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Санкт-Петербургский государственный политехнический университет

Факультет инноватики

Кафедра "Теоретических основ инноватики“

Курс

Многокитериальный анализ. Методы Саати.

Доц. Бобылев Николай Геннадьевич

E-mail: nikolaibobylev@daad-alumni.de Skype: nikolaibobylev Tel.: +7 911 759-89-71

Лекция 3Стратегия разработки многокритериальной

задачи

Содержание лекции 3

• Рассмотрение проблемы. Это мгогокритериальная проблема?

• Описание проблемы и постановка многокритериальной задачи

• Формулировка цели (целей) анализа• Существующие и генерируемые альтернативы• Критерии – виды, разработка, агрегирование,

дескрипторы• Выбор софта• Создание модели в софте• Результат, итерации, анализ, решение, рекоммендация

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Рассмотрение проблемы. Это мгогокритериальная проблема?

• Сложная• Комплексная• Решение не очевидно• Конфликт целей\альтернатив

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Терминология

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Term Alternative terms Explanations Example related to risk analysis

Hierarchy structure Value tree - -

Assessment goal Objective The essence of the problem Environmental quality in the area affected by the initiative

Elements of the hierarchy structure

Sub-objectives, attributes, criteria, nodes

Minor issues describing the assessment goal

Biosphere, concentration of pollutants in groundwater

Criterion Attribute Lowest element of the hierarchy structure, something to which value is given for different alternatives

e.g. percentage green space in a city

Alternatives Decision alternative; options Variations in the assessed initiative design solutions, policies

Value function Utility function Function, which assigns a value to criteria

The value is assigned using pairwise comparisons

Determining the value of alternatives

Scoring Assigning a value to the lowest level elements, criteria, based on assessment of alternatives

Calculating the normalised difference between groundwater level deviation under two alternative water abstraction schemes

Determining the weight of criteria

Weighting Assigning weights to elements of the hierarchy structure which are in one group

Expert assessment of the relative importance of groundwater versus surface water elements for environmental quality in the study area

Sensitivity analysis - Provides understanding of the outcomes if weights or values were assigned differently

Finding out that the criterion “organic contamination in groundwater” is the key to deciding which alternative has less environmental impact

Result - Ranking of alternatives A programme for the development of mitigation measures.

Описание проблемы и постановка многокритериальной задачи

• Дискуссия по возможным решениям• Дискуссия по возможным критериям• Формулировка целей анализа

• Сколько многокритериальных задач?• Сколько моделей? Какие методы можно применить?• Стратегия принятия решения (пример: две модели

(МАИ+рейтинги), третья МАС для надежности, итоговая - простые экспертные рейтинги)

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Шаги (Bobylev, 2008)

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Step ExplanationsDefine the decision context What is the decision needed to be made? Why it can not be made

without conducting AHP? It is important to establish a brief problem description, specifying main conflicting criteria and possible trade-offs needed to be made.

Formulate an assessment goal This step naturally derives out of the first one by more strict and clear formulation of the AHP objective. If the first step addresses more general questions about outcomes of AHP, the second step should provide solid base for structuring the AHP.

Identify alternatives Usually some alternatives exist, if not they can be generated by analysis of the decision problem.

Specify criteria This step is one of the most time-consuming, unless a set of criteria is available from other studies. Criteria are the measures of performance by which the alternatives will be judged.

Elaborate a hierarchy structure Hierarchy structure resembles a tree at the top of which is an assessment goal and brunches are criteria. Criteria should be composed into groups; this allows prioritizing their impact on assessment goal. There are different approaches for elaborating a hierarchy structure (see section 3).

Weight the criteria Assign weights for each of the criteria to reflect their relative importance to the assessment goal. Pairwise comparisons between criteria are used.

Valuate the alternatives Assess the expected performance of each alternative against the criteria. Pairwise comparisons between alternatives are used.

Combine the weights and values for each of the alternatives to rate alternatives

This step represents calculations using specific AHP equations, computer software is also available.

