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An analytics solution for harvesting operations in
an oil palm plantation
Jorge Leal, M.Sc.
Mariana Escallón , M.Sc.
Daniel Castillo-Gómez, M.Sc.
Andrés Medaglia, Ph.D.
Center for the Optimization and Applied Probability (COPA)
Industrial Engineering Department
Carlos Montenegro, Ph.D.
Center for Orinoquia Studies (CEO)
Universidad de los Andes (Colombia)
1
II International Conference on
Agro BigData and Decision
Support Systems in Agriculture12-14 July 2018. Lleida (Spain)
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Agenda
Introduction
Project stages
Results
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Agenda
Introduction
Motivation
Context
Problem definition
Literature review
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Motivation
*Fedepalma (2018).
Introduction Project stages Results
Palm oil
Economic:
By 2015, valued at USD 66 billion (global)
Major job provider in Colombia (140,000)*
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Motivation
54%31%
3%
2% 2%
8%
Palm oil market
Indonesia
Malaysia
Thailand
Colombia
Nigeria
Others (23 countries)
Introduction Project stages Results
Fedepalma (2015); Euromonitor International (2018).
Palm oil
Economic:
By 2015, valued at USD 66 billion (global)
Major job provider in Colombia (140,000)*
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Motivation
Higher productivity in:
• Malaysia – 26%
• Indonesia – 23%
Introduction Project stages Results
Fedepalma (2015); Euromonitor International (2018).
Palm oil
Economic:
By 2015, valued at USD 66 billion (global)
Major job provider in Colombia (140,000)*
54%31%
3%
2% 2%
8%
Palm oil market
Indonesia
Malaysia
Thailand
Colombia
Nigeria
Others (23 countries)
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Motivation
Main uses:
Alimentary: cooking oil, margarine and ice cream
Non-alimentary: biodiesel, soap and cosmetics
Introduction Project stages Results
Palm oil
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Motivation
Main uses:
Alimentary: cooking oil, margarine and ice cream
Non-alimentary: biodiesel, soap and cosmetics
Environmental issues:
Deforestation in Southeast Asia
Plantations in flooded savannas as in Colombian
Orinoquia have less impact in the ecosystem
Introduction Project stages Results
Palm oil
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Agenda
Introduction
Motivation
Context
Problem definition
Literature review
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Context
Introduction Project stages Results
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Context
Introduction Project stages Results
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Context - La Ilusión plantation
• 2,090 hectares
Introduction Project stages Results
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Context - La Ilusión plantation
• 2,090 hectares
• 87 land plots
• Sowing years 2009, 2010 y 2011
• 200 workers (direct and outsourced)
• 100 km of cableway
• 8 aerial tractors
Introduction Project stages Results
2009
2010
2011
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Context - La Ilusión plantation
Introduction Project stages Results
Planting, fertilization
and maintenance
Harvest Transport Oil extraction
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Context - La Ilusión plantation
Introduction Project stages Results
Planting, fertilization
and maintenance
Harvest Transport Oil extraction
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Planting, fertilization
and maintenance
Harvest Transport Oil extraction
16
Context - La Ilusión plantation
Introduction Project stages Results
8 20 days
Buffalo
Mechanized
Harvest crew
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Planting, fertilization
and maintenance
Harvest Transport Oil extraction
17
Context - La Ilusión plantation
Introduction Project stages Results
• 30 containers per trip
• 150 kg per container
• 3 - 4.5 tons per trip
8 aerial tractors
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Planting, fertilization
and maintenance
Harvest Transport Oil extraction
18
Context - La Ilusión plantation
Introduction Project stages Results
Cableway network
• Main cable
• Secondary cables
• Tertiary cables
• Stockpiling center
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Business problem
Introduction Project stages Results
Average harvest cycle length: 19.6 days
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Business problem
How to visit the plantation to
reduce the harvest cycle length?
Introduction Project stages Results
HarvestTransport
8 20 days
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Business problem
Introduction Project stages Results
HarvestTransport
8 20 days
Reduce costs
Optimize resource allocation
Reduce uncertainty in task scheduling
How to visit the plantation to
reduce the harvest cycle length?
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Agenda
Introduction
Motivation
Context
Problem definition
Literature review
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Literature review
23
Oil palm
Harvest Transport
Gen
eral
ana
lysi
sLi
near
optim
izat
ion
• Durán, Sierra & García (2004).
Extraction potential.
• Mosquera, Fontanilla & Donado
(2008). Harvest studies for oil
palm.
• Mosquera et al. (2008).
Harvest comparison, invidual or
group.
• Solah, Hitam & Borhan (2004).
