Problem Structuring

Y. İlker TOPCU, Ph.D.

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Structuring the Problem

• Both defining the problem and identifying the elements of the model to be used in the analyzing the various alternative courses of action.

• An imaginative creative process of translating an initially ill-defined problem into a set of well-defined elements, relations and operations.

• These problem elements include “events, values, actors, and decision alternatives”, and are related to each other by “influence relations, inclusion relations, hierarchical ordering relations, etc.”.

Structuring Process

Structuring is a three step process (Masser &Wallace, 1996;

Rosenhead, 1989; Volkema, 1983):

Value focused thinking (Keeney, 1992)

1. Recognizing and defining a decision problem

2. Specifying values and objectives

3. Identifying and generating alternatives

Alternative focused thinking• Steps 2 & 3 are switched

Recognizing and Defining a Decision Problem

• Ask what triggered this decision: "Why am I even considering it?"

• A brief statement of “what is broken” or if this is not possible, “why we know that something is broken”

• Question the constraints in the problem statement• Identify the essential elements of the problem• Understand what other decisions impinge on or hinge

on this decision• Expand statement of the problem in four dimensions:

identity - “what”; location - “where”; timing - “when”; magnitude - “how much, how many”

Specifying Values

• Values are principles used for evaluation • We should spend more of our decision making time

concentrating on “what is important?” by: • articulating and understanding our values and • using these values

• to select meaningful decisions to ponder, • to create better alternatives than those already

identified, and • to evaluate more carefully the desirability of the

alternatives

Objectives

• An objective is a statement of something that one desires to achieve.

• It is characterized by three features: a decision context, an object, and a direction of preference.

Types of objectives:• Fundamental objective

Context dependent. Characterizes essential reason for interest in the decision situation.

• Means objective: Context dependent. Implies for the degree to which another (more fundamental) objective can be achieved.

Specifying Objectives

• When you faced with a difficult decision situation, start by thinking about your values

• Ask what you hope to achieve in the decision context you face. Write down a list of your responses.

• Then push yourself to think of anything else that should be on the list.

• When you have a preliminary list, first ask why each objective is important. The responses will probably add objectives to your list.

• Once you feel the list of objectives is reasonably complete, it is important to specify clearly what each objective includes.

Identifying and Generating Alternatives

• When people are faced with a problem, they first measure its similarity to a set of common or previous problems stored in their long-term memories:

One potential bias resulting from this heuristic involves the failure to create new nodes

• Alternative generation techniques (Keller & Ho, 1988):• Objective/Attribute based procedures• Alternative based procedures• State based procedures• General creativity techniques

Objective/Attribute Based Procedures

• Present attributes one at a time. Elicit alternatives which will help meet each individual attribute

• Design alternatives to do well on the heavily weighted attributes

• Completely enumerate all possible alternatives by combining all possible levels of each attribute

• Invent or replace attributes

Alternative Based Procedures

• Present examples of alternatives and elicit more alternatives

• Specify the characteristics or generic structure of alternatives; then select alternatives which will meet the required structure

• Visualize the ideal alternative and design alternatives which are close to it

• Present examples of alternatives framed in a different way

State Based Procedures

• Present possible states of nature one at a time; elicit alternatives which will be effective in each individual state

• Design alternatives to do well in the more probable states of nature

• Use strategy generation tables to generate strategies (strategic alternatives)

General Creativity Techniques

• Brainstorming

Rapid generation of ideas• Synectics

A set of techniques which rely on metaphorical thinking with analogies to create new ideas

Structuring Methods

• Value Hierarchy (Value Tree)• Top down (objectives driven) approach• Bottom up (alternatives driven) approach

• Cognitive Mapping• Soft Systems Methodology• Influence Diagrams • Lateral Thinking

Value Hierarchy

• A value structure with a hierarchical or treelike structure is called a value tree or value hierarchy (Belton et al., 1997; Hammond et al., 1999; Keeney, 1996; Kirkwood, 1997; Watson & Buede, 1987; Von Winterfeldt & Edwards, 1986; Buede, 1986; Gregory & Keeney, 1994)

• Generally, it is necessary to develop a value hierarchy that is specific to a particular decision. This is because a general-purpose value hierarchy that would be applicable to a wide range of decisions would be so complex as to be impractical

Value Hierarchy

• A value hierarchy should be (Keeney & Raiffa, 1976; Keeney, 1992)• complete (all important aspects of the problem are captured)• operational (it can be used with reasonable effort) • decomposable (allowing different parts of the tree to be

analysed separately)• non-redundant (avoid double counting of impacts) • minimal or concise (keeping the level of detail to the

minimum required)• understandable (to facilitate generation and communication

of insights) • measurable (possible to specify in a precise way the degree

to which objectives are achieved through the association of appropriate attributes)

Top–Down Approach

• If Value Focused Thinking is being used or the alternatives are not well specified at the start of the analysis, then a top-down (objectives-driven) approach may be appropriate

• Approach starts with the overall/fundamental objective and successively subdivides objectives, then develops the attributes in successively greater detail

Bottom–Up Approach

• If Alternative Focused Thinking is being used or the alternatives are known at the time the hierarchy is being developed, then a bottom-up (alternatives-driven) approach may be appropriate.

