Modeling and Analysis-1 February 2013Decision Support Systems Course.. Dr. Aref Rashad1 Decision Support System Course Dr. Aref Rashad Part: 2

Modeling and Analysis-1

February 2013Decision Support Systems Course .. Dr. Aref Rashad

1

Decision Support System Course

Dr. Aref Rashad

Part: 2


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Learning Objectives

• Understand basic concepts of DSS modeling. • Describe DSS models interaction.• Understand different model classes.• Structure decision making of alternatives.• Understand the concepts of optimization,

simulation, and heuristics.• Learn to develop model component in DSS


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Model Component

• Key element in DSS• Many classes of models• Specialized techniques for each model• Allows for rapid examination of alternative

solutions• Multiple models often included in a DSS


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The purpose of the model is to represent critical relationships in such a way to guide decision makers toward a desired goal

Modeling is the simplification of some phenomenon for the purpose of understanding its behavior. Keep the structures which are essential for the Problem and neglect unnecessary details.

This is the essence of modeling !!!

Modeling Concept


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– Mental (arranging furniture)

– Visual (blueprints, road maps)

– Physical/Scale (aerodynamics, buildings)

– Mathematical (what we’ll be studying)

Types of models

Decision Support Systems Course .. Dr. Aref Rashad

6February 2013

Dimensionality of Models

•Representation

•Time Dimension

• Linearity of the Relationship

• Deterministic vs. Stochastic

• Descriptive vs. Normative

• Methodology Dimension


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Models rely upon either:• Experiential data• Objective data Experiential models rely upon the preparation and information processing of people, include judgments, expert opinions, and subjective estimates. Objective models rely upon specified, detached data and its analysisby known techniques. They are considered "objective" because the data are specified, constant, and independent of the specific decision maker's experiences.

Representation


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Static Models

• A snapshot in time of all factors affecting the decision environment.

• Assume no dependence of later decisions or actions on the choice under consideration.

• Single interval• Time can be rolled forward, a photo at a time• Usually repeatable• Unvarying Steady state• Primary tool for process design

Model Types:• Static models • Dynamic models

Time Dimension


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Dynamic Model

• Consider the decision environment over some specified time period.

• May consider the same phenomenon during different periods of time or interrelated decisions that will be considered during different time periods

• Represent changing situations• Time dependent• Varying conditions• Generate and use trends• Occurrence may not repeat

Time Dimension


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Looking at Intervals of Time for Patterns


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Linear models The relation between variables are linear. They are easier and faster to solve, and generally have a straightforward approach to solution. They can be used to approximate the nonlinear data.

Nonlinear models The relation between variables are nonlinear. They are harder and slower to solve

Linearity of the RelationshipModel Types:• Linear models • Nonlinear models


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Nonlinear Relationships


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Deterministic models use specified values for variables in the model. No randomness are considered

Stochastic models use probabilistic distributions forone or more variables in the model to view how situations might evolve over time The most common form of stochastic modeling is based on Monte Carlo analysis.

Deterministic Versus Stochastic


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Nonlinearity with Randomness

Results of a Monte Carlo Analysis


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Descriptive models:•Report what is happening in the data• Provide decision makers with a quantitative view of what is happening in the organization • Serve as predictive analytics, which attempt to forecast how factors

Normative models:• Represent an ideal value•Illustrate how the current organization is competing relativeto a set of standards or values.

Descriptive Versus Normative


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Complete enumeration, information about all feasibleoptions is collected and evaluated. Ex: CensusAlgorithmic , development of a set of procedures that can be repeated and will define the desired characteristics of the decision environment. Ex: Operations ResearchHeuristic, applied to large or ill-structured problems that cannot be solved algorithmically. Simulation ,to imitate reality either quantitatively or behaviorally. It involves the repetition of an experiment and the description of the characteristics of certain variables over time.Analytic, the process of breaking up a whole into its parts to determine their nature, proportion, function, and interrelationships

Methodology Dimension


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Model Categories


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Structure of Mathematical Model


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Example: Iron Works, Inc.Iron Works, Inc. manufactures twoproducts made from steel and just receivedthis month's allocation of b pounds of steel.It takes a1 pounds of steel to make a unit of product 1

and a2 pounds of steel to make a unit of product 2.

