Chapter 4: Modeling and Analysis Decision Support and Business Intelligence Systems (9th Ed., Prentice Hall) Chapter 4: Modeling and Analysis

Learning Objectives Understand the basic concepts of management support system (MSS) modeling Describe how MSS models interact with data and the users Understand the well-known model classes and 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; when to use which

Learning Objectives 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

Opening Vignette: “Model-Based Auctions Serve More Lunches in Chile” Background: problem situation Proposed solution Results Answer and discuss the case questions

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

MSS Modeling A key element in most MSS 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)…

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 MSS can include several models, each of which represents a different part of the decision-making problem Categories of models >>> Model management

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, …

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

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)

Certainty, Uncertainty and Risk

Influence Diagrams (Posted on the Course Website) 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 MSS 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)

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

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

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

Analytica Influence Diagram of a Marketing Problem: The Marketing Model

Analytica: The Price Submodel

Analytica: The Sales Submodel

MSS 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

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

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

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

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

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%

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

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

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

MSS 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

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

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

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

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) 300 500 <= 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

LP Solution

LP Solution Decision Variables: X1: unit of CC-7 X2: unit of CC-8 Objective Function: Maximize Z (profit) Z=8000X1+12000X2 Subject To 300X1 + 500X2  200K 10000X1 + 15000X2  8000K X1  100 X2  200

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

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 >>>

Heuristic Programming - SEARCH

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 5 12 6 60 9 20,160 20 1.22 1018

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

Modern Heuristic Methods Tabu search Intelligent search algorithm Genetic algorithms Survival of the fittest Simulated annealing Analogy to Thermodynamics

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

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 !

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

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

Simulation Methodology Model real system and conduct repetitive experiments. Steps: 1. Define problem 5. Conduct experiments 2. Construct simulation model 6. Evaluate results 3. Test and validate model 7. Implement solution 4. Design experiments

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 Steady State vs. Transient Simulation Simulation Implementation Visual simulation Object-oriented simulation

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

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

End of the Chapter Questions / Comments…

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