Cableway system for oil palm
FFB evacuation.
• Fontanilla & Castiblanco (2009).
Cableway at the harvesting.
• Fontanilla et al. (2010).
Comparison between FFB
evacuation systems.
Adarme, Fontanilla & Arango (2011).
General logistic model and single
sourcing.
García-Cáceres (2007). Tactical
and operative optimization of
the supply chain in the oil palm
industry.
Supply chain
Fontanilla (2012). Stockpilling center location model for an oil palm
plantation.
Oth
er Ademosun (1982). Location-allocation models for oil palm
production (feasible set approach).
Cableway
Introduction Project stages Results
Euler, Hoffmann, Fathoni, &
Schwarze (2016). Exploring yield
gaps in oil palm production
systems.
• Corley & Tinker (2016).
The Oil Palm.
• Murphy (2014). Oil palm
crop challenges.
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• Plà-Aragonés
(2015). Handbook
of Operations
Research in
Agriculture and the
Agri-Food Industry
Literature review
24
Other crops
Harvest Transport Supply chain
Dis
cret
e-ev
ent
sim
ulat
ion
• Yates (2014). Harvest, transport and processing of
vegetables.
• van der Vorst et al. (2000). Modelling and simulating
multi-echelon food systems.
• van der Vorst et al. (2009). Simulation modeling for
food supply chain redesign.
Heu
ristic
s
Edwards et al. (2015). Tabu search task allocation in agriculture.
• Ali et al. (2009). Infield logistics planning for crop-
harvesting operations.
• Caixeta-Filho (2006). Orange
harvesting scheduling management:
A case study. MIP optimal harvest
for juice extraction and acidity level.
Line
ar
optim
izat
ion
• Amorim et al. (2012). Multi-objective integrated production
and distribution planning of perishable products.
• Jiao, Higgins, & Prestwidge (2005). An integrated
statistical and optimization approach to increasing sugar
production within a mill region.
Introduction Project stages Results
• Borodin et al. (2014). A
quality risk management
problem: Case of annual
crop harvest scheduling.
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Agenda
Introduction
Project stages
Results
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Project stages
Introduction Project stages Results
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Ripeness
cost
function
Yield
forecast
Q: Quarterly
W: Weekly
D: Daily
Parameter estimation
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Project stages
Introduction Project stages Results
Transport allocation
model D
Resource allocation
model W
Q: Quarterly
W: Weekly
D: Daily
Harvest cycle
model Q
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Project stages
Introduction Project stages Results
Transport allocation
model D
Resource allocation
model W
Q: Quarterly
W: Weekly
D: Daily
Harvest cycle
model Q
What day and how
much fruit should be
collected for each
land plot?
Strategical
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Project stages
Introduction Project stages Results
Transport allocation
model D
Resource allocation
model W
Q: Quarterly
W: Weekly
D: Daily
How to allocate
harvest crews
throughout the
plantation?
Tactical
Harvest cycle
model Q
What day and how
much fruit should be
collected for each
land plot?
Strategical
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Project stages
Introduction Project stages Results
Harvest cycle
model Q
Transport allocation
model D
Resource allocation
model W
Q: Quarterly
W: Weekly
D: Daily
What are the aerial
tractor routes for
fruit evacuation?
Operational
How to allocate
harvest crews
throughout the
plantation?
Tactical
What day and how
much fruit should be
collected for each
land plot?
Strategical
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Project stages
Introduction Project stages Results
Feasible?
Add constraints
Amount (kg) of fresh fruit
to be harvested each day
Amount (kg) of fresh
fruit to pick in each
land plot each day
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Feasible?
Add constraints
Ripeness
cost
function
Yield
forecast
Q: Quarterly
W: Weekly
D: Daily
Parameter estimation
Aerial
tractor
order
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Project stages
Introduction Project stages Results
Amount (kg) of fresh fruit
to be harvested each day
Amount (kg) of fresh
fruit to pick in each
land plot each day
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Feasible?
Add constraints
Ripeness
cost
function
Yield
forecast
Parameter estimation
Feasible?
Add constraints
Q: Quarterly
W: Weekly
D: Daily
Aerial
tractor
order
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1. We assign a penalization for not visiting the palm on time
FFB state
Ripeness cost function
Introduction Project stages Results
Unripe Ripe Overripe Rotten
< 8 days
No fruitlets
detachment
8-12 days
< 50% fruitlets
detachment
12-17 days
>50% fruitlets
detachment
17-20 days
Dehydrated
bunch
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Ripeness cost function
Introduction Project stages Results
Oil yield loss
Higher
harvesting
time
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Project stages
Introduction Project stages Results
Amount (kg) of fresh fruit
to be harvested each day
Amount (kg) of fresh
fruit to pick in each
land plot each day
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Feasible?
