Transcript Decision Support System

Decision Support System
Chapter 4: Modeling and Analysis
Current modeling issues
• Problems exist in identifying correct measures that lead to
overall goal success.
• Objectives to indicate model’s objective function/measure(s)
must be properly and accurately determined.
• Issues include:
– Identification of the problem and environmental analysis.
– Variable indentification
– Forecasting (Predictive Analytics)
– Multiple models
– Model categories
– Model management
– Knoweldge-based modeling
Problem Identification & Env. analysis
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First phase in Simon’s decision phases.
Environmental scanning and analysis is part of analysis.
BI/BA help in identifying problems.
The problem must be well understood and everyone involved
should share the same frame of understanding because the
problem will ultimately be presented by the model in one
form or another.
Variable identification
• Identification of a model variable (decision, result,
uncontrollable) is critical as the relationships of the variables.
– Tools: influnce diagrams, cognitive maps.
Forecasting (Predictive Analytics)
• Forecasting: predicting the feature.
• Is essential for construction and manipulating models because
when a decision is implemented, the results usually occur in
the future. Whereas DSS are typically designed to determine
what will be.
• Tradition MIS report what is or what was, there is no point in
running a what-if(sensitivity) analysis on the past.
• CRM & RMS [Cox Communication application case 4.2]
Multiple models
• DSS can include several models, each representing different
part of the decision-making problem.
• AHP: Analytic hierarchical Process is used in such situations.
Model categories
Model management & Knowledge-base Modeling
• Model management :models like data must be managed.
• Knowledge-based modelling :
• DSS uses mostly quantitative models whereas expert systems
qualitative , knowledge based models.
• Trend toward transparency
– Multidimensional modeling exhibits as spreadsheet
Static and Dynamic models
STATIC ANALYSIS:
• Single photograph of situation
• Single interval
• Time can be rolled forward , but it is nonetheless static.
• Decision-making situations usually repeat with the identical
condition
• Example:
• Process simulation begins with Steady state which models a
static representation of a plant to find its
Optimal operating parameters.
– assumption: flow of material will be Continuous and
unvarying
– Primary tool for process design
Static and Dynamic models
DYNAMIC ANALYSIS:
• Represent scenarios that change over time .
• Example:5-years profit- and-loss projection in which input
data(cost , prices,….) change from year to year.
• Time dependent
• Varying conditions
• Generate and use trends and patterns over time.
• Occurrence may not repeat
• Static model can be expanded to be dynamic.
• Dynamic simulation ,in contrast to steady-state(variation in
materials flow)
Certainty, Uncertainty and Risk
• Decision situations are often classified on the basis of what the decision
maker knows about the forecasted results.
• This knowledge classified into three categories
ranging from complete knowledge to total ignorance
• These categories are:
• Certainty
• Uncertainty
• risk
Increasing knowledge
Complete knowledge
certainty
Risk
decreasing knowledge
Ignorance, total
uncertainty
Decision making under certainty
• Certainty
– Assume complete knowledge (deterministic environment)
– Example: U.S. Treasury bill investment(complete information about
the future of ROI).
– All potential outcomes known(assumed only one for each
course of action).
– Easy to develop , solve model ,and yield optimal solution.
• Typically for structured problems with short time horizons.
• Sometimes DSS approach is needed for certainty situations.
Decision making under uncertainty
• Uncertainty
– Situations in which several outcomes are possible for each
course of action.
– BUT the decision maker does not know, or cannot
estimate, the probability of occurrence of the possible
outcomes.
– More difficult - insufficient information
– Managers attempt to avoid uncertainty as much as
possible.
– Modeling involves assessing the decision maker's (and/or
the organizational) attitude toward risk.
Decision making under risk
• (Probabilistic or stochastic decision situation)
• Decision maker must consider several possible outcomes for each
alternative, each with a given probability of occurrence
• Long-run probabilities of the occurrences of the given outcomes are
assumed known or can be estimated
– Decision maker can assess the degree of risk associated with each
alternative (calculated risk)
– Risk analysis
• Calculate value of each alternative
• Select best expected value
Modeling with Spreadsheets
• Flexible and easy to use
• Popular end-user modeling tool (financial , mathematical ,
statistical ,….. Functions)
• Allows linear programming and regression analysis(add-ins
solver)
• transparent data analysis tools
• Features what-if analysis, data management, macros.
• Incorporates both static and dynamic models
Modeling with Spreadsheets
Static model example
Modeling with Spreadsheets
Decision analysis of few alternatives (decision tables & decision trees)
• Decision analysis is used to model a decision situations that
have a finite number of alternatives.
• Single goal situation can be modeled with decision tables or
decision trees.
• Multiple goals can be modeled by another
techniques(described later).
Decision tables
• Example : an investment company want to investing in three alternatives :
1. Bonds,
2. Stocks,
3. Or certificates of deposit(CDs).
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Goal :maximize profit
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The yield depends on state of economy : solid growth , stagnation, or
inflation .
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If solid growth then annual yields are 12%,15%,or 6.5% for bonds,
stocks ,CDs respectively.
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If stagnation then annual yields are 6%,3%,6.5%
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for bonds ,stocks ,CDs respectively.
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If inflation then annual yields are 3%,-2%,6.5%
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for bonds ,stocks ,CDs respectively.
