A MILP model for planning at operative level in a meat packing...
Transcript of A MILP model for planning at operative level in a meat packing...
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By Sara Verónica Rodríguez Sánchez
University Autonomous of Nuevo Leon, Mexico
San Francisco, CA, November 4th, 2014
A MILP model for planning at operative level in a
meat packing plant
3RD INTERNATIONAL WORKSHOP ON FOOD SUPPLY CHAIN
Víctor Albornoz, Matías GripeUniversity Federico Santa María, Chile
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OUTLINE
• Introduction about pork production
• The pork supply chain structure
• Planning production in a meat packing plant
• Challenges and Opportunities
• Conclusions
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IS MEAT PRODUCTION AN ISSUE?
In 2012, around 304 million tonnes of meat were produced worldwide. For 2014,
FAO forecasts an increase to 311.8 million tonnes.
Year
Po
pu
latio
n (
Bill
ion
s)
EXPECTATIONS OF WORLD POPULATION GROWTHANUAL MEAT CONSUMPTION (PER CAPITA)
Kg Per capita
USA
Brazil
China
Word
Developing countries
Year
Nowadays we are approximate 7 thousand of millions of people
Source FAOSTAT
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WHAT WE NEED?
More agricultural land?But the agricultural land is
being devoted to build houses.
Bio-energy
PRODUCTIVITY
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TECHNOLOGY
Food and Agriculture Organization of the United Nations had
point out TECHNOLOGY is the cornerstone to increase
productivity.
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TECHNOLOGY
Here is where OR Researchers could play an important role
By developing Decision Support Systems
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TECHNOLOGY
My job is to provide tools to help you to get more money for
your company with the resourses you already have.
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TECHNOLOGY
and moreover how to change your assets to be more productive
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PORK INDUSTRY EVOLUTION
FAMILIAR INDUSTRIAL
• Pork is the most widely produced meat worldwide.• In many countries the number of pig farms is being reduced, while the herd size
of the remaining ones is increasing.
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CHANGES IN THE MANAGEMENT
2 to 5 animals per week 100 to 10000 animals per day
Before Now
Size of Operations
Decision Making
is more complex
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• Habits and practices are changing.
CONSUMER EVOLUTION
• Quality.
EU
RE
GU
LA
TIO
NS
• Animal welfare.
• Safety
• Traceability
• Sustainable
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ADOPTION OF CAPITAL INTENSIVE SYSTEMS
Climate control
Automatic feeding systems
Animal identification devices
PDASoftware
Pig production has been evolving towards a progressive
concentration in larger and more specialized and efficient
production units
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PORK SUPPLY CHAIN
The competition today is more between supply chains than individual
firms.
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THE PSC MANAGEMENT
The chain manager now must make decisions on pig production
agents considering the integration and coordination of the whole
supply chain at different time horizons (Stadler, 2005).
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PORK PRODUCTION IN A MP PLANT
• Kjærsgaard, N., 2008. Optimization of the Raw Material Use at Danish Slaughterhouses. Technical University of
Denmark. PhD Thesis.
FARMS
SLAUGHTER AREA
PACKING AREALairage area
Equalization room
Processing Lines
A meat packing plant is the facility where the processing and packing
of the meat is done.
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DIFERENT PORK PRODUCTS
• Multiproduct.
• Process planning for product disassembly.
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DIFERRENT CUTTING PATTERNS
• $ reward
• $ cost
• Set of products
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PROBLEM DESCRIPTION
Yield
kgCutting Patterns
Demand
kg
The mayor difficulty is to balance the benefits of selling products from one
part of the carcass when there are no demand from other parts or the
carcass
Carcass
Dem
an
d
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MATHEMATICAL FORMULATION
• OBJECTIVE FUNCTION is oriented to maximize the net profit.
• The net profit is obtained through the difference between the incomes
from selling the products yielded by the cutting patterns, minus the
operational costs incurred. These operational costs involve inventory,
freezing costs, unsatisfied- demand penalties and labor costs to perform the
cutting-patterns.
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MATHEMATICAL FORMULATION
CONSTRAINTS
• Bounds for carcasses to be processed. The number of carcasses to
process in each period needs to be bounded (upper and lower limits), given
by the animal availability from suppliers according to different types of
carcasses.
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MATHEMATICAL FORMULATION
CONSTRAINTS
• Cutting patterns balance. Carcasses are partitioned into sections and for
each section a different cutting pattern can be applied.
This constraint ensures a balance between cutting patterns and the number
of carcasses processed. Equality is forced because the infeasibility to let
unprocessed raw material, due to perishability issues.
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MATHEMATICAL FORMULATION
CONSTRAINTS
• Cutting pattern yield. Different cutting patterns can be applied on the
carcass to make different products. A cutting pattern is therefore defined by
a combination of a set of products and their respective yields. The following
constraint calculates the total amount of product i, retrieved from all the
cutting patterns applied in each period.
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MATHEMATICAL FORMULATION
CONSTRAINTS
It is recognized that the pork industry works with perishable products
subject to spoilage. In order to extend the life of the product, it undergoes to
a freezing process. Thereby, a product can be sold in two presentations,
fresh and frozen. A product is considered fresh if it is sold within 4 days after
elaboration. On the other hand, frozen products can be kept this way for
almost 2 years. However, the profit of selling frozen products decays
considerably.