Add constraints
Ripeness
cost
function
Yield
forecast
Parameter estimation
Feasible?
Add constraints
Q: Quarterly
W: Weekly
D: Daily
Aerial
tractor
order
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Yield forecast
Introduction Project stages Results
1. Time series fitting and forecast
Methodology
Forecast for average yield zone 9 for short harvest cycle lengths
0
200
400
600
800
1000
1200
Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2
2015 2016 2017 2018
kg /
ha
Quarter
Real
Forecast
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0
200
400
600
800
1000
1200
Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2
2015 2016 2017 2018
kg /
ha
Quarter
Real
Forecast
37
Yield forecast
Introduction Project stages Results
2. Variability for each land plot
Methodology
Forecast for average yield zone 9 for short harvest cycle lengths
ln 𝑦9,𝑄2 , 𝜎2010
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Yield forecast
Introduction Project stages Results
2. Variability for each land plot
Methodology
0
200
400
600
800
1000
1200
Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2
2015 2016 2017 2018
kg /
ha
Quarter
Real
Forecast
Forecast for average yield zone 9 for short harvest cycle lengths
𝑦52′
Simulation
land plot 52
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Yield forecast
Introduction Project stages Results
1. Quarterly average per zone (Holt-Winters) captures seasonality and long-term trend
2. Monte Carlo simulation (particular value per land plot)
3. Increase in production due to accumulation (harvest cycle length)
• Polynomial regression
Yield increase - land plot 52
𝑓(𝑥) = 𝑦52′ 1 + 𝛽2𝑥
2 + 𝛽3𝑥3
750
900
1050
1200
1350
1500
0 2 4 6 8 10 12
Yie
ld (
kg /
ha)
Days from optimal cycle length
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Project stages
Introduction Project stages Results
Feasible?
Add constraints
Amount (kg) of fresh fruit
to be harvested each day
Amount (kg) of fresh
fruit to pick in each
land plot each day
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Feasible?
Add constraints
Ripeness
cost
function
Yield
forecast
Parameter estimation
Q: Quarterly
W: Weekly
D: Daily
Aerial
tractor
order
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Harvest cycle model
When and how much fruit to collect from each land plot?
Planning horizon: 3 months
Objective: Reduce harvest cycle length
Subject to:
• Transport capacity
• Daily labor time
• Daily production capacity
Introduction Project stages Results
Q
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1 2 3 4 5 6 7 8 9 10
42
Harvest cycle model
Aim
X X XLand plot 1
Days
Introduction Project stages Results
Q
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1 2 3 4 5 6 7 8 9 10
43
Harvest cycle model
Aim
Land plot 1
Days
Introduction Project stages Results
Q
X X X
X X X
X X X
X X X
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1 2 3 4 5 6 7 8 9 10
44
Harvest cycle model
Aim
Land plot 1
Days
Introduction Project stages Results
Q
X X X
X X X
X X X
X X X
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1 2 3 4 5 6 7 8 9 10
45
Harvest cycle model
Aim
X X XLand plot 1
Days
Introduction Project stages Results
Q
X X X
X X XLand plot 2
Land plot 3 X X X
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Harvest cycle model
Column generation
Introduction Project stages Results
Q
Auxiliary
problem
Visit pattern
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Harvest cycle model
Column generation
Introduction Project stages Results
Q
Master
problem
𝑥𝑝𝐻 ≥ 0
Auxiliary
problem
End
𝕨T
𝕒𝑠𝑟𝑠 > 0
Master
problem
𝑥𝑝𝐻 ∈ {0,1}
Sí No
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Objective function
max
𝑖∈𝒯
𝑗∈𝒯
𝓁∈ℒ
𝑦𝑖𝑗𝓁𝐻 𝑔 ∙ 𝛿𝑖𝑗𝓁 − 𝜍𝑖𝑗𝓁 − 𝕨
T𝕒𝑠
48
Harvest cycle model
Mathematical model
Introduction Project stages Results
QAuxiliary problem
𝑟𝑠
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Objective function
max
𝑖∈𝒯
𝑗∈𝒯
𝓁∈ℒ
𝑦𝑖𝑗𝓁𝐻 𝑔 ∙ 𝛿𝑖𝑗𝓁 − 𝜍𝑖𝑗𝓁 − 𝕨
T𝕒𝑠
49
Harvest cycle model
Mathematical model