Let x1 and x2 denote this month's production level of

product 1 and product 2, respectively. Denote by p1 and

p2 the unit profits for products 1 and 2, respectively.

Iron Works has a contract calling for at least m units of product 1 this month. The firm's facilities are such that at most u units of product 2 may be produced monthly.


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Example: Iron Works, Inc.

Mathematical Model– The total monthly profit =

(profit per unit of product 1) x (monthly production of product 1)

+ (profit per unit of product 2) x (monthly production of product 2)

= p1x1 + p2x2

We want to maximize total monthly profit:Max p1x1 + p2x2


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Example: Iron Works, Inc.Uncontrollable InputsUncontrollable Inputs

$100 profit per unit Prod. 1$200 profit per unit Prod. 22 lbs. steel per unit Prod. 13 lbs. Steel per unit Prod. 22000 lbs. steel allocated60 units minimum Prod. 1720 units maximum Prod. 20 units minimum Prod. 2

$100 profit per unit Prod. 1$200 profit per unit Prod. 22 lbs. steel per unit Prod. 13 lbs. Steel per unit Prod. 22000 lbs. steel allocated60 units minimum Prod. 1720 units maximum Prod. 20 units minimum Prod. 2

60 units Prod. 1626.67 units Prod. 2 60 units Prod. 1626.67 units Prod. 2

Controllable InputsControllable Inputs

Profit = $131,333.33Steel Used = 2000Profit = $131,333.33Steel Used = 2000

OutputOutput

Mathematical ModelMathematical Model

Max 100(60) + 200(626.67)s.t. 2(60) + 3(626.67) < 2000 60 > 60 626.67 < 720 626.67 > 0

Max 100(60) + 200(626.67)s.t. 2(60) + 3(626.67) < 2000 60 > 60 626.67 < 720 626.67 > 0


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Part: 2


Dr. Aref Rashad


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Decision Making Overview

Decision Making

Certainty Nonprobabilistic

Uncertainty Probabilistic

Decision Environment Decision Criteria

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The Decision Environment

Certainty

Uncertainty

Decision EnvironmentCertainty: The results of decision alternatives are known

Example:

Must print 10,000 color brochures

Offset press A: $2,000 fixed cost + $.24 per page

Offset press B: $3,000 fixed cost + $.12 per page

*

February 2013


Chap 17-42

The Decision Environment

Uncertainty

Certainty

Decision EnvironmentUncertainty: The outcome that will occur after a choice is unknown

Example:

You must decide to buy an item now or wait. If you buy now the price is $2,000. If you wait the price may drop to $1,500 or rise to $2,200. There also may be a new model available later with better features.

*

(continued)

February 2013


Chap 17-43

Decision Criteria

Nonprobabilistic

Probabilistic

Decision CriteriaNonprobabilistic Decision Criteria: Decision rules that can be applied if the probabilities of uncertain events are not known. *

maximax criterion

maximin criterion

minimax regret criterion

February 2013


Chap 17-44

Decision Criteria

Nonprobabilistic

Probabilistic

Decision Criteria

*

Probabilistic Decision Criteria: Consider the probabilities of uncertain events and select an alternative to maximize the expected payoff of minimize the expected loss

maximize expected value

minimize expected opportunity loss

(continued)

February 2013


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Decision Tables

• Multiple criteria decision analysis• Features include:– Decision variables (alternatives)– Uncontrollable variables– Result variables

• Applies principles of certainty, uncertainty, and risk


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Decision Tree

• Graphical representation of relationships• Multiple criteria approach• Demonstrates complex relationships• Cumbersome, if many alternatives


Chap 17-47

Add Probabilities and Payoffs

Large factory

Small factory

Decision

Average factory

Uncertain Events(States of Nature)

