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CHAPTER 5 Modeling and Analysis

CHAPTER 5 Modeling and Analysis. Outline. 5.1 Opening vignette 5.2 Modeling for MSS 5.3 Static and dynamic models 5.4 Treating certainty, uncertainty, and risk 5.5 Influence diagrams 5.6 MSS modeling in spreadsheets 5.7 Decision analysis of a few alternatives (decision tables and trees)

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CHAPTER 5 Modeling and Analysis

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  1. CHAPTER 5Modeling and Analysis

  2. Outline • 5.1 Opening vignette • 5.2 Modeling for MSS • 5.3 Static and dynamic models • 5.4 Treating certainty, uncertainty, and risk • 5.5 Influence diagrams • 5.6 MSS modeling in spreadsheets • 5.7 Decision analysis of a few alternatives (decision tables and trees) • 5.8 Optimization via mathematical programming

  3. 5.1 Opening Vignette (p.166) • DuPont simulates rail transportation system and avoids costly capital expense

  4. 5.2 Modeling for MSS • Key element in most DSS • Necessity in a model-based DSS • Can lead to massive cost reduction / revenue increases

  5. Major Modeling Issues • Problem identification • Environmental analysis • Variable identification • Forecasting • Multiple model use • Model categories or selection (Table 5.1) • Model management (Section 5.16) • Knowledge-based modeling (Chapter 6)

  6. 5.3 Static and Dynamic Models • Static Analysis • Single snapshot • Dynamic Analysis • Dynamic models represent scenarios that change over time • Time-dependent • Trends and patterns over time

  7. 5.4 Treating Certainty, Uncertainty, and Risk • Certainty Models • Easy to develop and solve • Yield optimal solution • Uncertainty • Information unavailable • Risk • The actual probabilities are known • Estimate the risk

  8. 5.5 Influence Diagrams • Graphical representations of a model • Visual communication • Framework for expressing MSS model relationships Rectangle = a decision variable Circle = uncontrollable or intermediate variable Oval = result (outcome) variable: intermediate or final Variables connected with arrows Example (Figure 5.1)

  9. 5.5 Influence Diagrams Considering the following profit model: Profit= income-expenses Income= units sold * unit price Units sold= 0.5*amount used in ad Expenses= unit cost * units sold+ fixed cost

  10. 5.5 Influence Diagrams • Representative software products • Analytica • DecisionPro • DATA Decision Analysis Software • Definitive Scenario • PrecisionTree

  11. 5.6 MSS Modeling in Spreadsheets • Spreadsheet: most popular end-user modeling tool • Powerful functions: financial, statistical, mathematical, and other functions • Add-in functions • Important for analysis, planning, modeling

  12. 5.6 MSS Modeling in Spreadsheets • Other important feature: • What-if analysis • Goal seeking • Data management • Programmability(macro) • Microsoft Excel & Lotus1-2-3 • Static and dynamic models can be built in a spreadsheet(Figure 5.3, Figure 5.4)

  13. 5.6 MSS Modeling in Spreadsheets • Excel spreadsheet static model example

  14. 5.6 MSS Modeling in Spreadsheets • Excel spreadsheet dynamic model example

  15. 5.7 Decision Analysis of Few Alternatives(Decision Tables and Trees) • Finite and not too large number of alternatives • Single-goal situations

  16. 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

  17. Decision Tables • 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% Decision Variables

  18. Treating Uncertainty • Optimistic approach • Assume that thebest possible outcome of each alternative will occur and then selects the best of the best • Pessimistic approach • Assume that the worst possible outcome for each alternative will occur and selects the best one of those

  19. Treating Risk • Risk analysis: Use known probabilities to compute expected values (Table 5.3) • Can be dangerous • An infinitesimal chance of a catastrophic loss may cause the expected value reasonable 12(0.5)+6(0.3)+3(0.2)=8.4

  20. Decision Trees • Graphically show the relationship of the problem • Can handle complex situations in a compact form

  21. Multiple Goals • A simplified investment case of multiple goals is shown in Table 5.4 • Multicriteria decision-making software packages- Analytic Hierarchy Process(e.g., Expert Choice software) is a leading one

  22. 5.8 Optimization via Mathematical Programming • Linear programming (LP) • Best-known technique in optimization • Used extensively in DSS • Mathematical Programming • Family of tools to solve managerial problems in allocating scarce resources among various activities to optimize a measurable goal

  23. 5.8 Optimization via Mathematical Programming • LP Allocation Problem Characteristics • Limited quantity of economic resources • Resources are used in the production of products or services • Two or more ways (solutions, programs) to use the resources • Each activity (product or service) yields a return in terms of the goal • Allocation is usually restricted by constraints

  24. LP Allocation Model • Rational economic assumptions • Returns from allocations can be compared in a common unit • Independent returns • Total return is the sum of different activities’ returns • All data are known with certainty • The resources are to be used in the most economical manner • Solutions can be infinite or finite • Optimal solution: at least one best solution, found algorithmically

  25. Linear Programming • Components of LP problem • Decision variables • Objective function • Objective function coefficients • Constrains • Capacities • Input-output coefficients • Two best known modeling system: Lindo & Lingo

  26. Lindo LP Product-Mix ModelDSS in Focus 5.4 • The product-mix model described in Chapter 2 (p.61) Objective function X1, X2: Decision variables << The Lindo Model: >> MAX 8000 X1 + 12000 X2 SUBJECT TO LABOR) 300 X1 + 500 X2 <= 200000 BUDGET) 10000 X1 + 15000 X2 <= 8000000 MARKET1) X1 >= 100 MARKET2) X2 >= 200 END Constraints Capacities

  27. 5.9 Heuristic Programming (1) • Determination of optimal solution could involve amount of time and cost in some complex decision problems. • Simulation approach may be lengthy, complex, inaccurate. • Therefore, by using heuristics we can arrive at satisfactory solutions more quickly and less expensively.