Introduction Project stages Results
QAuxiliary problem
Pattern usefulness
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Harvest cycle model
Mathematical model
Introduction Project stages Results
QAuxiliary problem
Objective function
max
𝑖∈𝒯
𝑗∈𝒯
𝓁∈ℒ
𝑦𝑖𝑗𝓁𝐻 𝑔 ∙ 𝛿𝑖𝑗𝓁 − 𝜍𝑖𝑗𝓁 − 𝕨
T𝕒𝑠
Problem linking
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Harvest cycle model
Mathematical model
Introduction Project stages Results
QAuxiliary problem
Objective function
max
𝑖∈𝒯
𝑗∈𝒯
𝓁∈ℒ
𝑦𝑖𝑗𝓁𝐻 𝑔 ∙ 𝛿𝑖𝑗𝓁 − 𝜍𝑖𝑗𝓁 − 𝕨
T𝕒𝑠
𝕒𝑠 =
𝑗∈𝒯
𝑦𝑠𝑗𝓁𝐻 ∀𝓁 ∈ ℒ ,
𝑗∈𝒯
𝓁∈ℒ
𝑦𝑖𝑗𝓁𝐻 𝛿𝑖𝑗𝓁
𝑘𝑡𝓁 ∀𝑖 ∈ 𝒯,
𝑗∈𝒯
𝓁∈ℒ
𝑦𝑖𝑗𝓁𝐻 𝛿𝑖𝑗𝓁 ∀𝑖 ∈ 𝒯,
𝕨T: dual variables from master problem constraints
Pattern type
Utilization of aerial tractors
Amount of fruit collected
Problem linking
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Harvest cycle model
Mathematical model
Introduction Project stages Results
QAuxiliary problem
⋮
𝑠 𝑒Lan
d p
lots
1
2
ℒ
⋮
Days
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Harvest cycle model
Mathematical model
Introduction Project stages Results
QAuxiliary problem
⋮
𝑠 𝑒Lan
d p
lots
1
2
ℒ
⋮
Days
1,0 1,3 1,7 1,9
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Harvest cycle model
Mathematical model
Introduction Project stages Results
QAuxiliary problem
⋮
𝑠 𝑒Lan
d p
lots
1
2
ℒ
⋮
Days
1,0 1,3 1,7 1,9
𝛿0,3,1
𝛿3,7,1 𝛿7,9,1
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Harvest cycle model
Column generation
Introduction Project stages Results
Q
Master
problem
Pattern selection
for each land plot
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Project stages
Introduction Project stages Results
Feasible?
Add constraints
Amount (kg) of fresh fruit
to be harvested each day
Amount (kg) of fresh
fruit to pick in each
land plot each day
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Feasible?
Add constraints
Ripeness
cost
function
Yield
forecast
Q: Quarterly
W: Weekly
D: Daily
Parameter estimation
Aerial
tractor
order
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Resource allocation model
Introduction Project stages Results
W How to arrange the land plots programmed in a timetable?
Planning horizon: 1 week
Objective: Minimize yield loss (earliness)
Subject to:
• Available personnel
• Harvesting time for each land plot
• Deadline per land plot
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Resource allocation model
Introduction Project stages Results
WAim Harvest crew 1
Time interval Day
Start End M T W Th F S Su
06:00 07:00
07:00 08:00
08:00 09:00
09:00 10:00
10:00 11:00
11:00 12:00 Land plot 1
13:00 14:00 Land plot 2
14:00 15:00 Land plot 3
15:00 16:00 Land plot 4
Land plot 5
Land plot 6
Land plot 7
Land plot 8
Land plot 9
Rest/travel time
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Resource allocation model
Introduction Project stages Results
WAim Harvest crew 1
Time interval Day
Start End M T W Th F S Su
06:00 07:00
07:00 08:00
08:00 09:00
09:00 10:00
10:00 11:00
11:00 12:00 Land plot 1
13:00 14:00 Land plot 2
14:00 15:00 Land plot 3
15:00 16:00 Land plot 4
Land plot 5
Harvest crew 2 Land plot 6
Time interval Day Land plot 7
Start End M T W Th F S Su Land plot 8
06:00 07:00 Land plot 9
07:00 08:00 Rest/travel time
08:00 09:00
09:00 10:00
10:00 11:00
11:00 12:00
13:00 14:00
14:00 15:00
15:00 16:00
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Resource allocation model
Introduction Project stages Results
WScheduling
Machine-oriented
Harvest crews Land plots to harvest
time
0 5 10 15 20 25
M1 L2 L3
M2 L1 L5
M3 L28 L29
M4 L14 L18
M5 L21 L20
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Optimization
61
Resource allocation model
Introduction Project stages Results
𝑒∗𝑠∗
1
2
ℳ
1 2 3 ℒ
⋮
⋯
1,1 1,2 1, |ℒ|1,3
2,1 2, |ℒ|
|ℳ|, 1 |ℳ|, 2 |ℳ|, |ℒ||ℳ|, 3
Har
vest
cre
ws
Land plots
⋮ ⋮ ⋮ ⋮
⋯
⋯
⋯
2,3
Arcs 𝐴1 Arcs 𝐴2 Arcs 𝐴3
Network structureSequence
W
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Optimization
62
Resource allocation model
Introduction Project stages Results
𝑒∗𝑠∗
1
2
ℳ
1 2 3 ℒ
⋮
⋯