Strong Economy

Stable Economy

Weak Economy

Strong Economy

Stable Economy

Weak Economy

Strong Economy

Stable Economy

Weak EconomyPayoffs

Probabilities

200

50

-120

40

30

20

90

120

-30

(.3)

(.5)

(.2)

(.3)

(.5)

(.2)

(.3)

(.5)

(.2)

February 2013


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Influence Diagrams

• Graphical representation of model• Provides relationship framework• Examines dependencies of variables• Any level of detail• Shows impact of change• Shows what-if analysis


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Influence Diagrams

• An influence diagram is a graphical device showing the relationships among the decisions, the chance events, and the consequences.

• Squares or rectangles depict decision nodes.• Circles or ovals depict chance nodes.• Diamonds depict consequence nodes.• Lines or arcs connecting the nodes show the direction of

influence.

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Influence Diagrams

Decision Intermediate or uncontrollable

Variables:Result or outcome (intermediate or final)

Certainty

Uncertainty

Arrows indicate type of relationship and direction of influence

Amount in CDs

Interest earned

PriceSales


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Influence Diagrams

Random (risk)Place tilde above variable’s name

~ Demand

Sales

Preference(double line arrow)

Graduate University

Sleep all day

Ski all day

Get job

Arrows can be one-way or bidirectional, based upon the direction of influence


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Sensitivity, What-if, and Goal Seeking Analysis

• Sensitivity– Assesses impact of change in inputs or parameters on solutions– Allows for adaptability and flexibility– Eliminates or reduces variables– Can be automatic or trial and error

• What-if– Assesses solutions based on changes in variables or assumptions

• Goal seeking– Backwards approach, starts with goal– Determines values of inputs needed to achieve goal– Example is break-even point determination


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Search Methods


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Search Approaches

• Analytical techniques (algorithms) for structured problems– General, step-by-step search– Obtains an optimal solution

• Blind search– Complete enumeration

• All alternatives explored

– Incomplete • Partial search

– Achieves particular goal– May obtain optimal goal


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Search Approaches• Heurisitic– Repeated, step-by-step searches– Rule-based, so used for specific situations– “Good enough” solution, but, eventually, will obtain

optimal goal– Examples of heuristics

• Tabu search – Remembers and directs toward higher quality choices

• Genetic algorithms– Randomly examines pairs of solutions and mutations


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• A network model is one which can be represented by a set of nodes, a set of arcs, and functions (e.g. costs, supplies, demands, etc.) associated with the arcs and/or nodes.

• Transportation, assignment, PERT/CPM and transshipment problems are all examples of network problems.

Network model


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Transportation Problem

Network Representation

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c11

c12

c13

c21

c22c23

d1

d2

d3

s1

s2

Sources Destinations

33

22

11

11


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Transportation ProblemNetwork Representation

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c11

c12

c13

c21

c22c23

d1

d2

d3

s1

s2

Sources Destinations

33

22

11

11


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Example: Shortest RouteFind the Shortest Route From Node 1 to All Other Nodes

in the Network:

6644

4

7

3

5 1

8

6

2

5

3

6

2

3311

22 55

77


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Project Network

Start Finish

B3

D3

A3

C2

G6

F3

H2

E7

PERT/CPM is used to plan the scheduling of individual activities that make up a project.


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Simulation• Imitation of reality• Allows for experimentation and time compression• Descriptive, not normative• Can include complexities, but requires special skills• Handles unstructured problems• Optimal solution not guaranteed• Methodology

– Problem definition– Construction of model– Testing and validation– Design of experiment– Experimentation– Evaluation– Implementation


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Simulation• Probabilistic independent variables– Discrete or continuous distributions

• Time-dependent or time-independent• Visual interactive modeling – Graphical– Decision-makers interact with simulated

model– may be used with artificial intelligence

• Can be objected oriented


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Simulation Process


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Multicriteria Decisions

• Goal Programming• Goal Programming: Formulation

and Graphical Solution• Scoring Models• Analytic Hierarchy Process (AHP)

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Goal Programming• Goal programming may be used to solve linear

programs with multiple objectives, with each objective viewed as a "goal".

