1. Chapter 4: Modeling and Analysis
Decision Support and Business Intelligence Systems (8th Ed., Prentice Hall)
Chapter 4:
Modeling and Analysis

2. Learning Objectives
Understand the basic concepts of management support system (MSS) modeling
Describe how MSS models interact with data and the user
Understand some different, well-known model classes
Understand how to structure decision making with a few alternatives
Describe how spreadsheets can be used for MSS modeling and solution
Explain the basic concepts of optimization, simulation, and heuristics, and when to use them
Describe how to structure a linear programming model
Understand how search methods are used to solve MSS models
Explain the differences among algorithms, blind search, and heuristics
Describe how to handle multiple goals
Explain what is meant by sensitivity analysis, what-if analysis, and goal seeking
Describe the key issues of model management

3. Opening Vignette: Background: problem situation Proposed solution
Results
Answer and discuss the case questions

4. Opening Vignette: “Lessons Learned Form Modeling”
DuPont learned how different approaches to rail transportation would work out.
Procter & Gamble learned the best shipping options from product sources to distribution centers.
American Airlines learned the optimum ascent and descent profiles for its aircraft.

5. Major Modeling Issues
problem identification and environmental analysis: scanning the environment to figure out what problems exist and can be solved via a model
variable identification: identifying the critical factors in a model and their relationships
ex: Influence diagram : Graphical representations of a model
Rectangle = a decision variable
Circle = uncontrollable or intermediate variable
Oval = result (outcome) variable: intermediate or final
Variables are connected with arrows  indicates the direction of influence (relationship)

6. Major Modeling Issues forecasting: predicting the future
It is essential for construction models because when a decision implemented, the results occur in the future.
E-Commerce ( Information about purchases should be analyzed to predict demand)
5 Rights (How to get the right product(s) to the right customer at the right price at the right time in the right format
CRM and RMS rely heavily on forecasting techniques
Predict the most profitable customers
use of multiple models: combining them to solve many parts of a complex problem
Each of which represents a different part of the decision – making problem
E.g., the Procter and Gamble supply chain DSS include:
Location model to locate distribution centre , a product strategy model, a demand- forecasting model, cost generation model ,….

7. Major Modeling Issues use of multiple models
Types of models:
Standard : built in to DSS or freestanding soft ware that can interface with a DSS
Nonstandard : constructed from scratch.
model categories: selecting the right type of model for the problem or sub-problem (table 4.1)
model management: coordinating a firm’s models and their use
Models like data, must be managed to maintain their integrity and their applicability
Management is done by MBMS
knowledge-based modeling: how to take advantage of human knowledge in modeling
DSS use mostly quantitive models, wheres Expert systems use qualitiative

8. Categories of Models Table 4.1
Category
Objective
Techniques
Optimization of problems with few alternatives
Find the best solution from a small number of alternatives
Decision tables, decision trees
Optimization via algorithm
Find the best solution from a large number of alternatives using a step-by-step process
Linear and other mathematical programming models
Optimization via an analytic formula
Find the best solution in one step using a formula
Some inventory models
Simulation
Find a good enough solution by experimenting with a dynamic model of the system
Several types of simulation
Heuristics
Find a good enough solution using “common-sense” rules
Heuristic programming and expert systems
Predictive and other models
Predict future occurrences, what-if analysis, …
Forecasting, Markov chains, financial, …

9. Static and Dynamic Models
Static Analysis
Single snapshot of the situation, every thing occurs in a single interval
describes relationships among parts of a system at a point in time.
Ex: A decision about buy a product , Annual income statement.
Dynamic Analysis
Evaluate scenarios that change over time
Time dependent
Ex: In determining how many checkout points should be open in a supermarket.
A 5 year Profit and Loss projection in which input data (costs, prices, and quantities ) change from year to year

10. Excel spreadsheet - static model example: Simple loan calculation of monthly payments

11. Excel spreadsheet - Dynamic model example: Simple loan calculation of monthly payments and effects of prepayment

12. MSS Modeling with Spreadsheets
Spreadsheet: most popular end-user modeling tool
Flexible and easy to use
Powerful functions
Add-in functions and solvers (small programs designed to extend the capabilities of a spreadsheet package)
Programmability (via macros)
What-if analysis
Goal seeking
Simple database management
Incorporates both static and dynamic models
Examples: Microsoft Excel, Lotus 1-2-3