1,1 1,2 1, |ℒ|1,3
2,1 2, |ℒ|
|ℳ|, 1 |ℳ|, 2 |ℳ|, |ℒ||ℳ|, 3
Har
vest
cre
ws
Land plots
⋮ ⋮ ⋮ ⋮
⋯
⋯
⋯
2,3
Arcs 𝐴1 Arcs 𝐴2 Arcs 𝐴3
Network structureSequence (example)
W
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Resource allocation model
Introduction Project stages Results
WMathematical model
time
0 5 10 15 20 25
M1 L2 L3
𝑡2𝑠 𝑡2
𝑐𝑝12 𝑡3𝑠 𝑡3
𝑐𝑝13
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Resource allocation model
Introduction Project stages Results
WMathematical model
time
0 5 10 15 20 25
M1 L2 L3
𝑡2𝑐 𝑡3
𝑠𝜏23
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Resource allocation model
Introduction Project stages Results
WMathematical model
time
0 5 10 15 20 25
M1 L2
𝑡2𝑐 𝑑2𝑡2
𝑒
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Project stages
Introduction Project stages Results
Feasible?
Add constraints
Amount (kg) of fresh fruit
to be harvested each day
Amount (kg) of fresh
fruit to pick in each
land plot each day
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Feasible?
Add constraints
Ripeness
cost
function
Yield
forecast
Q: Quarterly
W: Weekly
D: Daily
Parameter estimation
Aerial
tractor
order
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Transport allocation model
Introduction Project stages Results
D
Which should be the daily routes for the aerial tractors?
Planning horizon: one day
Objective: Collect all the estimated production
Subject to:
• Maximum pulling capacity
• Daily operational time
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Transport allocation model
Introduction Project stages Results
D
Calculate number
of trips per land
plot
Create route for
unattended
demand
Assign routes to
every aerial
tractor
-
http://copa.uniandes.edu.co/
Land
plot
Demand
(kg)
Number of
trips
Unattended
demand (kg)
L1 12,300 2.7 3,300
L8 8,500 1.9 4,000
L2 10,200 2.3 1,200
69
Transport allocation model
Introduction Project stages Results
D
4,500 Kg
Calculate number
of trips per land
plot
Create route for
unattended
demand
Assign routes to
every aerial
tractor
-
http://copa.uniandes.edu.co/
Land
plot
Demand
(kg)
Number of
trips
Unattended
demand (kg)
L1 12,300 2.7 3,300
L8 8,500 1.9 4,000
L2 10,200 2.3 1,200
70
Transport allocation model
Introduction Project stages Results
D
4,500 Kg
L8 L1
L2
Calculate number
of trips per land
plot
Create route for
unattended
demand
Assign routes to
every aerial
tractor
-
http://copa.uniandes.edu.co/ 71
Transport allocation model
Introduction Project stages Results
D
L1
L2
L1L8
Route A Route CRoute B
3 times 2 times
Calculate number
of trips per land
plot
Create route for
unattended
demand
Assign routes to
every aerial
tractor
-
http://copa.uniandes.edu.co/ 72
Transport allocation model
Introduction Project stages Results
D
-
http://copa.uniandes.edu.co/ 73
Transport allocation model
Introduction Project stages Results
D
Route A
SPC
AA AB 14A 11A 8A
L8
8A 11A 14A AB AA
SPC
L8
Route A
Calculate number
of trips per land
plot
Create route for
unattended
demand
Assign routes to
every aerial
tractor
-
http://copa.uniandes.edu.co/ 74
Transport allocation model
Introduction Project stages Results
D
Calculate number
of trips per land
plot
Create route for
unattended
demand
Assign routes to
every aerial
tractor
Route-A
Route-B
Route-C
On hold
-
http://copa.uniandes.edu.co/ 75
Transport allocation model
Introduction Project stages Results
D
Route-A
Route-B
Route-C
Local search with
swap moves
Discrete-event
simulation
Calculate number
of trips per land
plot
Create route for
unattended
demand
Assign routes to
every aerial
tractor
On hold
-
http://copa.uniandes.edu.co/ 76
Transport allocation model
Introduction Project stages Results
D
Route-A
Route-B
Route-C
Discrete-event
simulation
Calculate number
of trips per land
plot
Create route for
unattended
demand
Assign routes to
every aerial
tractor
On hold
New sequence Time calculation
Local search with
swap moves
-
http://copa.uniandes.edu.co/ 77
Project stages
Introduction Project stages Results
Feasible?
