Introduction Zeleny (1982) dalam bukunya "Multiple Criteria Decision Making", mengatakan:
"Semakin sulit melihat dunia di sekitar kita secara unidimensional dan hanya menggunakan satu kriteria saat menilai apa yang kita lihat"
Examples of Multi-Criteria Problems • Wife selection problem. This problem is a good example of multi-criteria decision problem. Criteria include: • • • • • •
Religion Beauty Wealth Family status Family relationship Education
3
Agama
Harta
Keturunan
Kecantikan/Kegantengan
http://trial.expertchoice.com/Comparion.aspx#Project/Evaluate/Default.aspx?resetproject=yes
Banyak masalah sektor publik dan bahkan keputusan pribadi melibatkan banyak pertimbangan, tujuan dan sasaran.
Sebagai contoh: Menemukan pembangkit listrik tenaga nuklir melibatkan tujuan seperti: 1. Keamanan 2. Kesehatan 3. Lingkungan Hidup 4. Biaya
• Luna wants to go on a vacation. • She has 3 options Hogwarts
Hogsmeade Azkaban
How to decide..??? Pranav Mishra
Let us consider… • Each option can be evaluated against certain criteria. • Criteria for vacation destinations can be: • • • •
Entertainment Facilities Accommodation cost Travel cost
Important terms…
• Weights – These estimates relative importance of criteria.
Each attribute is given certain points on 0-10 or 0-100 rating scale by a team of experts or decision makers. Example:
criteria
Entertainment Facilities Travel costAccomodation
weight 6 -
rating scale
4 10 very good -1 none 2 10 very good -1 none 10 low-1 very high 8 10 low-1 very high
Similarly… Selecting a source of information (library, internet, etc…) involves various criteria such as: Reliability of information Time to gather information Cost of acquiring information
These are examples of MULTI-CRITERIA problems and requires MCDM approach.
• Land is a scarce resource: • Identifying suitability for •Where to build a dam •Water flow •Mountainous? • Where to place a hospital •Costs •Access •Greatest need • Criteria can be based on human or physical geography factors
Beberapa istilah: Multi Criteria Analysis Multi Criteria Evaluation (MCE) Multi Criteria Preference Analysis Multi Criteria Decision Making Multi Objective Evaluation
These methods are essentially one and the same! MCE = Multi-criteria evaluation is primarily concerned with how to combine the information from several criteria to form a single index of evaluation Professor Kenneth E., 2010
Mengapa DCDM: • Bagus untuk mengambil keputusan dari masalah yang kompleks. • Memungkinkan pengambil keputusan untuk menunjukkan pemikiran mereka. • Berguna dalam analisis GIS dimana beberapa kriteria digabungkan. • Termasuk kemampuan untuk menimbang kriteria. • Sering digunakan untuk penentuan alokasi lahan.
MCDM Multiple Criteria Decision Making • Selection of the best, from a set of alternatives, each of which is evaluated against multiple criteria. Some problem solving techniques are : • SAW (Simple Additive Weighting) • TOPSIS (Technique for Order Preference by Similarity to the Ideal Solution) • ELECTRE (Elimination et Choice Translating Reality) • AHP (The Analytical Hierarchy Process) • SMART (The Simple Multi Attribute Rating Technique ) • ANP (Analytic network process)
Definitions • Decisions: a choice between alternatives • Criterion: some basis for a decision. Two main classes: •Factor: enhances or detracts from the suitability of a land use alternative (e.g. distance from a road) •Constraint: limits the alternatives • Goal or target: some characteristic that the solution must possess (a positive constraint)
The Basics
Principles of MCE • Methodology: 1. Determine criteria (factors/constraints) to be included 2. Determining the weights for each factor 3. Sensitivity analysis of results
1st Step: Determine the criteria to be included • Criteria determine the alternatives • Oversimplification of the decision problem could lead to too few criteria being used
• Using a large number of criteria reduces the influence of any one criteria • Often proxies must be used since the criteria of interest may not be determinable
Example: Case study of a suitable dam and reservoir site Criteria used: River Urban Forest Accumulated water flow Existing reservoir Watershed boundary City Hydraulic head Undulation
Determine the weights • A decision is the result of a comparison of one or more alternatives with respect to one or more criteria that we consider relevant for the task at hand. • Among the relevant criteria we consider some as more important and some as less important; this is equivalent to assigning weights to the criterion according to their relative importance.
2nd stage, assigning weights
Weights assigned using AHP
Weights assigned using the Rank Order method
Sensitivity analysis → sensitivity analysis: vary the scores/weights of the factors to determine the sensitivity of the solution to minor changes • Choice of criteria (e.g. why included?) • Assesses the reliability of data: how stable is the final result? • Choice for weighting factors is subjective • Will the overall solution change if you use other weighing factors?