13. Types of Decision Making Environments
Decision Making under Certainty
Decision Making under Risk (Decision
making with probability)
Decision Making Under Uncertainty (Decision making without probability)

14. The Six Steps in Decision Theory
Clearly define the problem at hand
List all the possible alternatives (decisions to be made)
Identify the possible outcomes (state of nature) of each alternative
List the payoff or the profit of each combination of alternatives and outcomes
Select one of the mathematical decision theory models (e.g. Decision Making under Risk)
Apply the model and make your decision

15. Certainty, Uncertainty and Risk
The Zones of Decision Making

16. Decision Making:Treating Certainty
Certainty Models
Assume complete knowledge
All potential outcomes are known
May yield optimal solution
The decision maker knows exactly what the outcome of each course of action will be.
decision maker is to compute the optimal alternative or outcome with some optimization criterion in mind.
Ex: if the optimization criterion is least cost and you are considering two different brands of a product, which appear to be equal in value to you, one costing 20% less than the other, then, all other things being equal, you will choose the less expensive brand.
decision making under certainty is rare because all other things are rarely equal.
Linear programming is one of the techniques for finding an optimal solution under certainty

17. Decision Making: Uncertainty and Risk
Several outcomes for each decision
Probability of each outcome is unknown
Knowledge would lead to less uncertainty
Decision under uncertainty is very difficult
Managers attempt to avoid uncertainty.
Instead they attempt to obtain more information so it can be treated under certainty Or
Some estimated probabilities are assigned to the outcomes and the decision making is done as if it is decision making under risk.

18. Decision Making Under Uncertainty
Four Criteria
MAXIMAX - find the alternative that maximizes the maximum outcome for every alternative (Optimistic approach ) Ex: stocks
MAXIMIN - find the alternative that maximizes the minimum outcomes for every alternative (Pessimistic approach ) Ex : CDs
EQUALLY LIKELY- find the alternative with the highest average outcome
MINIMAX REGRET- minimizes the maximum regret (regret is the difference between the payoff from the best decision and all the other decision payoffs)

19. Decision Analysis: A Few Alternatives
Single Goal Situations
Decision tables :organize information and knowledge in a systmatic ,tabular manner to prepare it for analysis
Multiple criteria decision analysis
Features include :
Decision variables: describe alternatives course of variable),
Uncontrollable variables, Parameters : factors that effect the result variables nut not under control of decision maker
Result variables: reflect intermediate outcomes in mathematical models.

20. Decision Tables
Investment example: An investment company investing in one of the three alternatives :bonds stock or CDs
One goal: maximize the yield after one year
Yield depends on the status of the economy
(the state of nature)
Solid growth
Stagnation
Inflation

21. Investment Example: Possible Situations
1. If solid growth in the economy, bonds yield 12%; stocks 15%; CDs 6.5%
2. If stagnation, bonds yield 6%; stocks 3%; CDs 6.5%
3. If inflation, bonds yield 3%; stocks lose 2%; CDs yield 6.5%

22. Investment Example: Decision Table
Payoff Decision variables (alternatives)
Uncontrollable variables (states of economy)
Result variables (projected yield)
Tabular representation:

23. Investment Example Decision Making Under Uncertainty
MAXIMAX
State of nature
Alternative
Solid Growth
Stagnation
Inflation
Maximum
Bonds 12 6 3
Stocks 15 -2
CDs
6.5
Max

24. Investment Example Decision Making Under Uncertainty
MaxiMin
State of nature
Alternative
Solid Growth
Stagnation
Inflation
Minimum
Bonds 12 6 3
Stocks 15 -2
CDs
6.5
Max

25. Decision Making Under Uncertainty
Equally Likely
State of nature
Alternative
Solid Growth
Stagnation
Inflation
Row Avg.
Bonds 12 6 3 7
Stocks 15 -2
5.3
CDs
6.5
Highest Avg.