Add constraints
Amount (kg) of fresh fruit
to be harvested each day
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Feasible?
Add constraints
Ripeness
cost
function
Yield
forecast
Q: Quarterly
W: Weekly
D: Daily
Parameter estimation
Aerial
tractor
order
Amount (kg) of fresh
fruit to pick in each
land plot each day
-
http://copa.uniandes.edu.co/ 78
Discrete-event simulation
Introduction Project stages Results
-
http://copa.uniandes.edu.co/ 79
Discrete-event simulation
Introduction Project stages Results
-
http://copa.uniandes.edu.co/
Introduction Project stages
80
Discrete-event simulation
General
modeling
Results
Node types
Intersection
Land plot
X
X X
X
X
FFB: Fresh fruit bunches
-
http://copa.uniandes.edu.co/
Node types
Intersection
Land plot
Introduction Project stages
81
Discrete-event simulation
General
modeling
Results
X
X
X
X
XX
FFB: Fresh fruit bunches
-
http://copa.uniandes.edu.co/
Introduction Project stages
82
Discrete-event simulation
General
modeling
Results
Node types
Intersection
Land plot
Aerial tractor
Transits through the network
FFB: Fresh fruit bunches
-
http://copa.uniandes.edu.co/
Introduction Project stages
83
Discrete-event simulation
General
modeling
Results
Node types
Intersection
Land plot
Aerial tractor
Transits through the network
Stockpiling center
FFB: Fresh fruit bunches
-
http://copa.uniandes.edu.co/
Introduction Project stages
84
Discrete-event simulation
General
modeling
Results
Node types
Intersection
Land plot
Aerial tractor
Transits through the network
Stockpiling center
Entities
Represent containers of FFB
Transported by aerial tractors
FFB: Fresh fruit bunches
-
http://copa.uniandes.edu.co/
Introduction Project stages
85
Discrete-event simulation
General
modeling
Aerial tractors
Loading time
Unloading time (workers in
SPC)
Time between failures
Repair Time
Uncertainty
Scenarios
Number of aerial tractors
Results
FFB: Fresh fruit bunches
-
http://copa.uniandes.edu.co/ 86
Project stages
Introduction Project stages Results
Feasible?
Add constraints
Amount (kg) of fresh fruit
to be harvested each day
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Feasible?
Add constraints
Ripeness
cost
function
Yield
forecast
Q: Quarterly
W: Weekly
D: Daily
Parameter estimation
Aerial
tractor
order
Amount (kg) of fresh
fruit to pick in each
land plot each day
-
http://copa.uniandes.edu.co/
Introduction Project stages
87
Modeling
logic
Discrete-event simulation
Results
1 2 3 4 5 6 7
Land
plo
ts
X
X
… X …
X
X X
Days
Inputs
Harvest cycle
model
-
http://copa.uniandes.edu.co/
Introduction Project stages
88
Modeling
logic
Discrete-event simulation
Results
1 2 3 4 5 6 7
Land
plo
ts
X
X
… X …
X
X X
Days
InputsLand
plot
Day 7
L1 15 ton
L2 -
… -
… 2.5 ton
LX -
.. -
… 20 ton
L86 -
L87 10 ton
Harvest cycle
model
-
http://copa.uniandes.edu.co/
Introduction Project stages
89
Modeling
logic
Discrete-event simulation
Results
Containers (daily)
-
http://copa.uniandes.edu.co/
Containers in land plots
Number of trips
Route to land plot
Introduction Project stages
90
Modeling
logic
Discrete-event simulation
Results
-
http://copa.uniandes.edu.co/
Containers in land plots
Number of trips
Route to land plot
Shortest path between
SPC and land plot
How to avoid collisions?
Introduction Project stages
91
Modeling
logic
Discrete-event simulation
Results
-
http://copa.uniandes.edu.co/
Introduction Project stages
92
Modeling
logic
Discrete-event simulation
Results
Containers in land plots
Number of trips
Route to land plot
Shortest path between
SPC and land plot
How to avoid collisions?
