1. Decision Support System
Chapter 4: Modeling and Analysis

2. 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

3. Problem Identification & Env. analysis
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.

4. Variable identification
Identification of a model variable (decision, result, uncontrollable) is critical as the relationships of the variables.
Tools: influnce diagrams, cognitive maps.

5. 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]

6. 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.

7. Model categories

8. 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

9. 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

10. 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)

11. 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 Risk Ignorance, total
certainty uncertainty
decreasing knowledge

12. Decision making under 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.

13. Decision making under 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.

14. 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

15. 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

16. Modeling with Spreadsheets
Static model example

17. Modeling with Spreadsheets

18. 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).

19. Decision tables
Example : an investment company want to investing in three alternatives :
Bonds,
Stocks,
Or certificates of deposit(CDs).
Goal :maximize profit
The yield depends on state of economy : solid growth , stagnation, or inflation .
If solid growth then annual yields are 12%,15%,or 6.5% for bonds, stocks ,CDs respectively.
If stagnation then annual yields are 6%,3%,6.5%
for bonds ,stocks ,CDs respectively.
If inflation then annual yields are 3%,-2%,6.5%

20. State of nature (uncontrollable variables)
Decision tables
State of nature (uncontrollable variables)
Alternative
Solid growth %
Stagnation %
Inflation %
bonds
12.0
6.0
3.0
stocks
15.0
-2.0
CDs
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 :
Optimistic approach : Select the best from the best (stocks)
Pessimistic approach: Select the best from the worst(CDs)

21. 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
-2.0
8.0
CDs
6.5

22. 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 probability that you will double your money, but unfortunately there is a probability that you will be liable for $500,000 out-of-pocket loss”, the expected value of this investment is as follows:
* ($ $1000) * (-$500,000 - $1000)
= $ $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.

23. Decision Tree 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.

24. 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.

25. General Structure of Quantitative Model
Intermediate
Variables

26. Examples of components of Models

27. 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
Calculate the present value of a payment of $to be made of 5 years from today at 10% interest rate ?
P= / (1+0.1) 5 =$62.092

28. 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).

29. 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.
LP assumptions
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

30. 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:
1x1+1x2<=300 and
3x1+0x2<=100

31. Assignment: The Product-Mix Linear Programming Model
MBI Corporation
Decision: How many computers to build next month?
Two types of computers
Labor limit
Materials limit
Marketing lower limits Constraint CC7 CC8 Rel Limit Labor (days) <= 200,000 / mo Materials $ 10,000 15,000 <= 8,000,000/mo Units >= 100 Units >= 200 Profit $ 8,000 12,000 Max Objective: Maximize Total Profit / Month

32. Assignment: The Product-Mix Linear Programming Model
solve problem by using add-in solver in Excel