26. Investment Example Decision Making Under Uncertainty
The Minimax Regret
Construct a regret table :
Find the best payoff for that state of nature.
State of nature
Alternative
Solid Growth
Stagnation
Inflation
Bonds 12 6 3
Stocks 15 -2
CDs
6.5

27. Decision Making Under Uncertainty
The Minimax Regret
calculate for each state of nature the difference between each payoff and the best payoff for that state of nature.
Find the maximum regret for each alternative. Select the alternative with the minimum of these values
State of nature
Alternative
Solid Growth
Stagnation
Inflation
Maximum
Regret
Bonds 3 .5
3.5
Stocks
8.5
CDs
Min

28. Decision Making: Risk Risk analysis (probabilistic decision making)
Several outcomes for each decision
Probability of each outcome is known
Instead of optimizing the outcomes, the general rule is to optimize the expected outcome.
As an example: if you are faced with a choice between two actions one offering a 1% probability of a gain of $10000 and the other a 50% probability of a gain of $400, you as a rational decision maker will choose the second alternative.

29. Investment Example Decision Making Under Risk
Let us suppose that based on several economic forecasts, the investor is able to estimate
0.50% Solid Growth
0.30% Stagnation
0.20% Inflation
State of nature
Alternative
Solid Growth
.50%
Stagnation
.30%
Inflation
.20%
Bonds 12 6 3
Stocks 15 -2
CDs
6.5

30. Investment Example Decision Making Under Risk
Risk analysis
Compute expected values or Expected payoff (EP)
(outcome of first state of nature)*(its prob.) + (outcome of second state of nature)*(its prob.)+…+ (outcome of last state of nature) * (its prob.)
E.g. , In bonds yield = 12(.5)+6(.3)+3(.2) = 8.4 percent
The Best decision is the one with the greatest EP
If the payoffs were in terms of costs, the best decision would be the one with the lowest EP

31. Investment Example Decision Making Under Risk
Alternative approach in decision making under risk is to minimize expected opportunity loss (EOL).
Opportunity loss, also called regret
EOL for an alternative is sum of all possible regrets of alternative, each weighted by probability of state of nature for that regret occurring.
EOL (alternative i ) = (regret of first state of nature) x (probability of first state of nature) + (regret of second state of nature) x (probability of second state of nature) (regret of last state of nature) x (probability of last state of nature)

32. Investment Example Decision Making Under Risk
EOL: Opportunity loss table (=regret table)
State of nature
Alternative
Solid Growth
.50%
Stagnation
.30%
Inflation
.20%
EOL $
Bonds 3 .5
3.5
2.35
Stocks
8.5
2.75
CDs
4.25
Min

33. Investment Example Decision Making Under Risk
The Maximum Likelihood Criterion
Identify the state of nature with the largest Probability.
2. Choose the decisions alternative that has the largest Payoff
State of nature
Alternative
Solid Growth
.50%
Stagnation
.30%
Inflation
.20%
Bonds 12 6 3
Stocks 15 -2
CDs
6.5

34. Investment Example Decision Making Under Risk
Expected Value of Perfect Information (EVPI)
Is used to place an upper limit on what you should pay for information that will aid in making a better decision.
Is the increase in the EP that could be obtained if it were possible to learn the true state of nature before making the decision
Is the difference between the expected value under certainty and the expected value under risk

35. Investment Example Decision Making Under Risk
Expected Value of Perfect Information (EVPI)
EVPI = A – B
A = expected value with perfect information
B = expected value without perfect information
For A: The optimal values for each value are:
Max Value (A)= 15* * *.2 =10.75
State of nature
Alternative
Solid Growth
.50%
Stagnation
.30%
Inflation
.20%
Bonds 12 6 3
Stocks 15 -2
CDs
6.5

36. Investment Example Decision Making Under Risk
Expected Value of Perfect Information (EVPI)
B = expected value without perfect information
For B: we compute the expected values for each column first, and then select the max as below:
EVPI = = 2.55 $

37. Decision Analysis: A Few Alternatives
Multiple goals : Having multiple goals means that a decision maker hopes to obtain the best possible combination of several factors, all of which depend on the decision to be made.
Ex: Yield, safety, and liquidity

38. Decision Analysis: A Few Alternatives
Single Goal Situations
Decision trees
Graphical representation of relationships
Multiple criteria approach
Demonstrates complex relationships
Cumbersome, if many alternatives exists
How can a decision tree be used in decision making?
By showing the decision maker the possible outcomes that could result from a given choice, the tree gives the decision maker information by which to compare choices

39. Decision trees The Five Steps 1. Define the problem
2. Structure or draw the decision tree
3. Assign probabilities to the states of nature
4. Estimate the payoffs for each possible combination of alternative and state of nature  Solve the problem by computing expected payoff (EP) for each state of nature node
5. Make your decision

