1 Санкт-Петербургский государственный политехнический университет Факультет инноватики Кафедра "Теоретических основ инноватики“ Курс Многокитериальный анализ. Методы Саати. Доц. Бобылев Николай Геннадьевич Skype: nikolaibobylev Tel.: Лекция 3 Стратегия 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 2

Рассмотрение проблемы. Это мгогокритериальная проблема? Сложная Комплексная Решение не очевидно Конфликт целей\альтернатив 3

Терминология 4 Term Alternative terms ExplanationsExample related to risk analysis Hierarchy structure Value tree -- Assessment goal Objective The essence of the problemEnvironmental 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 initiativedesign 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 alternativesA 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) 5

Шаги (Bobylev, 2008) 6 Step Explanations Define 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 7

Альтернативы Имеющиеся Генерируемые Реалистичные Четко сформулированные и описанные Сратегия – агрегирование \ детализация 8

Критерии Количественные, качественные, смешанные Критерий может быть описан различными дескрипторами Разработка структуры (список, иерархия) Иерархия: Сверху вниз – детализация Снизу вверх - агрегирование 9

Виды критериев (Bobylev, 2008) 10 Criteria typeExampleExplanation of AHP practicalities QuantitativeConcentration of suspended matter Pairwise comparisons are conducted using ratio of figures under different alternatives QualitativeArea’s historical valuePairwise comparison is based on expert judgement Qualitative scored on the basis of quantitative data Groundwater levelNumerical data can not be subject to direct pairwise comparisons, expert judgement is required

11 Elaboration of hierarchy bottom-up technique Water security Groundwater level Surface waterGroundwater Seasonal mode DynamicsPollutants Groundwater level in the first horizon Groundwater gradient Groundwater level in the second horizon

bottom-up technique 12 Environmental quality Groundwater level Groundwater Dynamics Groundwater level in the first horizonGroundwater level in the second horizon Hydrosphere

13 Elaboration of hierarchy top-down technique Heavy metals ? Nutrients ? Water security Surface waterGroundwater Seasonal mode DynamicsPollutants

top-down technique 14 Heavy metals ? Oils ? Nutrients ? Organic toxins ? Suspended matter ? Hydrosphere environmental quality Surface waterGroundwater Seasonal mode Dynamics Pollutants

Разработка иерархии (Bobylev, 2008) 15 Particular AspectTop-down techniqueBottom-up technique Timing of hierarchy elaboration in the assessment process Early stageLater 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 changedLiberal approach – easy to changeStrict approach – difficult to change Main difficultyIdentification of criteria or indicators Aggregation of elements Main drawbackInitial lack of clarity about lower elements Possibility of disagreements and uncertainty about nodes at the middle level (how to aggregate elements into groups) Main strengthGoal-led approach allows strict adherence to purpose of assessment Impact-led approach allows close- linked assessment to input data (criteria or indicators) Underlying intentionsEnhancing positive impactsMitigating negative impacts

Шаги (Bobylev, 2011) 16

Софт Бесплатный – ограничения по числу уровней иерархии и альтернатив Концепции методов в софте хорошо подходят и технически удобны для Вашей задачи 17

Работа! 18

Лекция 3 Домашнее задание 19 Продумать стратегию решения Вашей задачи (проекта) Работать с софтом