• The alternatives are examined to determine the ways in which they differ. Attributes are developed to measure the evaluation considerations for which the alternatives differ, and these attributes are grouped together to form higher layers in the value hierarchy.

• Thus, this approach starts with the alternatives develops the bottom layer of the value hierarchy, and constructs the rest of the hierarchy on top of this bottom layer.

Cognitive Mapping

• A cognitive map is an image of cognitive processes and an attempt to utilize expert(s) opinion and cognition about ill-structured social relationships (Axelrod, 1976; Lee et al., 1992)

• One of the practical aims of cognitive mapping is to attain an appropriate and powerful link between the qualitative aspects of a problem definition and the role of quantitative analysis (Eden et al., 1986)

• Cognitive mapping is a tool which enables a group of experts and/or specialists to negotiate a definition of the problem that is visualized in the form of a model amenable to further elaboration and to the analysis of complexity (Eden, 1988)

Directed Graph

• The problem is represented by a signed digraph (directed graph) of basic elements where • A concept variable is symbolized as a point, and • The causal assertion (belief) of how one concept

variable affects another (relationship between the variables) is symbolized as an arrow

• A plus sign is attached to the arrows that show positive relationships (changes occur in the same direction)

• A minus sign is attached to the arrows that show negative relationships (changes occur in the opposite direction)

Signed Digraph for Energy Demand

Energy capacity

Energy use

# of jobs

Quality of environment

Energy price

# of factories

Population

– –

– –

–

Deriving Cognitive Map

• There are three basic ways of deriving a cognitive map of the expert opinion (Hwang & Lin, 1987): • questionnaire survey, • documentary coding, and • interviews.

• A questionnaire survey can be divided into three phases (Roberts, 1976): • identifying potentially relevant variables, • limiting the number of variables by rating their

importance, and • the choice of arrows and signs

Analysing Cognitive Map

• Decision Explorer software package (Banxia Software, 1996)

• Domain analysis (centrality)• Head-Tail analysis”• Cluster analysis• ... ... ....

• Centrality• The total number of concept variables (directly)

affected by concept i is “outdegree” of variable i• The total number of concept variables (directly)

affects concept i is “indegree” of variable i• outdegree + indegree = total degree (centrality)

Soft Systems Methodology

• If the OR approach is an inadequate methodology for the synthesis of decisions, soft systems may be used (Checkland, 1989)

• Its essence involves a more open minded, iterative, and flexible way of thinking about a problem than is typical of the traditional kinds of OR and the harder kinds of system thinking

• SSM articulates a process of enquiry which leads to the action, but that is not an end point unless you choose to make it one. .

Influence Diagrams

• The only rigorous modeling aid developed by decision analysts for their use is the influence diagrams. This research was begun in the mid-seventies and first published discussion appeared in Miller, Merkhofer, and Howard (1976).

• The early research focused exclusively on the use of influence diagrams during model structuring with a natural carry over into probability elicitation. This work has continued and has been generalised.

• Also efforts have shown that in addition to being used to structure the model, influence diagrams can replace decision trees for some problems as the solution mechanism.

• Compact graphical /mathematical representation of a decision situation

• It is a generalization of a Bayesian network, • probabilistic inference problems

• decision making problems

Influence Diagrams

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• Nodes• Decision node [rectangle]• Uncertainty node [oval]• Deterministic node [double oval]• Value node [diamond]

• Arcs• Functional arcs (ending in value node)• Conditional arcs (ending in uncertainty /

deterministic node)• Informational arcs (ending in decision node)

Influence Diagrams

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ID of a Plan for Vacation

http://en.wikipedia.org/wiki/Influence_diagram

Decisions about the Marketing Budget and Product Price

http://www.lumina.com/software/influencediagrams.html

Lateral Thinking

• Developed by de Bono (1985) as a way of breaking out of logical thought processes to develop radical views of problem

• The three primary activities are used in lateral thinking to stimulate new ideas:• becoming aware of the problem (inc. boundaries

and assumptions)• generating as many alternative views of the

problem as possible using old concepts of the problem

• the use of provocative methods for introducing discontinuities into the thought process.