40. Decision Tree Example (Self Study)
This is just a beginning of ADM2302 course and Andrew does not know if he should attend all classes. He consulted some other students and came to the following conclusions:
• chances of passing a course while attending all classes are 80%
• chances of passing a course while attending randomly are 50%.
It is well known that professor who is teaching that course is giving second chance to the students who failed. They have to solve a pretty nasty case study.
Again, Andrew estimates that chances of solving this case if he would go to all the classes are 60%, while they drop to just 10% if he would attend classes randomly.
Andrew would be very happy if he passes the course (5 on a happiness scale of 0 - 5). Clearly, he would be very disappointed if he fails (0 on a happiness scale).
Going to a classroom requires an effort and diminished happiness associated with passing the course.
It goes down by 3 points (happiness scale) for attending all classes and 1 point for 39 random attendance.

42. The Structure of MSS Mathematical Models
A very simple Financial model is :
P= R – C
Where P= profit, R=revenue, and C=cost
R=unit sold X unit price
C=unit cost X unit sold + fixed cost
Present -value cash flow model Pv= ___CFn__
(1+r)n
Where CFn = Future cash flow , r= interest rate and n= # of years
The Present value of a payment of $100,000 to be made five years from today, at a 10 percent (0.1) interest rate :
Pv=100,000/(1+0.1)5

43. Optimization via Mathematical Programming
A family of tools designed to help solve managerial problems in which the decision maker must allocate scarce resources among competing activities to optimize a measurable goal
Optimal solution: The best possible solution to a modeled problem
Linear programming (LP): A mathematical model for the optimal solution of resource allocation problems. All the relationships are linear
Limited quantity of economic resources
Allocation is usually restricted by constraints

44. Linear Programming Steps
1. Identify the …
Decision variables
Objective function
Objective function coefficients
Constraints
Capacities / Demands
2. Represent the model
LINDO: Write mathematical formulation
EXCEL: Input data into specific cells in Excel
3. Run the model and observe the results
Line

45. LP Example The Product-Mix Linear Programming Model
MBI Corporation, which manufactures special-purpose computers, needs to make a decision: How many computers should it produce next month at the Boston plant?
MBI is considering two types of computers: the CC–7 which requires 300 days of labor and $10,000 in materials, and the CC–8, which requires 500 days of labor and $15,000 in materials. The profit contribution of each CC–7 is $8000 whereas that of each CC–8 is $12,000. The plant has a capacity of 200,000 working days per month, and the material budget is $8 million per month. Marketing requires that at least 100 units of the CC–7 and at least 200 units of the CC–8 be produced each month. The problem is to maximize the company's profits by determining how many units of the CC–7 and how many units of the CC–8 should be produced each month.

46. LP Example The Product-Mix Linear Programming Model MBI Corporation
Decision: How many computers to build next month?
Two types of mainframe computers: CC7 and CC8
Constraints: Labor limits, Materials limit, Marketing lower limits CC7 CC8 Rel Limit Labor (days) <= 200,000 /mo Materials ($) 10,000 15,000 <= 8,000,000 /mo Units 1 >= 100 Units 1 >= 200 Profit ($) 8,000 12,000 Max Objective: Maximize Total Profit / Month

47. LP Solution

48. LP Solution Decision Variables: X1: unit of CC-7 X2: unit of CC-8
Objective Function:
Maximize Z (profit)
Z=8000X X2
Subject To
300X X2  200K
10000X X2  8000K
X1  100
X2  200

49. Linear Programming (Self Study)
You need to buy some filing cabinets. You know that Cabinet X costs $10 per unit, requires six square feet of floor space, and holds eight cubic feet of files. Cabinet Y costs $20 per unit, requires eight square feet of floor space, and holds twelve cubic feet of files. You have been given $140 for this purchase, though you don't have to spend that much. The office has room for no more than 72 square feet of cabinets. How many of which model should you buy, in order to maximize storage volume?
Objective Function
Volume: V = 8x + 12y
Subject To
Cost: 10x + 20y < 140
Space: 6x + 8y < 72

50. Sensitivity, What-if, and Goal Seeking Analysis
Assesses impact of change in inputs on outputs
Eliminates or reduces variables
Can be automatic or trial and error
Automatic Sensitivity analysis is performed in standard quantitative model implementation such as LP
Trial and Error
Change in any variable or in several
Two approaches: What-if and Goal Seeking

51. Sensitivity, What-if, and Goal Seeking Analysis
Assesses solutions based on changes in variables or assumptions (scenario analysis)
Ex: What will happen to the total inventory cost if the cost of carrying inventories increases by 10 percent?