  28. Heuristic Programming (2) • Finding rules that help to solve complex problems. • Finding ways to retrieve and interpret information on each experience. • Finding methods that lead to a computational algorithm or general solution.

  29. Heuristic Programming (3) • Are used for solving ill-structured problems. • Can be used to provide satisfactory to certain complex well-structured problems • More cheaply and quickly than optimization algorithms • But only for the specific situation. • Heuristics may obtain a poor solution.

  30. Heuristic Programming (4) • Heuristic programming： • the approach of using heuristics to at feasible and “good enough” solutions to complex problems • “good enough” = 90%-99.9% of the objective value of an optimal solution. • Can be quantitative or qualitative.

  31. Methodology (1) Searching Learning Evaluating Judging Knowledge Knowledge

  32. Methodology (2) • Tabu search • “remember” high-quality and low-quality solutions. • Move toward to high-quality solutions, away from low-quality solutions. • Genetic algorithms • Start with a set of randomly solutions. • Recombine pairs of solutions to produce offspring.

  33. When to use Heuristics • Input data are inexact or limited. • Reality is so complex that optimization models can’t be used. • Exact algorithm is not available. • Can combine heuristics and optimization to improve efficiency. • Optimization or simulation are not economical, or taking an amount of time. • Symbolic processing is involved. • Quick decisions, no computerization.

  34. Advantages • Simple to understand. • Training people to be creative. • Save formulation time. • Save computer programming and storage requirement. • Save computer running time. • Produce multiple acceptable solutions. • Develop a measure of the solution quality.

  35. Limitations • Not always optimal solutions • Too many exceptions to the rules • Sequential decision choices can fail to anticipate future consequences of each choices.

  36. 5.10 Simulation • To assume the appearance of the characteristics of reality. • A technique for conducting experiments with computer on a model of a management system. • Simulation is one of the most commonly used tools of DSS.

  37. Major Characteristics • Simulation “imitates” reality. • A technique for conducting experiments • Simulation is a descriptive tool. • Simulation is used only when a problem is too complex to be treated by numerical optimization techniques.

  38. Advantages of Simulation (1) • Simulation theory is fairly straightforward. • A great amount of time compression can be attained. • Simulation is descriptive rather than normative. • An accurate simulation model requires an intimate knowledge of the problem. • The simulation model is built form the manager’s perspective and decision structure. • The simulation model is built for one particular problem.

  39. Advantages of Simulation (2) • Simulation can handle an extremely wide variety of problem types. • The manager can experiment with different variables and different alternatives. • Allows for inclusion of the real-life complexities of problem. • It’s easy to obtain a wide variety of performance measures. • The only modeling tool for DSS where problems can be non-structured.

  40. Limitations of Simulation • An optimal solution can’t be guaranteed. • Constructing a simulation model can often be a slow and costly process. • Solutions and inferences from a simulation are not transferable to other problems. • Simulation software is not so user-friendly.

  41. The Methodology of Simulation (1) Real-World problem Problem definition Construct The Simulation model Test and Validate The model Design the Simulation experiments Conduct the experiments Implement The results Evaluate The results

  42. The Methodology of Simulation (2) • Problem definition • The real-world problem is examined and classified. • Construction of the simulation model • Involves the determination of the variables and their relationships and gathering necessary data. • Testing and validating the model • The simulation model must properly represent the system.

  43. The Methodology of Simulation (3) • Design of the experiments • Two important and conflicting objectives：accuracy and cost. • Conducting the experiments • Involves issues ranging from random number generation to presentation of the results. • Evaluating the results • Determine the meaning of the results. • Implement

  44. Types of Simulation • Probabilistic simulation • One or more of the variables are probabilistic. • Discrete distribution or Continuous distribution. • Time-dependent versus Time-independent simulation • Simulation software (5.15) • Visual Simulation (5.14) • Object-Oriented Simulation

  45. 5.11 Multidimensional Modeling-OLAP • Managers need to work with three or more dimensions. • The solution is provided by multidimensional modeling tools. • Most multidimensional analysis systems are embedded in online analytical processing (OLAP) systems.

  46. OLAP • The goal of OLAP is to capture the structure of real-world data and provide support to the decision maker. • OLAP reports are interactive reports that are highly formatted, easily deployed, and effortless to use. • Figure 5.6A, 5.6B, 5.6C, 5.6D

  47. OLAP • Business intelligence tools – user simply access a data warehouse and direct the software to show the data in interesting ways and automatically build model.

  48. 5.12 Visual Interactive Modeling & Visual Interactive Simulation (1) • Conventional simulation： • Simulation does not allow decision makers to see how a solution evolves over time. • Decision makers are not an integral part of simulation development and experimentation • If the results do not match the intuition or judgment of the decision maker, a confidence gap occurs.

  49. Visual Interactive Modeling & Visual Interactive Simulation (2) • One of the most exciting developments in computer graphics is visual interactive modeling (VIM). • VIM uses computer graphic displays to present the impact of different management decisions. • VIM can represent a static or a dynamic system.

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