Decision tables
State of nature (uncontrollable variables)
Alternative
Solid growth %
Stagnation %
Inflation %
bonds
12.0
6.0
3.0
stocks
15.0
3.0
-2.0
CDs
6.5
6.5
6.5
• If a decision making problem under certainty , then we would know what the
economy will be and could easily choose the best investment
• If a decision making problem under uncertainty:
Two approaches can be used :
1. Optimistic approach : Select the best from the best (stocks)
2. Pessimistic approach: Select the best from the worst(CDs)
Decision tables
• Treating risk : with risk analysis, select the alternative with the
greatest expected value .
• If experts estimate the chance of solid growth at 50%,
stagnation at 30%,and that inflation at 20%
• Expected value of bonds =12(.5)+ 6(.3)+3(.2)=8.4%
alternative
Solid
growth
50%
Stagnation
30%
Inflation 20%
Expected
values %
bonds
12.0
6.0
3.0
8.4
stocks
15.0
3.0
-2.0
8.0
CDs
6.5
6.5
6.5
6.5
Decision tables
• This approach may sometimes be a dangerous strategy because the utility
of each potential outcome may be different from the value. Even if there is
an infinitesimals chance of catastrophic loss.
• Example: A financial advisor presents you with an “almost sure”
investment of 1,000$ that can double your money in one day (2000$),
and then the advisor says “well, there is a 0.9999 probability that you
will double your money, but unfortunately there is a 0.0001 probability
that you will be liable for $500,000 out-of-pocket loss”, the expected
value of this investment is as follows:
0.9999 * ($2000 - $1000) + 0.0001* (-$500,000 - $1000)
=
$999.90
-$50.10 = $449.80
Clearly, the potential loss could be catastrophic for any investor who is not
a billionaire. Depending on the investor’s ability to cover the loss, an
investment has different expected utilities, remember that the investor
makes the decision only once.
Decision Tree
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Graphical representation of relationships
Multiple criteria approach
Demonstrates complex relationships
Cumbersome, if many alternatives
Consult Application case 4.3: Johnson &
Johnson Decides About New Pharmaceuticals
by Using Trees.
MSS Mathematical Models
• Components of MSS mathematical models:
• Decision variables, uncontrollable variables, parameters, and
result variables
– Decision variables: describe alternative choices.
– Uncontrollable variables :are outside decision-maker’s
control.
– Fixed factors are parameters.
– Intermediate outcomes: produce intermediate result
variables.
– Result variables :are dependent on chosen solution and
uncontrollable variables.
– Reflect the effectiveness of the system.
General Structure of Quantitative Model
Intermediate
Variables
Examples of components of Models
The Structure of Quantitative Models
• Mathematical expressions (e.g., equations or inequalities)
connect the components
• Example:
• Present-value model
P = F / (1+i)n
P:present value , F: a future single payment in$, i: interest rate% ,n: no of
years
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Calculate the present value of a payment of 100.000$to be made of 5 years
from today at 10% interest rate ?
P=100.000/ (1+0.1) 5 =$62.092
Mathematical programming optimization
• Linear programming (LP) is best known technique in a family
of optimization tools called mathematical programming
• LP is used extensively in DSS.
• Mathematical Programming: is a family of tools designed to
help solve managerial problem in which the decision maker
must allocate scarce resources among activities to optimize a
measurable goal.
• Example : distribution of machine time(resource) among
various products(activities).
Linear Programming
LP characteristics:
LP assumptions
• A limited quantity of resources is
available of allocation.
• Resources used in the production
of products or services.
• There are two or more ways in
which the resources can be used.
• Each activity (product or service)
in which the resources are used
yields a return in terms of the
stated goal.
• The allocations usually restricted
by several limitations and
requirements called constraints.
• Returns from different allocations
can be compared (measured by a
common unit) (ex: dollar or utility)
• The return of any allocation is
independent of other allocations
• The total return is the sum of the
returns yielded by the different
activities.
• All data are known with certainty .
• The resources are to be used in
the most economical manner
Mathematical Programming
• LP Consists of :
1- Decision variables (whose values are known and searched for).
2- Objective function (linear mathematical function) .
3- Object functions coefficients (unit profit or cost coefficients indicating the
contribution to the objective of one unit of a decision variable)
4- Constraints (expressed in the form of linear inequalities or equalities that
limit resource and/or requirements, theses relate the variables through
linear relationships).
5- Capacities (which describe the upper and sometimes lower limits on the
constraints and variables)
5- Input/output(technology) coefficients (which indicate resource utilization
for a decision variable).
Example :
Z=4x1+5x2 where:
1x +1x <=300 and
1
2
3x1+0x2<=100
Assignment: The Product-Mix Linear Programming Model
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MBI Corporation
Decision: How many computers to build next month?
Two types of computers
Labor limit
Materials limit
Marketing lower limits
Constraint
Labor (days)
Materials $
Units
Units
Profit $
CC7
CC8
300
500
10,000 15,000
1
1
8,000
12,000
Rel
<=
<=
Limit
200,000 / mo
8,000,000/mo
>=
100
>=
200
Max
Objective: Maximize Total Profit / Month
Assignment: The Product-Mix Linear Programming Model
• solve problem by using add-in solver in Excel