MCE – pros and cons •Cons: –
Dynamic problems strongly simplified into a linear model
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Static, lacks the time dimension
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Controversial method – too subjective?
•Pros: –
Gives a structured and traceable analysis.
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Possibility to use different evaluation factors makes it a good tool for discussion.
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Copes with large amounts of information.
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It works!
Approaches For MCDM • Several approaches for MCDM exist. We will cover the following: • • • •
Weighted score method ( Section 5.1 in text book). TOPSIS method Analytic Hierarchy Process (AHP) Goal programming ?
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Approaches For MCDM Some problem solving techniques are : • SAW (Simple Additive Weighting) • TOPSIS (Technique for Order Preference by Similarity to the Ideal Solution) • ELECTRE (Elimination et Choice Translating Reality) • BAYESIAN NETWORK BASED FRAMEWORK • AHP (The Analytical Hierarchy Process) • SMART (The Simple Multi Attribute Rating Technique ) • ANP (Analytic network process)
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MCDM problem has four elements: Goal Objectives Criteria
Alternatives
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An example of hierarchical value tree:
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Criteria characteristics Completeness: It is important to ensure that all of the important criteria are included. Redundancy: In principle, criteria that have been judged relatively unimportant or to be duplicates should be removed at a very early stage. Operationality: It is important that each alternative can be judged against each criterion.
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Problem solving steps: 1. Establish the decision context, the decision objectives (goals), and identify the decision maker(s). 2. Identify the alternatives. 3. Identify the criteria (attributes) that are relevant to the decision problem.
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Azas dalam Analisis Overlay Azas Dominan (Dominance Rule): satu nilai dominan
Azas Kontribusi (Contributory Rule) masing-masing nilai attribut berkontribusi terhadap hasil
Azas Interaksi (Interaction Rule) pasangan-pasangan dari nilai-nilai berkontribusi terhadap hasil.
2nd stage, assigning weights
AHP merupakan salah satu alat bantu (proses) dalam pengambilan keputusan yang dikembangkan oleh Thomas L Saaty pada tahun 70an.
STRUKTUR ANALYTIC HIERARCHY PROCESS (AHP) Konsep dasar AHP adalah penggunaan matriks pairwise comparison (matriks perbandingan berpasangan) untuk menghasiIkan bobot relative antar kriteria maupun alternative. Suatu kriteria akan dibandingkan dengan kriteria lainnya dalam hal seberapa penting terhadap pencapaian tujuan di atasnya (Saaty, 1986).
Combining performance indicators to one Key Performance Indicator (KPI) You can give each one with different WEIGHTS
Klaus Goepel
How to derive the weights? Mathematical method:
Klaus Goepel
AHP has many applications: 1. Select key performance indicators (KPIs) 2. Evaluate product features 3. Select from srategic alternatives 4. Make consilifated decisions with multiple inputs from different stakeholders
Klaus Goepel
Analytic Hierarchy Process (AHP) Deriving ratio scales from paired comparisons Allows some small inconsistency in judgment
INPUT:
Actual measurement Subjective opinion
Price, weight etc satisfaction feelings, preferences
OUTPUT: Ratio scales Consistency index
from Eigen vectors from Eigen value Klaus Goepel
Analytic Hierarchy Process (AHP) Step 1 : Define objective
Step 2: Structure elements in criteria, sub-criteria, alternatives etc.
Step 3: Make a pair wise compatison of elements in each group
Step 4: Calculate weighting and consistency ratio
Step 5: Evaluate alternatives according weighting
Get Ranking
Klaus Goepel
Price not taken as criterion separating benefits form cost allows for a costbenefit analysis
Paired comparison matrix
HASIL REKLASIFIKASI Mengetahui rekomendasi jalur pipa PDAM yang optimum dalam melayani konsumen
Kemiringan Lereng
Arah Hadap Lereng
Jalan
Penggunaan Lahan
Sungai
HASIL PERHITUNGAN AHP Parameter Jalan Penggunaan Lahan Kemiringan Lereng Arah Hadap Lereng
Jalan
Penggunaan Lahan
Kemiringan Lereng
Arah Hadap Lereng
Sungai
Priority Vector
Bobot
1
5
2
6
9
0.452744686
45%
0.2
1
0.33
4
5
0.139783822
14%
0.5
3
1
9
7
0.315980423
32%
0.11
0.25
0.11
1
3
0.056732268
6%
Sungai
0.11
0.2
0.14
0.33
1
0.0347588
3%
Jumlah
1.92
9.45
3.58
20.33
25
1
100.00%
Principle Eigen Value
:
5.344
Consistency Index (CI)
:
0.086
Consistency Ratio (CR)
:
0.077
Hasil CR dapat diterima karena lebih kecil dari 0,1
