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

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. 1 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 2

Notation (Influence Diagrams) x A variable (something that we can observe) A decision d Utility (e.g. money) u Causal influence x 1 x 2 d 3 The decision problem i 1 i 3 i 2 d 1 d 3 d 2 u 1 u 3 u 2 � i t is the state of the system at time t � d t is the decision made at time t � u t is the utility consequence at time t given state and decision � Limitations are ignored in the figure!!! 4

The state i 1 i 3 i 2 d 1 d 3 d 2 u 1 u 3 u 2 � 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 5 The decision i 1 i 3 i 2 d 1 d 3 d 2 u 1 u 3 u 2 � The decision concerns at least one factor � It is based on knowledge about the state � It influences the utility � It influences the future state 6

The utility i 1 i 3 i 2 d 1 d 3 d 2 u 1 u 3 u 2 � Depends on � The output (e.g. # piglets produced) � The value (e.g. the price of piglets) � Farmer’s preferences (what should be measured) 7 A strategy (or policy) i 1 i 3 i 2 d 1 d 3 d 2 u 1 u 3 u 2 � 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). 8

Example: Dairy cow replacement � The state space could be defined by the state variables � Milk yield Milk Preg. � Pregnancy status � Lactation number i Lact# Stage � Stage of lactation � Health status Health � The action space � Keep the cow d d � Replace it by a heifer 9 Observing the state � ”Milk yield” – the best possible basis for prediction � ”Pregnancy status” � None of them are observable! Genetype Permanent Heat Obs. Heat* Capacity Pregnancy Diagnosis* Test day 1* Test day 2* Test day 3* Test day 4* Test day 5* Test day 6* Temp 1 Temp 2 Temp 3 Temp 4 Temp 5 Temp 6 10

Example, feeding of dairy cows � Production function: = f x x ( , , x ) 1 2 3 + + + + + + + + 2 2 2 c x c x c x c x c x c x c x x c x x c x x 11 1 22 2 33 3 1 1 2 2 3 3 12 1 2 13 1 3 23 2 3 � - milk yield given energy, protein and fat � Adding uncertainty, the actual milk yield is Y = f ( x 1 , x 2 , x 3 ) + e 11 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 12

Feeding of dairy cows, III Silage obs.* Silage true Ration Milk yield* Concentr.* Herd size* � 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.) 13 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. 14

Feeding of dairy cows, V � Influence diagram for the full problem (student’s project, this course). Silage obs.* Silage true Ration Milk yield* Concentr.* Herd size* Method Price Mix Cost Rev. 15 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. 16

Decision Hierarchies � Time � Strategic � Tactical � Operational � Level � Herd � Group � Animal � In both cases decisions at different ”levels” interact 17 Methods : Linear programming � Minimize a linear cost function given a set of linear restraints. � Well known from ration formulation � Also applied for whole farm planning � Ignores uncertainty � Assumes linearity � Static method 18

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 19 Methods : Influence diagrams � Baysian networks with decisions and utilities added. Silage obs.* Silage true Ration Milk yield* Concentr.* Herd size* Method Price Mix Cost Rev. 20

Methods: Influence diagrams � Same advantages as Bayesian networks � Static model � No forgetting � Computationally very demanding 21 Methods : Dynamic programming � Basic setup: i1 i2 i3 i4 i5 d1 d2 d3 d4 d5 r1 r2 r3 r4 r5 � Markov property: No memory of the past 22

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. 23 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 24

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 25