1. Modeling and Analysis
Week 8

2. Modeling and Analysis Topics
Modeling for MSS (a critical component)
Static and dynamic models
Treating certainty, uncertainty, and risk
Influence diagrams (in the posted PDF file)
MSS modeling in spreadsheets
Decision analysis of a few alternatives (with decision tables and decision trees)
Optimization via mathematical programming
Heuristic programming
Simulation
Model base management

3. DSS Modeling A key element in most DSS
Leads to reduced cost and increased revenue
DuPont Simulates Rail Transportation System and Avoids Costly Capital Expenses
Procter & Gamble uses several DSS models collectively to support strategic decisions
Locating distribution centers, assignment of DCs to warehouses/customers, forecasting demand, scheduling production per product type, etc.
Fiat, Pillowtex (…operational efficiency)…

4. P&G Used optimization models to redesign its distribution system
Several models used:
Generating model (algorithm) to estimate transportation costs
Demand forecasting model (statistics based)
Distribution center location model
Linear programming transportation model to determine best shipping
Financial and risk simulation model that also considers some qualitative factors
GIS for a user interface
Some built in the DSS some external and some accessed as needed
500 employees involved over the course of a year

5. AMR
Used models to optimize the altitude ascent and descent profile for planes
Saved millions in fuel cost per week
Part of SABRE system that used models extensively incremental revenues eventually exceeded $1 billion annually

6. Major Modeling Issues
Problem identification and environmental analysis (information collection)
Variable identification
Influence diagrams, cognitive maps
Forecasting/predicting
More information leads to better prediction
Multiple models: A DSS can include several models, each of which represents a different part of the decision-making problem
Categories of models >>>
Model management
Knowledge based modeling

7. Influence Diagrams Graphical representations of a model
“Model of a model”
A tool for visual communication
Some influence diagram packages create and solve the mathematical model
Framework for expressing DSS model relationships
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) 7

8. Influence Diagrams: Relationships
The shape of the arrow indicates the type of relationship 8

9. Influence Diagrams: Example
An influence diagram for the profit model
Profit = Income – Expense
Income = UnitsSold * UnitPrice
UnitsSold = 0.5 * Advertisement Expense
Expenses = UnitsCost * UnitSold + FixedCost 9

10. Influence Diagrams: Software
Analytica, Lumina Decision Systems
Supports hierarchical (multi-level) diagrams
DecisionPro, Vanguard Software Co.
Supports hierarchical (tree structured) diagrams
DATA Decision Analysis, TreeAge Software
Includes influence diagrams, decision trees and simulation
Definitive Scenario, Definitive Software
Integrates influence diagrams and Excel, also supports Monte Carlo simulations
PrecisionTree, Palisade Co.
Creates influence diagrams and decision trees directly in an Excel spreadsheet 10

11. Analytica Influence Diagram of a Marketing Problem: The Marketing Model11

12. Analytica: The Price Submodel12

13. Analytica: The Sales Submodel13

14. Categories of Models 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, …

15. Static and Dynamic Models
Static Analysis
Single snapshot of the situation
Single interval
Steady state
Dynamic Analysis
Dynamic models
Evaluate scenarios that change over time
Time dependent
Represents trends and patterns over time
More realistic: Extends static models

16. Mathematical Models 4 basic components
Result variables
Reflect the level of effectiveness of a system
Decision variables
Alternative courses of action
Uncontrollable variables
constraints
Intermediate result variables
Intermediate outcomes
Mathematical relationships link the components together

17. Examples of the Components of Models
Area
Decision variables
Result variables
Uncontrollable variables
Financial investment
Investment alternatives and amounts
Total profit, risk, ROI, EPS, liquidity
Inflation rate, prime rate, competition
Marketing
Ad budget, where to advertise
Market share, customer satisfaction
Customer’s income, competitor’s actions
Manufacturing
What and how much to produce, inventory levels
Total cost, quality level
Machine capacity, material prices
Accounting
Audit schedule
Error rate
Tax rates, legal requirements
Transportation
Shipments schedule, use of smart cards
Total transportation cost
Delivery distance, regulations
Services
Staffing levels
Customer satisfaction
Demand for services