• In goal programming, di

+ and di- , deviation

variables, are the amounts a targeted goal i is overachieved or underachieved, respectively.

• The goals themselves are added to the constraint set with di

+ and di- acting as the

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Goal Programming• One approach to goal programming is to satisfy

goals in a priority sequence. Second-priority goals are pursued without reducing the first-priority goals, etc.

• For each priority level, the objective function is to minimize the (weighted) sum of the goal deviations.

• Previous "optimal" achievements of goals are added to the constraint set so that they are not degraded while trying to achieve lesser priority goals.

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Scoring Model

• Step 1: List the decision-making criteria.• Step 2: Assign a weight to each criterion.• Step 3: Rate how well each decision alternative

satisfies each criterion.• Step 4: Compute the score for each decision

alternative.• Step 5: Order the decision alternatives from

highest score to lowest score. The alternative with the highest score is therecom mended alternative.

February 2013

Mathematical Model

Sj = S wi rij

i

where:rij = rating for criterion i and decision alternative jSj = score for decision alternative j

Scoring Model for Job Selection

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Decision Alternative Analyst Accountant Auditor

Criterion Chicag Denver HoustonCareer advancement 8 6 4Location 3 8 7Management 5 6 9Salary 6 7 5Prestige 7 5 4Job security 4 7 6Enjoyable work 8 6 5

Scoring Model

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Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP), is a procedure designed to quantify managerial judgments of the relative importance of each of several conflicting criteria used in the decision making process.

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• Step 1: List the Overall Goal, Criteria, and Decision Alternatives

• Step 2: Develop a Pairwise Comparison Matrix

Rate the relative importance between each pair of decision alternatives. The matrix lists the alternatives horizontally and vertically and has the numerical ratings comparing the horizontal (first) alternative with the vertical (second) alternative.

Ratings are given as follows:

------- For each criterion, perform steps 2 through 5 -------------- For each criterion, perform steps 2 through 5 -------

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Step 2: Pairwise Comparison Matrix

Compared to the secondalternative, the first alternative is: Numerical rating

extremely preferred 9 very strongly preferred 7

strongly preferred 5 moderately preferred 3 equally preferred 1

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Step 2: Pairwise Comparison MatrixIntermediate numeric ratings of 8, 6, 4, 2 can

be assigned. A reciprocal rating (i.e. 1/9, 1/8, etc.) is assigned when the second alternative is preferred to the first. The value of 1 is always assigned when comparing an alternative with itself.

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• Step 3: Develop a Normalized Matrix Divide each number in a column of the

pairwise comparison matrix by its column sum.

• Step 4: Develop the Priority Vector Average each row of the normalized matrix.

These row averages form the priority vector of alternative preferences with respect to the particular criterion. The values in this vector sum to 1.

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Step 5: Calculate a Consistency RatioThe consistency of the subjective input in

the pairwise comparison matrix can be measured by calculating a consistency ratio. A consistency ratio of less than .1 is good. For ratios which are greater than .1, the subjective input should be re-evaluated.

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Step 6: Develop a Priority MatrixAfter steps 2 through 5 has been performed for

all criteria, the results of step 4 are summarized in a priority matrix by listing the decision alternatives horizontally and the criteria vertically. The column entries are the priority vectors for each criterion.

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Step 7: Develop a Criteria Pairwise Development Matrix

This is done in the same manner as that used to construct alternative pairwise comparison matrices by using subjective ratings (step 2). Similarly, normalize the matrix (step 3) and develop a criteria priority vector (step 4).

• Step 8: Develop an Overall Priority VectorMultiply the criteria priority vector (from step

7) by the priority matrix (from step 6).

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Determining the Consistency Ratio

• Step 1: For each row of the pairwise comparison matrix,

determine a weighted sum by summing the multiples of the entries by the priority of its corresponding (column) alternative.