52. Sensitivity, What-if, and Goal Seeking Analysis
Backwards approach, starts with goal
Determines values of inputs needed to achieve goal
Ex: what annual R&D budget is needed for an annual growth rate of 15 percent by 2014?

53. Sensitivity, What-if, and Goal Seeking Analysis
Computing a Break-Even Point Using Goal Seeking
Values that generate zero profit
Break –Even= Fixed cost / (selling cost – variable cost)
Where : fixed cost =cost that not change such as tax, insurance ,..
Selling price: the price that a unit sold for
Variable cost : related to production unit.

54. Problem –Solving Search Methods
Search methods used in the choice phase of problem solving includes:
Analytical techniques , algorithms , blind searching and heuristic searching
For normative models (Comparing all the outcomes of alternative) :
analytical approach is used
For descriptive models(a comparison of a limited number of alternatives is used) :
blindly or heuristic s are used.

55. Problem –Solving Search Methods

56. Problem –Solving Search Methods
Analytical Techniques
Use mathematical formulas to derive optimal solution
Solving structured problems (tactical or operational)
Ex: inventory management, resource allocation.
Analytical Techniques may use Algorithms
Algorithms
Step by step search process
Obtaining an optimal solution
Web search engines use algorithms To speed searches and produces accurate results

57. Problem –Solving Search Methods
Blind Searching
Problem solving is done by searching through the possible solutions
The first search methods of problem solving
Arbitrary search approaches that are not guided
Two types:
A complete enumeration : all alternatives are considered to find an optimal solution.
Incomplete (Partial) : continues until a good –enough solution is found
Heuristic Searching
Informal judgmental knowledge of an application area that constitute the rules of the good judgment in the field.

58. Traveling Salesman Problem
The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization
What is it?
A traveling salesman must visit customers in several cities, visiting each city only once, across the country. Goal: Find the shortest possible route
Total number of unique routes (TNUR):
TNUR = (1/2) (Number of Cities – 1)!
Number of Cities TNUR
,160

59. Simulation
Simulation is a process of designing a model of real system a model of real system
purpose of understanding the behavior for the operation of the behavior for the operation of the system.
Frequently used in DSS tools

60. Simulation System: State: System can be Discrete
Collection of entities, ex: people machines that act and interact towards the accomplishment.
State:
Collection of variables necessary to describe a system at a particular time relative to the objective of study
Bank model: Could include number of busy tellers, time of arrival of each customer, etc
System can be
Discrete
State variables change instantaneously at separated points in time
Bank model: State changes occur only when a customer arrives or departs

61. Continuous
State variables change that continuously tracks system response over time
Airplane flight: State variables like position, velocity change continuously

62. Major Characteristics of Simulation
Imitates reality and capture its richness
Technique for conducting experiments
Descriptive, not normative tool
Often to “solve” very complex problems
Simulation is normally used only when a problem is too complex to be treated using numerical optimization techniques !

63. Advantages of Simulation
The theory is fairly straightforward
Great deal of time compression
Experiment with different alternatives
The model reflects manager’s perspective
Can handle wide variety of problem types
Can include the real complexities of problems
Produces important performance measures
Often it is the only DSS modeling tool for non-structured problems

64. Limitations of Simulation
Cannot guarantee an optimal solution
Slow and costly construction process
Cannot transfer solutions and inferences to solve other problems (problem specific)
Software may require special skills

65. Simulation Methodology
Model real system and conduct repetitive experiments.
Steps:
1. Define problem Conduct experiments
2. Construct simulation model 6. Evaluate results
3. Test and validate model 7. Implement solution
4. Design experiments

66. Visual Interactive Modeling (VIM) / Visual Interactive Simulation (VIS)
Also called
Visual interactive problem solving
Visual interactive modeling
Visual interactive simulation
Uses computer graphics to present the impact of different management decisions
Often integrated with GIS
Users perform sensitivity analysis
Static or a dynamic (animation) systems

67. End of the Chapter
Questions / Comments…

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