Introduction. Zeleny (1982) dalam bukunya "Multiple Criteria Decision Making", mengatakan:

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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"

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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

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Agama Harta Keturunan Kecantikan/Kegantengan

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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

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• Luna wants to go on a vacation.

• She has 3 options

Hogwarts

Hogsmeade

Azkaban

How to decide..???

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Let us consider…

• Each option can be evaluated against certain

criteria.

• Criteria for vacation destinations can be:

• Entertainment • Facilities

• Accommodation cost • Travel cost

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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 weight rating scale

 Entertainment - 4 10 very good -1 none  Facilities - 2 10 very good -1 none  Travel cost- 6 10 low-1 very high

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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.

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• 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

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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

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• 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.

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MCDM

• 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)

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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)

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Principles of MCE

• Methodology:

1. Determine criteria

(factors/constraints) to be included

2. Determining the weights for each

factor

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1 st

_{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

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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

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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.

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Weights assigned using

AHP

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Weights assigned using the

Rank Order method

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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

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MCE – pros and cons

•Cons:

– Dynamic problems

strongly simplified into a linear model

– Static, lacks the time dimension

– Controversial method – too subjective?

•Pros:

– Gives a structured and traceable analysis.

– Possibility to use different evaluation

factors makes it a good tool for discussion.

– Copes with large

amounts of information. – It works!

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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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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:

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 Goal

 Objectives

 Criteria

 Alternatives

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An example of hierarchical value tree:

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Criteria characteristics

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

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

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Problem solving steps:

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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)

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AHP merupakan salah satu alat bantu (proses)

dalam pengambilan keputusan yang dikembangkan

oleh Thomas L Saaty pada tahun 70an.

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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).

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Klaus Goepel Combining performance indicators to one Key Performance

Indicator (KPI)

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Mathematical method:

How to derive the weights?

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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

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Allows some small inconsistency in judgment

Analytic Hierarchy Process (AHP)

Deriving ratio scales from paired comparisons

Actual measurement Subjective opinion

Ratio scales Consistency index

Price, weight etc satisfaction feelings, preferences

from Eigen vectors from Eigen value

INPUT:

OUTPUT:

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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

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Price not taken as criterion separating

benefits form cost allows for a

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HASIL REKLASIFIKASI Mengetahui rekomendasi jalur pipa PDAM yang optimum dalam melayani konsumen

Kemiringan Lereng Arah Hadap Lereng Penggunaan Lahan

Sungai Jalan

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HASIL PERHITUNGAN AHP

Parameter Jalan Penggunaan

Lahan

Kemiringan Lereng

Arah Hadap

Lereng Sungai Priority Vector Bobot

Jalan 1 5 2 6 9 0.452744686 45% Penggunaan Lahan 0.2 1 0.33 4 5 0.139783822 14% Kemiringan Lereng 0.5 3 1 9 7 0.315980423 32% Arah Hadap Lereng 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