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CHAPTER 5

CHAPTER 5. Modeling and Analysis. 5.1 Modeling and Analysis. Opening Vignette:

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CHAPTER 5

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  1. CHAPTER 5 Modeling and Analysis

  2. 5.1 Modeling and Analysis Opening Vignette: Siemens Solar Industries (SSI), is the world’s largest-volume maker of solar electric products. SSI operates in an extremely competitive market. Before 1994, the company suffered continuous problems in photocell fabrication, including poor material flow, unbalanced resource use, bottlenecks in throughput, and schedule delay. To overcome the problems, the company decided to build a cleanroom contamination-control technology. Cleanroom are standard practice in semiconductor business, but they had never been used in the solar industry. The new technology in which there is perfect control of temperature, pressure, humidity, and air cleanliness, was All right reserved, YAO Zhong, School of E&M, BUAA

  3. 5.1 Modeling and Analysis Shown in research to improve quality considerably. In addition, productivity is improved because of fewer defects, better material flow, and reduced cycle times. Because no one in the solar industry had ever used a cleanroom, the company decided to use a simulation, which provided a virtual laboratory where the engineers could experiment with various configurations of layouts and processes before the physical systems were constructed. Changes can be made quickly and expensively in a simulated world because physical changes need not be made. The simulation model enabled the prediction of the effects of changes and what-if analyses. A major benefit of the simulation-modeling process was the knowledge and insight the company gained in understanding the interactions of the systems All right reserved, YAO Zhong, School of E&M, BUAA

  4. 5.1 Modeling and Analysis Being designed. Computer simulation allowed SSI to compare numerous alternatives quickly. The company attempted to find the best design for the cleanroom and evaluate alternatives scheduling, delivery rules, and material flow with respect to queue (waiting line) levels, throughout, cycle time, machine utilization, and work-in-progress levels. The simulation was constructed with a tool called ProModel (from ProModel Corp. Orem, UT, http://www.promodel.com). The tool allowed the company constructs simulation models easily and quickly and to conduct what-if analyses. It also included extensive graphics and animation capabilities. All right reserved, YAO Zhong, School of E&M, BUAA

  5. 5.1 Modeling and Analysis The simulation involved the entire business process, the machines, equipment, workstations, storage and handling devices, operators, and material and information flows necessary to support the process. Many scenarios were developed and experiment run. Using brainstorming, the builders came up with many innovative suggestions that were checked by the simulation. Incidentally, the company involved a group of students from California Polytechnic University in San Louis Obispo in the design and implementation of the system. The solution identified the best configurations for the cleanroom, designed schedule with minimum interruptions and bottlenecks, and improved material flow, while reducing work-in-progress inventory levels to a minimum. All right reserved, YAO Zhong, School of E&M, BUAA

  6. 5.1 Modeling and Analysis All in all, the simulation enabled the company to improve the manufacturing process of different solar products significantly. The cleanroom facility has saved SSI over $75 million each year. The simulation showed how to integrate the cleanroom with manufacturing processes in the most efficient manner. What have we learned from this vignette? • A complex decision • Simulation approach is used • Commercial software vs. self-developing • Save money All right reserved, YAO Zhong, School of E&M, BUAA

  7. 5.1 Modeling and Analysis • Model is a Major DSS component, particular in Model base-DSS and model management • CAUTION - Difficult Topic Ahead • Familiarity with major ideas • Basic concepts and definitions • Tool--influence diagram • Model directly in spreadsheets All right reserved, YAO Zhong, School of E&M, BUAA

  8. 5.1 Modeling and Analysis • Structure of some successful models and methodologies • Decision analysis • Decision trees • Optimization • Heuristic programming • Simulation • New developments in modeling tools / techniques • Important issues in model base management All right reserved, YAO Zhong, School of E&M, BUAA

  9. 5.1 Modeling and Analysis • Modeling for MSS • Static and dynamic models • Treating certainty, uncertainty, and risk • Influence diagrams • MSS modeling in spreadsheets • Decision analysis of a few alternatives (decision tables and trees) • Optimization via mathematical programming • Heuristic programming • Simulation • Multidimensional modeling -OLAP • Visual interactive modeling and visual interactive simulation • Quantitative software packages - OLAP • Model base management All right reserved, YAO Zhong, School of E&M, BUAA