Conduct sensitivity analysis to examine how variation of the scores and weights affect the alternatives ratings.

This step allows analyzing alternatives performance using variation of scores and weights. Sensitivity analysis allows identifying how robust the decision-making model is and how ratings are sensitive to variation of particular criteria weights or scores.

Формулировка цели (целей) анализа

• МАИ – важна четкая формулировка цели• Четкая цель – просто делать попарные сравнения• МАС – вожможно нексолько целей – стратегические

критеии

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Альтернативы

• Имеющиеся• Генерируемые

• Реалистичные• Четко сформулированные и описанные

• Сратегия – агрегирование \ детализация

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Критерии

• Количественные, качественные, смешанные• Критерий может быть описан различными

дескрипторами

• Разработка структуры (список, иерархия)

Иерархия:• Сверху вниз – детализация• Снизу вверх - агрегирование

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Виды критериев (Bobylev, 2008)

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Criteria type Example Explanation of AHP practicalities

Quantitative Concentration of suspended matter

Pairwise comparisons are conducted using ratio of figures under different alternatives

Qualitative Area’s historical value Pairwise comparison is based on expert judgement

Qualitative scored on the basis of quantitative data

Groundwater level Numerical data can not be subject to direct pairwise comparisons, expert judgement is required

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Elaboration of hierarchy

bottom-up technique

Water security

Groundwater level

Surface water Groundwater

Seasonal mode

DynamicsPollutants

Groundwater level in the first horizon

Groundwater gradient

Groundwater level in the second horizon

bottom-up technique

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Environmental quality

Groundwater level

Groundwater

Dynamics

Groundwater level in the first horizon Groundwater level in the second horizon

Hydrosphere

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Elaboration of hierarchy

top-down technique

Heavy metals

?Nutrients

?

Water security

Surface water Groundwater

Seasonal mode

DynamicsPollutants

top-down technique

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Heavy metals?

Oils?

Nutrients?

Organic toxins?

Suspended matter?

Hydrosphere environmental quality

Surface water Groundwater

Seasonal mode

DynamicsPollutants

Разработка иерархии (Bobylev, 2008)

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Particular Aspect Top-down technique Bottom-up techniqueTiming of hierarchy elaboration in the assessment process

Early stage Later stage (after criteria are identified)

Acquisition of lower level elements (criteria or indicators)

Elicited during analysis of higher elements (elements description)

Obtained before MCDA assessment stages

Arrangement of nodes (grouping the elements)

Decomposition (description) of higher elements

Aggregation of lower elements (criteria or indicators as the first step)

Ability of a hierarchy to be changed Liberal approach – easy to change Strict approach – difficult to change

Main difficulty Identification of criteria or indicators

Aggregation of elements

Main drawback Initial lack of clarity about lower elements

Possibility of disagreements and uncertainty about nodes at the middle level (how to aggregate elements into groups)

Main strength Goal-led approach allows strict adherence to purpose of assessment

Impact-led approach allows close-linked assessment to input data (criteria or indicators)

Underlying intentions Enhancing positive impacts Mitigating negative impacts

Шаги (Bobylev, 2011)

•16Conducting sensitivity analysis; analyzing results; modifying and reiterating assessment if needed

Developing and formulating a number of alternatives on the basis of considered options

Input data: answering specific questions for each alternative and criterion. Quantitative and qualitative data can be used

Clear formulation of an assessment goal

Identifying strategic criteria on the basis of the assessment goal

Developing a set of criteria for each cluster (BOCR) on the basis of analysis of the facts, that may influence the decision. Criteria can be structured as a hierarchy

Defining a decision problem, possible options for resolving the problem, and facts that may influence the decision

Софт

• Бесплатный – ограничения по числу уровней иерархии и альтернатив

• Концепции методов в софте хорошо подходят и технически удобны для Вашей задачи

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Работа!

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Лекция 3Домашнее задание

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Продумать стратегию решения Вашей задачи (проекта)

Работать с софтом