• Step 2: For each row, divide its weighted sum by the

priority of its corresponding (row) alternative.• Step 3:

Determine the average, max, of the results of step 2.

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• Step 4: Compute the consistency index, CI, of the n

alternatives by: CI = (max - n)/(n - 1).• Step 5:

Determine the random index, RI, as follows:

Number of Random Number of Random Alternative (n) Index (RI) Alternative (n) Index (RI)

3 0.58 6 1.24 4 0.90 7 1.32 5 1.12 8 1.41

• Step 6:Compute the consistency ratio: CR = CR/RI.

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Determining the Consistency RatioAnalytic Hierarchy Process


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Group Decision Making TechniquesBrainstorming

The process of brainstorming involves members discussing and suggesting opinions as well as alternatives for a decision. The brainstorming session is facilitated by the group or team leader who will solicit ideas from the members and note them down. e divided into two groups who will debate on the pros and cons of the alternatives.

Nominal Group TechniqueA structured approach in decision making, the nominal group technique requires each member to develop a list of possible alternatives in writing. After that, the alternatives are presented to the group and are ranked according to order of preference.

Delphi TechniqueThe Delphi technique is applicable only when the members are on separate physical locations. The decision making process is usually done through email, fax or other forms of online technology where the members can meet and discuss.


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Brainstorming/Filtering

• Prepare for the Brainstorming• Determine the Brainstorming Method to use• Generate Ideas• Create Filters• Apply Filters• Wrap up the Brainstorming Session

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Nominal Group Technique

• Define the problem to be solved/decision• Silently generate ideas• State and record ideas• Clarify each on the list• Rank items silently; list rankings• Tally rankings• Wrap up NGT session

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Paired Choice Matrix

• Identify the issue, options, goals• Prepare for the session• Make decisions between pairs• Tally scores of paired choices• Discuss and clarify results• Wrap up

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Criteria Rating Technique

• Start session and list alternatives• Brainstorm decision criteria• Discuss the relative importance of each criteria• Establish a rating scale, then rate the alternatives• Calculate the final score• Select the best alternative• Wrap up

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The Delphi Technique

• Define the decision or problem• Team provides Round 1 input• Summarize Round 1: ask for Round 2 input• Team provides Round 2 input**• Summarize Round 2: ask for Round 3 input• Team provides Round 3 input• Summarize Round 3• Wrap Up

February 2013


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Model-Based Management System


Part: 2


Dr. Aref Rashad


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Easy Access to ModelsThe library of models is provided so as to allow decision makers easy access to the models.Easy access to the models means that users need not know the specifics of how the model runs or the specific format rules for commanding the model



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Model-Based Management System• Software that allows model organization

with transparent data processing• Capabilities– DSS user has control– Flexible in design– Gives feedback– GUI based– Reduction of redundancy– Increase in consistency– Communication between combined models


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• Relational model base management system– Virtual file– Virtual relationship

• Object-oriented model base management system– Logical independence

• Database and MIS design model systems– Data diagram, ERD diagrams managed by CASE tools


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Simple Model Selection


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Understandability of Results

In addition, the DSS should provide the results back to the user in an understandable form.Most models provide information to the user employing at least some cryptic form that is not comprehensible for people who do not use the package frequently.


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Manipulation of a Model


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Traditional Results Format


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Results with Decision Support


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Model Support


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Passive Warning of Model Problems


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Active Warning of Model Problems


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Integrating ModelsAnother task of the MBMS is to help integrate one model with another. For example, suppose the user needs to make choices about inventory policy and selects an economic order quantity (EOQ) model


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Integration of Models


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Modeling Results with Interpretative Support


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Model Results with Better Interpretative Support


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Model Management Support Tools

The kinds of issues associated with model-generated questions like those in the two exampleswill, of course, depend upon what model is being used.