  10. 5.2 Modeling for MSS • Modeling • is a Key element in most DSS : • is a Necessity in a model-based DSS • can lead to massive cost reduction / revenue increases • Good Examples of MSS Models • Siemens Solar Industries simulation model (opening vignette) • Procter & Gamble optimization supply chain restructuring models • Scott Homes AHP select a supplier model • IMERYS optimization clay production model All right reserved, YAO Zhong, School of E&M, BUAA

  11. 5.2 Modeling for MSS Major Modeling Issues • Problem identification • Environmental analysis • Variable identification • Forecasting • Multiple model use • Model categories or selection • Model management • Knowledge-based modeling We will discuss these topics in detail. All right reserved, YAO Zhong, School of E&M, BUAA

  12. 5.2 Modeling for MSS • Problem identification and Environmental analysis Environmental scanning and analysis, which is the monitoring, scanning, and interpretation of the collected information. It is often advisable to analyze the scope of the domain and the forces and dynamics of the environment. It is necessary to identify the organizational culture and the corporate decision-making process (who makes decisions, degree of centralization, and so on) • Variable identification The identification of the model’s variables (decision and other) is of utmost importance, and so are their relationships. Influence Diagrams is a useful tool. See later in section 5.5. All right reserved, YAO Zhong, School of E&M, BUAA

  13. 5.2 Modeling for MSS • Forecasting Is essential for the construction and manipulation of the models because the results of decision based on a model will usually occur in the future. • Multiple model: DSS may include several models (sometimes dozens, each of which represents different parts of the decision-making problem). • Model categories or selection (Table 5.1): Table classifies DSS models into seven groups. It also lists several representative techniques in each category and indicates where we discuss each one. Each technique may be applied to either a static or a All right reserved, YAO Zhong, School of E&M, BUAA

  14. 5.2 Modeling for MSS dynamic model, which may be constructed under assumed environments of certainty, uncertainty, or risk. To expedite model construction, one can use modeling language. • Model management: To maintain their integrity and thus their applicability, models like data, must be managed. Such management is done with the aid of model base management software. • Knowledge-based modeling: DSS uses mostly quantitative models, whereas expert systems use qualitative knowledge-based models in their application. All right reserved, YAO Zhong, School of E&M, BUAA

  15. Table 5.1 Category of models All right reserved, YAO Zhong, School of E&M, BUAA

  16. 5.3 Static and Dynamic Models • Static Analysis • Static models take a Single snapshot of a situation. During this snapshot everything occurs in a single interval. For example, a decision on whether to make or to buy a product is static in nature. A quarterly or monthly incomes statement is static, and so is the investment decision. • During a static analysis, stability of the relevant data is assumed. • Dynamic Analysis • Dynamic models are used evaluate scenarios that changed over time. E.g., a 5-year profits and loss projection in which the input data, such as costs, prices, and quantities, changed from year to year. All right reserved, YAO Zhong, School of E&M, BUAA

  17. 5.3 Static and Dynamic Models • Time dependent For example, in determining how many checkout points should be open in a supermarket, it is necessary to consider the time of day because there are changes in the number of people that arrive at different hours. • Show trends and patterns over time, also show averages per period, moving average, and comparative analysis. For example, profit this quarter against profits in the same quarter of last year. • Extend static models into dynamic nature of the problem For example, transportation model can be extended into a dynamic network flow model to accommodate inventory and backordering. All right reserved, YAO Zhong, School of E&M, BUAA

  18. 5.4 Treating Certainty, Uncertainty, and Risk We have introduced these concepts at chapter 2, here we emphasize modeling issues for each situations: • Certainty Models Easy to work with and yield a optimal solution. Many financial models are constructed under assumed certainty. • Uncertainty Managers attempt to avoid uncertainty as much as possible. However, if you are no enough information, you must treat them as an uncertain problems. • Risk Most business decisions are made under assumed risk. Several techniques can be used to deal with risk analysis. Section 5.7 will discuss in details. All right reserved, YAO Zhong, School of E&M, BUAA

  19. 5.5 Influence Diagrams • Influence Diagrams is a graphical representations of a model used to assist in model, design, development, and understanding. It can provide: • Visual communication to the model builders or development teams. • Some 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 connected with arrows; All right reserved, YAO Zhong, School of E&M, BUAA

  20. 5.5 Influence Diagrams Example, consider the following profit model: Profit = Income – Expenses Income= Units sold  Unit price Units Sold = 0.5  Amounts used in advertisement Expenses = Unit cost  Units sold + Fixed cost Then, a simple influence diagram can be drawn: All right reserved, YAO Zhong, School of E&M, BUAA

