01-09-2014 Outline Preconditions Outcome: What are you supposed to - - PDF document

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Advanced Quantitative Methods in Herd Management

Course introduction

Anders Ringgaard Kristensen

Outline

Preconditions Outcome: What are you supposed to learn? The framework and definition of herd management The management cycle Classical production theory Limitation of classical theories Outline of the course Teachers The concept of uncertainty

Preconditions Courses

• Mathematics: ”Matematik og

modeller”/”Matematik og planlægning”

• Statistics ”Statistisk dataanalyse 2”
• Mandatory first year (economics, statistics

etc)

Brush-up courses …

The course will start up with brush-up courses of

• Probability calculus and statistics
• Linear algebra

Learning outcome

After attending the course students should be able to participate in the development and evaluation of new tools for management and control taking biological variation and

• bservation uncertainty into account.

Outcome - knowledge

After completing the course the student should be able to: Describe the methods taught in the course Explain the limitations and strengths of the methods in relation to herd management problems. Give an overview of typical application areas of the methods.

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Outcome - skills

After completing the course the student should be able to: Construct models to be used for monitoring and decision support in animal production at herd level. Apply the software tools used in the course.

Outcome: Competencies:

After completing the course the student should be able to: Evaluate methods, models and software tools for herd management. Transfer methods to other herd management problems than those discussed in the course. Interpret results produced by models and software tools.

The management cycle: Classical theories

Utility Theory,

• Ch. 3.

Neo-classical Production Theory,

• Ch. 4.

(Scarce Resources) (Animal science, Production function) Basic Production Monitoring,

• Ch. 5.

Herd Management Science

Basic level:

• As we define the basic level, it consists of
• Utility theory
• Neo-classical production theory
• Basic production monitoring
• (Animal nutrition, animal breeding, ethology,

farm buildings)

• What any animal scientist should know about

management

• The starting level of this course
• Volume I of the textbook!

Neo-classical production theory

Answers 3 basic questions:

• What to produce.
• How to produce.
• How much to produce.

Marginal considerations Basic principle: Continue as long as the marginal revenue, MR, exceeds marginal costs, MC. At optimum we have MR = MC.

How much to produce One factor x and one product y Prices px and py A production function y = f(x). Profit u(x) = ypy – xpx = f(x)py – xpx Problem:

• Find the factor level that maximizes the profit

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How much to produce

Maximum profit where u’(x) = 0. u(x) = f(x)py – xpx u’(x) = f’(x)py – px u’(x) = 0 ⇔ f’(x)py = px Maximum profit where:

• Marginal revenue = Marginal

cost! How much to produce

,2 0,2 0,4 0,6 0,8 1

Total revenue, f(x)py Average revenue, f(x)py/x Marginal revenue, f’(x)py How much to produce, logical bounds

,2 0,2 0,4 0,6 0,8 1

Total revenue, f(x)py Average revenue, f(x)py/x Marginal revenue, f’(x)py How much to produce, optimum

,2 0,2 0,4 0,6 0,8 1

Total revenue, f(x)py Average revenue, f(x)py/x Marginal revenue, f’(x)py

Price of factor px

Limitations of neo-classical theory

Static approach:

• Immediate adjustment
• Only one time stage

Deterministic approach

• Ignores risk
• ”Biological variation”
• Price uncertainty

Knowledge representation (knowledge considered as certain):

• Unobservable traits
• ”Production functions”
• Detached from production: No information flow from
• bservations.
• No updating of knowledge.

Background for course

Structural development in the sector

• Increasing herd sizes
• Decreasing labour input

Technological development

• Sensors, automatic registrations
• Computer power
• Networking

Methodological development

• Statistical methods
• Operations Research

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Outline of course - I

Part I:

• Brush-up course on
• Probability calculus and statistics
• Linear algebra
• ”Advanced” topics from statistics
• Basic production monitoring
• Registrations and key figures
• Analysis of production results

Outline of course - II Part II: The problems to be solved

• From registrations to information, value of

information, information as a factor, sources of information

• Decisions and strategies, definition and knowledge

foundation

• Consequences of decisions and states
• Visualisation and user interfaces

Outline of course - III Part III: The methods to be used

• State of factors
• Monitoring and data filtering
• Bayesian networks
• Decision support
• Decision graphs
• Simulation (Monte Carlo)
• Linear programming (low priority)
• Markov decision processes (dynamic programming)
• Mandatory reports

Teachers

Anders Ringgaard Kristensen Cécile Cornou Dan Børge Jensen

Mandatory reports 4 minor reports must be handed in

• Based on the exercises

At least 3 must be approved in order to attend the oral exam The 4 reports are distributed over the following methods:

• Bayesian networks
• Monitoring and data filtering
• Linear programming
• Markov decision processes

The web Absalon Home page of the course

• http://www.prodstyr.ihh.kvl.dk/vp/
• Course description
• Plan
• Pages for each lesson with a description of the

contents, literature, exercises, software to use etc.

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Exercise, uncertainty

Production function:

• - milk yield given energy, protein and

fat

Adding uncertainty, the actual milk yield is

f x x x c x c x c x c x c x c x c x x c x x c x x ( , , )

1 2 3 11 1 2 22 2 2 33 3 2 1 1 2 2 3 3 12 1 2 13 1 3 23 2 3

= + + + + + + + +

Y = f(x1,x2,x3) + e

Uncertainty, II

Adding uncertainty to production function:

• Considerable improvement, BUT
• Significant uncertainty about true energy, protein

and fat content still ignored

• Example, only considering energy

Uncertainty - III

True energy content of silage is unknown The precision of the observed content depends heavily on the observation method (standard value from table, laboratory analysis etc.)

Silage obs.* Silage true Concentr.* Ration Milk yield* Herd size*

Uncertainty - IV Effects of decisions will be over-estimated if uncertainty about

• true state
• factor characteristics
• factor effects

is ignored. Wrong decisions may be made. Uncertainty, V Baysian networks with decisions and utilities added (student project).

Silage obs.* Silage true Concentr.* Ration Milk yield* Herd size* Method Mix Price Cost Rev.

Uncertainty - VI

Uncertainty is not the opposite of knowledge Uncertainty is a property of knowledge Reduction of uncertainty is often possible at some cost! Reducing uncertainty is not always profitable.