. 13-19.

Legis. (1950). Artículo 158 - Jornada Ordinaria. En Código Sustantivo del Trabajo (págs. 48-49).

Bogotá: Legis Editores. Obtenido de Ministerio del Trabajo:

https://encolombia.com/derecho/codigos/codigo-sustantivo-trabajo/jornada-trabajo/

Lima, L. J., Almeida, M. H., Nout, M. R., & Zweitering, M. H. (2011). Theobroma cacao L., "The

food of the Gods": quality determinants of commercial cocoa beans, with particular

reference to the impact of fermentation. Critical reviews in food science and nutrition,

págs. 731-761.

Page 56: Cocoa processing and commercialization: Processing plant

56

Ma, X., Tao, Z., Wang, Y., Yu, H., & Wang, Y. (2015). Long short-term memory neural network

for traffic speed prediction using remote microwave sensor data. En Transportation

Research Part C: Emerging Technologies (págs. 187-197).

McMahon, T. (2018, November 14). Monthly US Inflation Rate 1913 to Present. Retrieved from

https://inflationdata.com/Inflation/Inflation_Rate/Monthly_Inflation.aspx

My Maps. (n.d.). Retrieved November 29, 2018, from https://www.google.com/maps/d/u/0/

Nogales, F. J., Contreras, J., Conejo, A. J., & Espinola, R. (May de 2002). Forecasting next-day

electricity prices by time series models. IEEE Transactions on power systems, págs. 342-

348.

Oxford Business Group. (2014). Cacao production and exports on the rise. Obtenido de Oxford

Business Group: https://oxfordbusinessgroup.com/analysis/cacao-production-and-

exports-rise

Plà-Aragonés, L. M. (2015). Handbook of Operations Research in Agriculture and in the Agri-

Food Industry.

Proexport Colombia. (2012). Colombian Cocoa "High quality and distinctive aroma". Obtenido

de http://www.inviertaencolombia.com.co/en/images/Cocoa%20profile%202012.pdf

Producion cacao por departamento | Datos Abiertos Colombia. (n.d.). Retrieved November 29, 2018, from https://www.datos.gov.co/Agricultura-y-Desarrollo-Rural/producion-cacao-por-departamento/97ki-syuv

Production, Chemistry, and Use A Caligiani, A Marseglia, and G Palla, University of Parma,

Parma, Italy ã 2016 Elsevier. Encyclopedia of Food and Health. 185-190.

Ríos, F., Ruiz, A., Lecaro, J., & Rehpani, C. (2017). Estrategias país para la oferta de cacaos

especiales - Políticas e iniciativas privadas exitosas en el Perú, Ecuador, Colombia y

República Dominicana.

Schwan, R. F., & Fleet, G. H. (2014). Cocoa and coffee fermentations. Boca Raton: CRC Press.

Sociedad de Ergonomistas de México. (2009). Las Normas ISO 11228 en el Manejo Manual de

Cargas . Obtenido de Sociedad de Ergonomistas de México:

http://www.semac.org.mx/archivos/congreso11/Pres09.pdf

The Chocolate Society. (13 de October de 2010). The Different Varieties of Cocoa Beans: Criollo,

Trinitario & Forastero. Obtenido de The Chocolate Society:

https://www.chocolate.co.uk/blogs/news/the-different-varieties-of-Cocoa-beans-

criollo-trinitario-and-forastero

Useche, J. P., & Ardila, J. R. (2004). Guía técnica para el cultivo de cacao, 30p. Retrieved from http://201.234.78.28:8080/jspui/handle/123456789/3601

Weather Spark. (n.d.). Clima promedio en Arauca, Colombia, durante todo el año - Weather Spark. Retrieved December 3, 2018, from https://es.weatherspark.com/y/26641/Clima-

Page 57: Cocoa processing and commercialization: Processing plant

57

promedio-en-Arauca-Colombia-durante-todo-el-año

Weintraub, A., & Romero, C. (2006). Operations research models and the management of

agricultural and forestry resources: A review and comparison. Interfaces, págs. 446-457.

Yates, N. (2014). A Discrete Event Simulation for the Analysis of the Harvesting, Transportation

and Processing Systems of a Seasonal Vegetable Production Operation. En B. Tjahjono,

C. Heavey, & S. Onggo, GEnerating insights: The efectiveness of discrete-event simulation

models in creative problem solving (págs. 46-55). Worcestershire, UK: The OR Society.