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Advanced Herd ManagementCo se int od ction

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Course introduction

Anders Ringgaard Kristensen

Outline

PreconditionsOutcome: What are you supposed to learn?The framework and definition of herd managementThe management cycleObjectives of production, utility theoryClassical production theoryCl i l l h

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Classical replacement theoryLimitation of classical theoriesOutline of the courseTeachersThe concept of uncertainty

Preconditions

Courses• Animal production: ”Husdyrproduktion”• Mathematics: ”Matematik og

modeller”/”Matematik og planlægning”• Statistics ”Statistisk dataanalyse 2”• Mandatory first year (economics etc)

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Mandatory first year (economics etc)

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Brush-up courses …

The course will start up with brush-up courses of• Probability calculus and statistics• Linear algebra

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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 observation uncertainty into account.

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Outcome - knowledge

After completing the course the student should be able to:Describe the methods taught in the courseExplain 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.

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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.

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A pig (an animal)

Medicine

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Feed

MeatManure

Piglets

Milk

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Pig production = N × a pig?

Medicine

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Feed

MeatManure

Piglets

Milk

Medicine

Pig production = N × a pig?

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Feed

MeatManure

Piglets

Milk

Pigs:•Ages•Groups•Individuals

B ildi Fi ld N i hb i

Pig production

Slide 12 Feed

Buildings Fields

Farm hands

Owner

Neighbors, society, consumers

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Elements of production I

The factors (input to production)• Animals• Feed• Buildings, inventory• Labor• Management• Veterinary services• Energy

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• …

Elements of production II

Objectives: Maximization of the farmer’s welfare:• Income (personal)• Leisure time (personal)• Animal welfare (animals)• Working conditions (farm hands)• Environmental preservation (future generations)

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• Prestige (personal)• Product quality (consumers)

Elements of production III

Constraints limiting production• Physical (land, housing capacity, storage capacity)• Economical (capital, prices)• Legal (laws)• Personal (skills, education)

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Definition of herd management

Having discussed the three key elements:• Factors (input to production)• Objectives (farmer’s welfare)• Constraints (limitations)

we are now able to define what we mean by Herd Management:

Herd management is a discipline serving the purpose of

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g p g p pconcurrently ensuring that the factors are combined in such a way that the welfare of the individual farmer is maximized subject to the constraintsimposed on his production.

A dynamic optimization problem under constraints.Decisions! We decide how to combine the factors.

The management cycle: A never ending story

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The management cycle: Classical theories

UtilityTheory,Ch. 3.

N l i l

(ScarceResources)

Basic

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Neo-classicalProductionTheory,Ch. 4.

(Animal science,Production function)

ProductionMonitoring,Ch. 5.

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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,

fa m b ildings)

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farm buildings)• What any animal scientist should know about

management• The starting level of this course• Briefly revised today

Utility theory

We need a criterion for comparison of plans (“ways” to produce).Several concerns:

• The farmer• The staff• Consumers

Animals

F b ildi Land i hb i

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• The animals• Environment• …

Who decides the weighting?My answer: The farmer!

Slide 6 OwnerFarm handsFeed

Farm buildings Land Neighbors, society, consumers

Farmer’s preferences

The farmer has/defines a list of concerns:• Own direct concerns:

• Income, u1

• Leisure time, u2

• Prestige, u3

• ... • Indirect concerns (because he cares for others)

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( )• Animal welfare, u4

• Working conditions, u5

• Environment, u6

• Product quality, u7

• …The farmer knows/decides the weightingThe “items” on the list (u1, u2, … , uk) are called

attributes of the farmer’s utility.

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When is ”something” an attribute?

When it directly influences the subjective welfare of the farmer.

May NOT be an attribute:• Average milk yield of cows• Average daily gain of slaughter pigs• Animal welfare, ”because animals at a high level of

welfare also produce at a higher level”.