-
http://copa.uniandes.edu.co/
Introduction Project stages
93
Modeling
logic
Discrete-event simulation
Results
Containers in land plots
Number of trips
Route to land plot
Shortest path between
SPC and land plot
How to avoid collisions?
-
http://copa.uniandes.edu.co/
Branch system
Branch: subset of nodes and paths
Introduction Project stages
94
Discrete-event simulation
Results
-
http://copa.uniandes.edu.co/
Introduction Project stages
95
Discrete-event simulation
Results
X
XX
X
X
XX
X
X27
3736
32
35
34
33
Branch system
Branch: subset of nodes and paths
-
http://copa.uniandes.edu.co/
Introduction Project stages
96
Discrete-event simulation
Results
X
X
X
X44
43
38
Branch system
Branch: subset of nodes and paths
-
http://copa.uniandes.edu.co/
Introduction Project stages
97
Discrete-event simulation
Results
X
X
X
X
46
39
48
Branch system
Branch: subset of nodes and paths
-
http://copa.uniandes.edu.co/
Branch system
Branch: subset of nodes and paths
Assumptions
Only one aerial tractor per branch
Aerial tractors may park in the origin of a
branch
Aerial tractors parked do not block the path
Introduction Project stages
98
Discrete-event simulation
Results
-
http://copa.uniandes.edu.co/
Branch system
Branch: subset of nodes and paths
Assumptions
Only one aerial tractor per branch
Aerial tractors may park in the origin of a
branch
Aerial tractors parked do not block the path
Introduction Project stages
99
Discrete-event simulation
Results
-
http://copa.uniandes.edu.co/
Branch system
Branch: subset of nodes and paths
Assumptions
Only one aerial tractor per branch
Aerial tractors may park in the origin of a
branch
Aerial tractors parked do not block the path
Introduction Project stages
100
Discrete-event simulation
Results
-
http://copa.uniandes.edu.co/
Introduction Project stages
101
Modeling
logic
Discrete-event simulation
Results
Containers in land plots
Number of trips
Route to land plot
-
http://copa.uniandes.edu.co/ 102
Agenda
Introduction
Project stages
Results
-
http://copa.uniandes.edu.co/ 103
Results
Introduction Project stages Results
Feasible?
Add constraints
Amount (kg) of fresh fruit
to be harvested each day
Amount (kg) of fresh
fruit to pick in each
land plot each day
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Feasible?
Add constraints
Ripeness
cost
function
Yield
forecast
Parameter estimation
Q: Quarterly
W: Weekly
D: Daily
Aerial
tractor
order
-
http://copa.uniandes.edu.co/ 104
Results
Introduction Project stages Trabajo en cursoIntroduction Project stages Results
Average harvest cycle length: 8.3 days8 tractors
Land
plo
ts
Day in the quarter(days)
-
http://copa.uniandes.edu.co/ 105
Results
Introduction Project stages Trabajo en cursoIntroduction Project stages Results
Tons collected per day
8 tractors
Day
FF
B (
ton)
0
50
100
150
200
20 40 60 80
(days)
-
http://copa.uniandes.edu.co/ 106
Results
Introduction Project stages Trabajo en cursoIntroduction Project stages Results
8 tractors
Land
plo
ts
Day in the quarter
Average harvest cycle length: 10.9 days
(days)
-
http://copa.uniandes.edu.co/ 107
Results
Introduction Project stages Trabajo en cursoIntroduction Project stages Results
Tons collected per day
8 tractors
Day
0
50
100
150
20 40 60 80
FF
B (
ton)
(days)
-
http://copa.uniandes.edu.co/
Results
108
Introduction Project stages Trabajo en cursoIntroduction Project stages Results
Feasible?
Add constraints
Amount (kg) of fresh fruit
to be harvested each day
Amount (kg) of fresh
fruit to pick in each
land plot each day
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Feasible?
Add constraints
Ripeness
cost
function
Yield
forecast
Q: Quarterly
W: Weekly
D: Daily
Parameter estimation
Aerial
tractor
order
-
http://copa.uniandes.edu.co/
Results
110
Introduction Project stages Trabajo en cursoIntroduction Project stages Results
min
𝑗∈𝐽
𝑤𝑗𝑡𝑗𝑒
Earliness (hours)
-
http://copa.uniandes.edu.co/
Results
112
Introduction Project stages Trabajo en cursoIntroduction Project stages Results
min
𝑗∈𝐽
𝑡𝑗𝑒
Earliness (hours)
-
http://copa.uniandes.edu.co/
Results
113
min
𝑗∈𝐽
𝑡𝑗𝑒
min
𝑗∈𝐽
𝑤𝑗𝑡𝑗𝑒
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 2 3 4 5 6 7 8 9
Util
izat
ion
Harvest crew
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 2 3 4 5 6 7 8 9
Util
izat
ion
Harvest crew
-
http://copa.uniandes.edu.co/ 114
Project stages
Introduction Project stages Results
Feasible?
