Mini-course 1 Decision Analysis (Dr. Mariya Sodenkamp) / Class 2 / Paderborn_ITB_L2_ 2015_04_17 Students
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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 be`er 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 be`er 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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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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x1 |
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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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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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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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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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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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What to remember from this lecture?
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2)
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Mo@va@ng examples for decision analysis Research areas of decision theory
Study on decision success in organiza@ons by Paul Nu` Defini@on of decision making
Challenges of real-life decision making Decision process
Pareto op@mality
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Thank you very much!
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