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May be an attribute:• Monetary gain• Leisure time• Animal welfare, if the farmer is willing to accept that

it to some extent decreases the levels of other attributes.

Consequences measured by attributes

Attribute

Stage

1 2 … T

1 u11 u12 … u1T

2 u11 u22 … u2T

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2 u11 u22 … u2T

… … … … …

k u11 uk2 … ukT

At any stage, the attributes will depend on the production Yt andthe factors xt. The relation is given by the attribute function h:

ut = h(Yt , xt)

Aggregation of attributes: Utility function

The utility function• Aggregation over time

• Monetary gain• Animal welfare

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• …• Aggregation over attributes

Expected Utility Theorem: Maximization of U is all we need to care about!

Refer to Chapter 3 for details!

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Production function

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Production function

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In classical production theory, the uncertainty represented by the e’s is ignored.

Neo-classical production theory

Answers 3 basic questions:• What to produce.• How to produce.• How much to produce.

Marginal considerationsBasic principle: Continue as long as the

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marginal revenue, MR, exceeds marginal costs, MC. At optimum we have MR = MC.

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How much to produce

One factor x and one product yPrices px and py

A production function y = f(x).Profit u(x) = ypy – xpx = f(x)py – xpx

Problem:

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Problem: • Find the factor level that maximizes the profit

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

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Maximum profit where:• Marginal revenue = Marginal

cost!

How much to produce

0,8

1

Total revenue, f(x)py

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-0,2

0

0,2

0,4

0,6

Average revenue, f(x)py/x

Marginal revenue, f’(x)py

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How much to produce, logical bounds

0,8

1

Total revenue, f(x)py

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-0,2

0

0,2

0,4

0,6

Average revenue, f(x)py/x

Marginal revenue, f’(x)py

How much to produce, optimum

0,8

1

Total revenue, f(x)py

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-0,2

0

0,2

0,4

0,6

Average revenue, f(x)py/x

Marginal revenue, f’(x)py

Price of factor px

Classical replacement theory

The replacement problem in a broad sense is one of the most important decision problems in animal production.

Dynamics: What we decide at this stage (keep/replace) may influence production in many future stages.

Many other decision problems relate to the replacement

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y p pproblem:• Insemination• Treatment for diseases• Feeding level• …

A correct handling of the other problems implies that the question of replacement must be taken into account.

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Definition

Replacement:• When an existing asset is substituted by a new

one with (more or less) the same function.• Examples:

• Light bulbs• Cars

So s

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• Sows• Milking robots

Female production animals:• (Ewes, mink, goats)• Sows• Dairy cows

• Two levels:• Optimal lactation to replace• Optimal stage of lactation to replace

Replacement problems in animal production

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• Repeatability of milk yield over lactation rather high (as opposed to litter size in sows).

Replacement problems in animal production

Technical:• Examples:

• Farm buildings• Equipment & machinery

• Very similar to the sow replacement problem, except for the

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y p p , p”biological” variation

• Technological improvements probably more important than the corresponding genetic improvement in cows.

• Marginal/average considerations apply well

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Slaughter calves:• If housing capacity is limited and replacements are

available, the problem is in agreement with classical theory.• Marginal/average considerations

Slaughter pigs:

Replacement problems in animal production

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g p g• Two levels:

• When to deliver individual pigs (animal level)• When to deliver the remaining pigs (batch level)

Broilers:• At batch level (no animal level) in agreement with classical

theory.• Contracts may limit the decisions of the farmer

A chain of assets

Asset 1 Asset nAsset 3Asset 2

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tr

How do we determine an optimal value for tr - the length of the period to keep each asset in the chain?