Add constraints
Amount (kg) of fresh fruit
to be harvested each day
Amount (kg) of fresh
fruit to pick in each
land plot each day
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Feasible?
Add constraints
Ripeness
cost
function
Yield
forecast
Q: Quarterly
W: Weekly
D: Daily
Parameter estimation
Aerial
tractor
order
-
http://copa.uniandes.edu.co/ 115
Results - transport
Introduction Project stages Trabajo en cursoIntroduction Project stages Results
Tons collected8 tractors
day 7day 1 day 3
SPCSPCSPC
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Results - transport
Introduction Project stages Trabajo en cursoIntroduction Project stages Results
8 tractors
1st trip for aerial tractor i
2nd trip for aerial tractor i
3rd trip for aerial tractor i
4th trip for aerial tractor i
Aerial tractor 1
Aerial tractor 2
Aerial tractor 3
Aerial tractor 4
Aerial tractor 5
Aerial tractor 6
Aerial tractor 7
Aerial tractor 8
-
http://copa.uniandes.edu.co/ 117
Results - transport
Introduction Project stages Trabajo en cursoIntroduction Project stages Results
Routes for aerial tractor 6
Land plots visited
-
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Project stages
Introduction Project stages Results
Feasible?
Add constraints
Amount (kg) of fresh fruit
to be harvested each day
Harvest cycle
model Q
Transport allocation
model D
Discrete-event
simulation W
Resource allocation
model W
Feasible?
Add constraints
Ripeness
cost
function
Yield
forecast
Q: Quarterly
W: Weekly
D: Daily
Parameter estimation
Aerial
tractor
order
Amount (kg) of fresh
fruit to pick in each
land plot each day
-
http://copa.uniandes.edu.co/ 119
Introduction Project stages Trabajo en cursoIntroduction Project stages Results
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
5 6 7 8 9 10 11Cha
nge
Amount of aerial tractors
Tiempo jornal Mallas/hora
10 hours 60 containers/hour
Results – uncertainty
Working day Containers/hour
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Introduction Project stages Trabajo en cursoIntroduction Project stages Results
0,99%
0,10%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
5 6 7 8 9 10 11Cha
nge
Amount of aerial tractors
Tiempo jornal Mallas/hora
Results – uncertainty
10 hours 60 containers/hour
Working day Containers/hour
-
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Introduction Project stages Trabajo en cursoIntroduction Project stages Results
18,45%
-11,37%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
5 6 7 8 9 10 11Cha
nge
Amount of aerial tractors
Tiempo jornal Mallas/hora
Results – uncertainty
10 hours 60 containers/hour
Working day Containers/hour
-
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Introduction Project stages Trabajo en cursoIntroduction Project stages Results
-3,26%
16,04%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
5 6 7 8 9 10 11Cha
nge
Amount of aerial tractors
Tiempo jornal Mallas/hora
Results – uncertainty
10 hours 60 containers/hour
Working day Containers/hour
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Introduction Project stages Trabajo en cursoIntroduction Project stages Results
Results – uncertainty
60%
65%
70%
75%
80%
85%
90%
5 6 7 8 9 10 11
Util
izat
ion
Amount of aerial tractors
-20%
-10%
0%
10%
20%
30%
5 6 7 8 9 10 11Cha
nge
Amount of aerial tractors
Tiempo jornal Mallas/horaWorking day Containers/hour
-
http://copa.uniandes.edu.co/
Conclusions
• We showed the potential of reducing the harvest cycle length from
19.6 days to 8.3 days.
• We highlighted the benefits of combining harvest and transport
planning.
• We measured the impact on the fruit evacuation metrics under failure
scenarios.
• We delivered results in a visual interactive interface to facilitate
decision-making at the plantation.
124
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Thank you!
{m.escallon240, d.castillo1879, ja.leal222, andres.medaglia, copa}@uniandes.edu.co
http://copa.uniandes.edu.co
cmontene@uniandes.edu.co
http://ceo.uniandes.edu.co
COPA CEO
http://copa.uniandes.edu.co/https://ceo.uniandes.edu.co/
-
http://copa.uniandes.edu.co/
Future work
• Implement the planning in the plantation.
• Adjust parameters if necessary.
• Incorporate other activities from the plantation.
• Integrate the models in a single computational tool that enables
parameter modifications, model execution and result visualization.
126
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