18. Certainty, Uncertainty and Risk

19. Decision Making: Treating Certainty, Uncertainty and Risk
Certainty Models
Assume complete knowledge
All potential outcomes are known
May yield optimal solution
Uncertainty
Several outcomes for each decision
Probability of each outcome is unknown
Knowledge would lead to less uncertainty
Risk analysis (probabilistic decision making)
Probability of each of several outcomes occurring
Level of uncertainty => Risk (expected value)

20. DSS Modeling with Spreadsheets
Spreadsheet: most popular end-user modeling tool
Flexible and easy to use
Powerful functions
Add-in functions and solvers
Programmability (via macros)
What-if analysis
Goal seeking
Simple database management
Seamless integration of model and data
Incorporates both static and dynamic models
Examples: Microsoft Excel, Lotus 1-2-3

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

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

23. Decision Analysis: A Few Alternatives
Single Goal Situations
Decision tables
Multiple criteria decision analysis
Features include decision variables (alternatives), uncontrollable variables, result variables
Decision trees
Graphical representation of relationships
Multiple criteria approach
Demonstrates complex relationships
Cumbersome, if many alternatives exists

24. Decision Tables Investment example
One goal: maximize the yield after one year
Yield depends on the status of the economy
(the state of nature)
Solid growth
Stagnation
Inflation

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

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

27. Investment Example: Treating Uncertainty
Optimistic approach
Pessimistic approach
Treating Risk:
Use known probabilities
Risk analysis: compute expected values

28. Decision Analysis: A Few Alternatives
Other methods of treating risk
Simulation, Certainty factors, Fuzzy logic
Multiple goals
Yield, safety, and liquidity

29. DSS Mathematical Models
Non-Quantitative Models (Qualitative)
Captures symbolic relationships between decision variables, uncontrollable variables and result variables
Quantitative Models: Mathematically links decision variables, uncontrollable variables, and result variables
Decision variables describe alternative choices.
Uncontrollable variables are outside decision-maker’s control
Result variables are dependent on chosen combination of decision variables and uncontrollable variables
Independent Variables
Dependent Variables
Uncontrollable
Variables
Mathematical
Relationships
Decision
Variables
Result
Variables
Intermediate
Variables

30. 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

31. LP Problem Characteristics
1. Limited quantity of economic resources
2. Resources are used in the production of products or services
3. Two or more ways (solutions, programs) to use the resources
4. Each activity (product or service) yields a return in terms of the goal
5. Allocation is usually restricted by constraints

32. 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

33. 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

34. LP Solution

35. 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

36. 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
What-if
Assesses solutions based on changes in variables or assumptions (scenario analysis)
Goal seeking
Backwards approach, starts with goal
Determines values of inputs needed to achieve goal
Example is break-even point determination

37. Heuristic Programming
Cuts the search space
Gets satisfactory solutions more quickly and less expensively
Finds good enough feasible solutions to very complex problems
Heuristics can be
Quantitative
Qualitative (in ES)
Traveling Salesman Problem >>>

38. Heuristic Programming - SEARCH

39. Traveling Salesman Problem
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

40. When to Use Heuristics When to Use Heuristics
Inexact or limited input data
Complex reality
Reliable, exact algorithm not available
Computation time excessive
For making quick decisions
Limitations of Heuristics
Cannot guarantee an optimal solution

41. Simulation
Technique for conducting experiments with a computer on a comprehensive model of the behavior of a system
Frequently used in DSS tools

42. 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 !

43. 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

44. Limitations of Simulation
Cannot guarantee an optimal solution
Slow and costly construction process
Cannot transfer solutions and inferences to solve other problems (problem specific)
So easy to explain/sell to managers, may lead overlooking analytical solutions
Software may require special skills

45. 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

46. Simulation Types Stochastic vs. Deterministic Simulation
In stochastic simulations: We use distributions (Discrete or Continuous probability distributions)
Time-dependent vs. Time-independent Simulation
Time independent stochastic simulation via Monte Carlo technique (X = A + B)
Discrete event vs. Continuous simulation
Simulation Implementation
Visual simulation

47. 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

48. Model Base Management MBMS: capabilities similar to that of DBMS
But, there are no comprehensive model base management packages
Each organization uses models somewhat differently
There are many model classes
Within each class there are different solution approaches
Relations MBMS
Object-oriented MBMS