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Passive Prompting for Further Analysis


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Active Prompting for Further Analyses


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Sensitivity of a DecisionOne of the tasks of the model base management system in a DSS is to help the decision maker understand the implications of using a model

Sensitivity of a Decision


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•The failure to identify an important variable

•Select an inappropriate time horizon

•Overfit the model to some time period

•Not knowing if the assumptions are true

Problems of Models


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Basic Spreadsheet Modeling Concepts and Best Practices

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Modeling with Spreadsheets

• Flexible and easy to use• End-user modeling tool• Allows linear programming and regression analysis• Features what-if analysis, data management, macros• Seamless and transparent• Incorporates both static and dynamic models


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Spreadsheet modeling The process of entering the inputs and decision variables

into a spreadsheet and then relating them appropriately, by means of formulas, to obtain the outputs.

Once a model is created there are several directions in which to proceed.– Sensitivity analysis to see how one or more outputs

change as selected inputs or decision variables change.

– Finding the value of a decision variable that maximizes or minimizes a particular output.

– Create graphs to show graphically how certain parameters of the model are related.

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• Good spreadsheet modeling practices are essential.• Spreadsheet models should be designed with

readability in mind.• Several features that improve readability include:

• A clear logical layout to the overall model• Separation of different parts of a model• Clear headings for different sections of the model • Liberal use of range names• Liberal use of formatting features• Liberal use of cell comments• Liberal use of text boxes for assumptions, lists or

explanations

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Building a Model

• Randy Kitchell is a NCAA t-shirt vendor. The fixed cost of any order is $750, the variable cost is $6 per shirt.

• Randy’s selling price is $10 per shirt, until a week after the tournament when it will drop to $4 apiece. The expected demand at full price is 1500 shirts.

• He wants to build a spreadsheet model that will let him experiment with the uncertain demand and his order quantity.

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The logic behind the model is simple. An Excel IF function will be used.

February 2013

Building a Model

The profit is calculated with the formula

Profit = Revenue – Cost and the Cost = 750 + 6*B4 Revenue Case 1: Demand outstrips order (B3 > B4)In that case everything gets sold for 10 dollars Revenue is then simply 10*B4(since B4 is the number ordered)


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Revenue Case 2:You have ordered too many.That is order (B3) is less than peak demandThen you can only sell B3 at 10 dollars and the rest (B4-B3) at

4 dollarsRevenue = 10*B3+4*(B4-B3)

February 2013

Revenue = IF(B3>B4,10*B4,10*B3+4*(B4-B3))

Profit = IF(B3>B4,10*B4,10*B3+4*(B4-B3)) – (750 + 6* B4)

Building a Model


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The formula can be rewritten to be more flexible.=-B3-B4*B9+IF(B8>B9,10*B8+B6*(B9-B8))

It can be made more readable by using range names. The formula would then read=-Fixed_order_cost-Variable_cost*Order + IF(Demand > Order, Selling_price*Order, 10*Demand+Salvage_value* (Order-Demand)

Building a Model


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Spreadsheet for Loan problem


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END Part 2


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Decision Making without Probabilities

Three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is unavailable are: – the optimistic approach– the conservative approach– the minimax regret approach.

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Decision Making with ProbabilitiesExpected Value Approach– If probabilistic information regarding the states of

nature is available, one may use the expected value (EV) approach.

– Here the expected return for each decision is calculated by summing the products of the payoff under each state of nature and the probability of the respective state of nature occurring.

– The decision yielding the best expected return is chosen.

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• The expected value of a decision alternative is the sum of weighted payoffs for the decision alternative.

• The expected value (EV) of decision alternative di is defined as:

where: N = the number of states of nature P(sj ) = the probability of state of nature sj

Vij = the payoff corresponding to decision alternative di and state of nature sj

Expected Value of a Decision Alternative

EV( ) ( )d P s Vi j ijj

N

1

EV( ) ( )d P s Vi j ijj

N

1

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Brainstorming Support Tools

Documents

Modeling and Analysis-1 February 2013Decision Support Systems Course.. Dr. Aref Rashad1 Decision Support System Course Dr. Aref Rashad Part: 2