• Fresh and frozen balance. This constraint determines the amount of
product to be frozen and the ones to keep fresh to be sold in the next
periods.
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MATHEMATICAL FORMULATION
CONSTRAINTS
• Fresh product to be sold. As mentioned, fresh products are not allowed
to be kept for more than 4 days. Constraint 7 calculates the total amount of
fresh products that can be sold in a period t, but were produced in previous
periods.
• Frozen product to be sold. Fresh products need to stay at least 2 days
in the freezing tunnel, to be considered frozen. The following constraint
balance the inventory of frozen products at each period.
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MATHEMATICAL FORMULATION
CONSTRAINTS
• Demand of frozen products. Ensures that the requested level of each
frozen product is addressed, allowing the existence of unsatisfied-demand
in the case the raw materials are insufficient.
• Demand of fresh products. Ensures that the requested level of each
fresh product is addressed, allowing the existence of unsatisfied-demand in
the case the raw materials are insufficient.
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MATHEMATICAL FORMULATION
CONSTRAINTS
• Labor capacity.
• Wharehouse capacity for fresh products.
• Wharehouse capacity for frozen products.
• Freezing tunnel capacity.
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CASE OF STUDY
We are working with data from different companies
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SUCCESS CASE
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OUTPUT
• Moreover. The model gives the ability to ask ‘what if? questions such as
• What is the effect on profit as further cutting patterns and extra products
become available?
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OPTIMAL MARKETING OF PIGS
•The fattened pig ready for slaughtering is the output from several productive
and reproductive biological processes .
Fattening farm
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OPTIMAL MARKETING OF PIGS
•The fattening is the last biological process before the pig is marketed as a live
animal, and sent it to the slaughterhouse to be processed as a meat.
Fattening farm
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OPTIMAL MARKETING OF PIGS
• As pigs reach marketable weights near the end of the finishing phase, a pork
producer must devise a marketing strategy to determine when to sell pigs, which
and how many pigs to sell.
SlaughterhouseRe
ari
ng
farm
s
Fattening farm
11 a 17 weeks
Marketable
weight
15 to 35 kg
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OPTIMAL MARKETING OF PIGS
• The major complexity faced in this problem is in managing the biological
variance; owing to it, pigs reach optimal conditions for slaughter at different
times of the fattening period.
SlaughterhouseRe
ari
ng
farm
s
Fattening farm
11 a 17 weeks
Marketable
weight
15 to 35 kg
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CHALLENGES AND OPPORTUNITIES
FATTENING FARM 6
FATTENING FARM 1
FATTENING FARM 2
FATTENING FARM 3MEAT PACKING PLANT
FATTENING FARM 4
FATTENING FARM 5
SLAUGHTERING/PROCESSING
Figure 1. The structure of the pork supply chain considering two levels, fattening farms and the meat packing plant.
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CONCLUSIONS
• Adoption of OR methods in the PSC progress slowly like in other industries of
the primary sector. It may benefit of the development of user-friendly DSSs in a
narrow collaboration with the industry.
• Traditionally, judgement based on experience had been the basis for the
production planning. However recent changes have driven to a more complex
business planning enviroment, and thereby made the development of more
formal planning methos necessary.
• The new competitive strategy in pig farming is no longer based on individual
farms units, but rather integrated into a supply chain.
• Analitical tools has the potential to increase profits through a better
undertanding and new insights for their marketing strategy and production
operation.
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REFERENCES
Rodríguez, S.V., Plà, L.M., Faulin, J., New Oportunities in
Operations Research to improve pork supply chain
efficiency, 2014. Annals of Operations Research, 219, 5-
13.
Pla, L.M., Rodriguez, S.V., Rebillas, V. 2013. A mixed
integer linear programming model for optimal delivery of
fattened pigs to the abattoir. Journal of Applied Operations
Research, 5(4), 164-175.
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REFERENCES
• Plà, L.M., (1997) Review of mathematical models for sow
herd management. Livestock Science, 106, 107-119.
Rodriguez, S. V., Albornoz, V., & Plà, L. M. (2009). A two
stage stochastic programming model for scheduling
replacements in sow farms. TOP, 17(1), 171–179.
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THE SOW REPLACEMENT PROBLEM
• The piglet production capacity
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THE SOW REPLACEMENT PROBLEM
• The piglet production capacity
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SET AND INDEXES
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SET AND INDEXES
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REFERENCE
• Whitaker, D. and Cammell, S. 1990. A partitioned Cutting-Stock Problem
Applied in the meat industry. Journal of Operations Research Society, 41(9),
801-807.
• Bixby, A., Dows, B., and Self, Mike. 2006. A Schedule and Capable to
promise application for Swift & Company. Interfaces. 36(1), 69-86.
• Reynisdóttir, K., 2012. Linear optimization model that maximizes the value of
pork products. MSc Thesis. Reykjavík University.
• Kjærsgaard, N., 2008. Optimization of the Raw Material Use at Danish
Slaughterhouses. Technical University of Denmark. PhD Thesis.
• Wikborg, U., N., 2008. Online meat cutting operations. MSc Thesis. Norwegian
University of Science and Technology.
• Rodriguez, S., Albornoz, V., Gripe, M., Gonzalez, M., 2014. A mixed integer
linear program for planning and scheduling the meat production in a pork
supply chain, ISCO_2014.