Optimal time for replacement

Assume that the price of a new asset is SThe salvage value of the asset at time t is

st

The net returns from the asset in stage (time step) t is rt

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The total net revenue T(t) from the asset if it is replaced at stage t is then

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Optimal time for replacement

Average net revenue, if replaced at time t:

Marginal net revenue at time t

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g

Optimal replacement time where

Replace where:marginal revenue = average revenue

Graphical illustration

The replacement problem

200

300

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-200

-100

0

100

200

0 5 10 15 20

Time

Reve

nue

MarginalAverage

Marginal revenue

Typically decreasing because of decreasing productivity and increasing maintenance costs.

The net returns adjusted for change in salvage value.

The marginal curve crosses the average curve where the average is maximal.

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Limitations of neo-classical theory

Static approach:• Immediate adjustment• Only one time stage

Deterministic approach• Ignores risk

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Ignores risk• ”Biological variation”• Price uncertainty

Knowledge representation (knowledge considered as certain):• Unobservable traits• ”Production functions”• Detached from production: No information flow from

observations. • No updating of knowledge.

Limitations of classical replacement theory

Uncertainty: The classical replacement theory assumes full certainty about the marginal profit function, the investment costs and all prices. As discussed in details in Chapter 2, uncertainty is an inherit property of the decision making process in herd management. The uncertainty is partly a consequence of imperfect knowledge, and partly of random variation.

Uniqueness: The general theory implicitly assumes that the marginal and average profit functions are as h i Fi 4 5 ith i l d t i d

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shown in Figure 4.5 with a uniquely determined intersection. For several applications the intersection is not unique. This is, for instance, the situation in dairy cows, where the average and marginal profits are as shown in Figure 4.7.

Availability: The theory assumes that a new asset for replacement is always available.

Background for course

Structural development in the sector• Increasing herd sizes• Decreasing labour input

Technological development• Sensors, automatic registrations

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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

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• 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

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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

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• Simulation (Monte Carlo)• Linear programming (low priority)• Markov decision processes (dynamic programming)

• Mandatory reports

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Teachers

Part I:• Anders Ringgaard Kristensen• Cécile Cornou

Part II:• Anders Ringgaard Kristensen

Part III:

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Part III:• Anders Ringgaard Kristensen• Cécile Cornou (Post Doc IPH)• Tina Birk Jensen (Post Doc IPH)• Nils Toft (associate professor, • Guests:

• Thomas Nejsum Madsen (TNM Consult)• Thomas Algot Søllested (Egebjerg)• Tage Ostersen (Master student)• Lars Relund Nielsen (University of Aarhus)• Others …

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:• Linear programming• Monitoring and data filtering

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• Monitoring and data filtering• Markov decision processes• Bayesian networks (including decision graphs)

The web

AbsalonHome page of the course

• http://www.prodstyr.ihh.kvl.dk/vp/• Course description• Plan

• Pages for each lesson with a description of the li i f

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contents, literature, exercises, software to use etc.

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Exercise, uncertainty

Production function:

• - milk yield given energy, protein and fat

f x x xc x c x c x c x c x c x c x x c x x c x x

( , , )1 2 3

11 12

22 22

33 32

1 1 2 2 3 3 12 1 2 13 1 3 23 2 3

=

+ + + + + + + +

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fat

Adding uncertainty, the actual milk yield is

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

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Uncertainty - III

Silage obs.* Silage true

Concentr.*

Ration Milk yield*

Herd size*

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True energy content of silage is unknownThe precision of the observed content depends

heavily on the observation method (standard value from table, laboratory analysis etc.)

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Uncertainty - IV

Effects of decisions will be over-estimated if uncertainty about• true state• factor characteristics• factor effects

is ignored

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is ignored.Wrong decisions may be made.

Uncertainty, V

Baysian networks with decisions and utilities added (student project).

Silage obs.* Silage true Ration Milk yield*

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g g

Concentr.*

y

Herd size*Method

MixPrice Cost Rev.

Uncertainty - VI

Uncertainty is not the opposite of knowledgeUncertainty is a property of knowledgeReduction of uncertainty is often possible at some

cost!Reducing uncertainty is not always profitable.

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