Decision making A decision is an intention to use/not to use a - - PDF document

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Decision making

A decision is an intention to use/not to use a factor at a given level:

Use 4 kg of concentrates per cow Cull cow no. 678 Call for the vet! Build a new barn.

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Necessary information

When a decision is made concerning a unit, the following information is necessary:

The present state of the unit The relation between factors and production

Immediate production Future production

The farmer’s personal preferences All restraints of legal, economic, physical or personal kind

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Notation (Influence Diagrams)

x

d u

A variable (something that we can observe) A decision Utility (e.g. money) Causal influence

x1

d

x2

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The decision problem

it is the state of the system at time t dt is the decision made at time t ut is the utility consequence at time t given state and decision Limitations are ignored in the figure!!! d1 u1 i1 d2 i2 d3 i3 u2 u3

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The state

The state is a sufficient description of the system at time t A description is sufficient if it contains all relevant information about the system Defined by the value of one or several state variables each representing a trait (e.g. litter size, parity, health) Probability distribution given previous state and decision d1 u1 i1 d2 i2 d3 i3 u2 u3

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The decision

The decision concerns at least one factor It is based on knowledge about the state It influences the utility It influences the future state

d1 u1 i1 d2 i2 d3 i3 u2 u3

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The utility

Depends on

The output (e.g. # piglets produced) The value (e.g. the price of piglets) Farmer’s preferences (what should be measured) d1 u1 i1 d2 i2 d3 i3 u2 u3

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A strategy (or policy)

Let Ω be the set of all possible states and D be the set of all posible decisions A strategy s is a function s: Ω→D. For any state i∈Ω, the strategy s specifies the decision d∈D to make. A general rule: ”If state i is observed, decision d should be made. Problem: To determine a strategy that maximizes the utility of the farmer (under the limitations). d1 u1 i1 d2 i2 d3 i3 u2 u3

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Example: Dairy cow replacement

The state space could be defined by the state variables

Milk yield Pregnancy status Lactation number Stage of lactation Health status

The action space

Keep the cow Replace it by a heifer i Milk Preg. Stage Health d d Lact#

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Capacity Test day 1* Test day 2* Test day 3* Test day 4* Test day 5* Test day 6* Genetype Permanent Temp 1 Pregnancy Temp 2 Temp 3 Temp 4 Temp 5 Temp 6 Diagnosis* Heat

• Obs. Heat*

Observing the state

”Milk yield” – the best possible basis for prediction ”Pregnancy status” None of them are observable!

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Example, feeding of dairy cows

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

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Feeding of dairy cows, 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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Feeding of dairy cows, 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*

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Feeding of dairy cows, IV

Effects of decisions will be over-estimated if unceratainty about

true state factor characteristics factor effects

is ignored. Wrong decisions may be made.

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Feeding of dairy cows, V

Influence diagram for the full problem (student’s project, this course).

Silage obs.* Silage true Concentr.* Ration Milk yield* Herd size* Method Mix Price Cost Rev. 16

Uncertainty

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.

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Decision Hierarchies

Time

Strategic Tactical Operational

Level

Herd Group Animal

In both cases decisions at different ”levels” interact

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Methods: Linear programming

Minimize a linear cost function given a set

• f linear restraints.

Well known from ration formulation Also applied for whole farm planning Ignores uncertainty Assumes linearity Static method

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Methods: Bayesian Networks

The ideal tool for representation of uncertainty Graphical model description with well defined elements: Ellipses are random variables and arrows represent a causal relation Combination of information from many sources

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Methods: Influence diagrams

Baysian networks with decisions and utilities added.

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

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Methods: Influence diagrams

Same advantages as Bayesian networks Static model No forgetting Computationally very demanding

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Methods: Dynamic programming

Basic setup:

i1 i2 i3 i4 i5 d1 r1 d2 r2 d3 r3 d4 r4 d5 r5

Markov property: No memory of the past

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Methods: Dynamic programming

Dynamic method Many kinds of uncertainty may be represented State representation less flexible than in influence diagram Hope for the future: A combination of influence diagrams and advanced variants of dynamic programming.

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Methods: Simulation

Monte Carlo simulation:

Random numbers Excellent for representation of herd restraints Excellent for representation of uncertainty No good methods to use in search for optimal strategies

Probabilistic (“Markov chain”) simulation

Dynamic programming without decisions

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Methods: Overview

Method Dynamic Herd restraints Uncertainty Unobservable states Linear programming No Excellent Not good Not good Influence diagrams No Not good Excellent Excellent Dynamic programming Yes Not good Excellent Difficult Monte Carlo simulation Yes Excellent Excellent Excellent Markov chain simulation Yes Not good Excellent Difficult

Challenge for the future:

Combination of methods