Mini-course 1 Decision Analysis (Dr. Mariya Sodenkamp) / Class 3 / ITB_L3_ 2015_04_20
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, uncertainty and risk
Agenda
1.
2.
3.
Pareto op+mality
Decision making under certanty
Decision making under uncertanty and risk (most probaly next +me)
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Pareto Optimality
Originally, Pareto Op*mality designates a state of alloca+on of resources in which it is impossible to to make any one individual beDer o without making at least one individual worse o .
Given an ini+al allocaion of goods among a set of individuals, a change to a di erent alloca+on that makes at least one individual beDer o without making any other individual worse o is called a Pareto Improvement. An alloca+on is „Pareto op+mal“ when no further improvements can be made.
* Example: Given consumers A and B distribute equally resource X=20:
{1;1}, {2;2}, {3;3}, {4,4}, …, {10;10} – Pareto Improvements.
Resources are exhausted
Further redistribu+ons lead to points {11;9}, {9;11}, {12;8} etc.
Source: Wikipedia
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Folie 3 |
Pareto Set
Ø In DA, alterna+ves belong to Pareto Set (P) if each of them exceeds any other on some criterion
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All alterna+ves from |
Pareto set are non-dominated (think about |
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Even Swaps!) |
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Alterna+ve A1 dominates Alterna+ve A2 if it |
than A2 |
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on some criteria and |
worse than A2 on all other criteria |
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Y1
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Y2 |
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Folie 4 |
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C2(ai)
a2
a1
A.
ai – alternatives (cars)
Cj - criteria
2). C1 – price, C2 – quality
C1 à min,
C2 à max
a1, a2 and a3 belong to the Pareto Set, none of them dominated by another one
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Folie 5 |
C2(ai)
ai – alternatives (cars) Cj - criteria
a2
a1
B.
2). C1 – price, C2 – quality
C1 à min,
C2 à max
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Folie 6 |
C2(ai)
ai – alternatives (cars) Cj - criteria
a1
a2
C.
2). C1 – maintinence costs, C2 – style
C1 à min,
C2 à max
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Folie 7 |
C2(ai)
ai – alternatives (cars) Cj - criteria
a2
a1
D.
2). C1 – fuel consumption, C2 – quality
C1 à min,
C2 à max
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Folie 8 |
Exercise
Look at the |
comparing compe3ng producers of yoghurt |
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drinks. Eliminate |
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the |
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Iden3fy what producers |
to Pareto |
cases |
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Price
a3
a9
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a7 |
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a2 |
a2 |
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a5 |
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a1 |
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a6 |
Brand |
Quality |
Image |
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Folie 9 |
Exercise: Pareto op+mality
Building a power sta+on (homework)
We want to build a hydraulic power sta+on with maximal power output in shortest possible +me.
The resul+ng power sta+on can have power output (P) in the range between 0 MW and 20’000 MW.
The cost for the power plant can be calculated as C=P/(20’000 MW) * 10 Mio €.
The construc+on of the power plant will take 2 years. We can reduce this +me by at most 10 months, but reduc+on of the +me by a month will increase the overall cost by 1 Mio €.
The available budget for the project is 15 Mio €.
What are the Pareto op+mal configura+ons for this power plant?
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