  21. 5.5 Influence Diagrams Figure 5.1 Fixed Cost Expenses Unit Cost Profit ~ Amount used in advertisement Unit sold Income Unit Price All right reserved, YAO Zhong, School of E&M, BUAA

  22. 5.5 Influence Diagrams The variables are connected with arrows, which indicate that direction of the influence. The shape of the arrows also indicates the type of relationship. For example, Expenses Amount in CDs Interest Collected Certainty Profit Unit sold Uncertainty Price Sales ~ Demand Risk Sales All right reserved, YAO Zhong, School of E&M, BUAA

  23. 5.5 Influence Diagrams • Random (risk) variable : place a tilde (~) above the variable’s name. • Preference (usually between outcome variables) : a double-line arrow  • Arrows can be one-way or two-way(bidirectional), depending on the direction of influence of a pair of variables. • Can be constructed at any degree of detail and sophistication. All right reserved, YAO Zhong, School of E&M, BUAA

  24. 5.5 Influence Diagrams • There are some software to create a Influence Diagram, such as • Analytica (Lumina Decision System, Los Altos, CA, http://www.lumina.com). Analytica supports hierarchical diagram, multidimensional arrays, integrated documentation, and parameter analysis. • DPL (from Applied Decision Analysis, Menlo Park, CA) • DS Lab (from DS Group Inc. Greenwich,CT) • INDIA (From Decision focus Inc. Palo Alto, CA, http://www.dfi.com). • Precision Tree (from Palisade Corp. Newfield, NY, http://www.palisade.com). this software can directly creates influence diagram and decision tree in the Excel spreadsheet. All right reserved, YAO Zhong, School of E&M, BUAA

  25. 5.6 MSS Modeling in Spreadsheets • Spreadsheet: most popular end-user modeling tool • Powerful functions • Add-in functions and solvers • Important for analysis, planning, modeling • Programmability (macros) • Software: • @Risk (Winston Corp) • What best! (Lindo system) • Solver (Frontline Systems Inc. Now integrated in MS Excel) • Lotus 1-2-3 (Lotus Inc.) All right reserved, YAO Zhong, School of E&M, BUAA

  26. 5.7 Decision Analysis of Few Alternatives(Decision Tables and Trees) Decision situations that involve a finite and usually not too large number of alternatives are modeled by an approach called decision analysis, in which the alternatives are listed with their forecasted contributions to the goals, and the probability of realizing such as a contribution, in a table or graph. They can be evaluated to selected the best alternative. There are two distinct cases: a single goal and multiple goals. Single-goal situations can be approached by using decision tables or decision trees. Multiple goals (criteria) can be approached by several other techniques. All right reserved, YAO Zhong, School of E&M, BUAA

  27. 5.7 Decision Analysis of Few Alternatives(Decision Tables and Trees) Decision tables are a convenient way to organize information in a systematic manner. For example, an investment company is considering investing in one of three alternatives: bonds, stocks, or certificates of deposit (CDs). they interested in one goal : maximize the yield after one year. (if it were interested in other goals such as safety or liquidity, then problem would be classified as one of multicriteria decision analysis) • Yield depends on the status of the economy (the state of nature) such as • Solid growth • Stagnation • Inflation All right reserved, YAO Zhong, School of E&M, BUAA

  28. 5.7 Decision Analysis of Few Alternatives(Decision Tables and Trees) 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% Note: investment combination must also be considered in practice. For example, 50% Stock, 50% bonds) All right reserved, YAO Zhong, School of E&M, BUAA

  29. 5.7 Decision Analysis of Few Alternatives(Decision Tables and Trees) View Problem as a Two-Person Game Investment decision-making problem may be viewed as a two-person game. The investor makes a choice (a Move) and then nature happens (make a move). The payoff is shown in a table representation that represents a mathematical model. According to our definition in Chapter 2, the table includes decision variables (alternatives), uncontrollable variables (the states of economy), and the result variables (projected yield). Note that all of the them structured in a spreadsheet. All right reserved, YAO Zhong, School of E&M, BUAA

  30. 5.7 Decision Analysis of Few Alternatives(Decision Tables and Trees) View Problem as a Two-Person Game Payoff Table 5.2 All right reserved, YAO Zhong, School of E&M, BUAA

  31. 5.7 Decision Analysis of Few Alternatives(Decision Tables and Trees) Treating Uncertainty: Several approaches can handle uncertainty. • Optimistic approach: involves considering the best possible outcome of each alternatives and selecting the best of the bests (stock). • Pessimistic approach: involves considering the worst possible outcome for each alternative and select the best one (CDs) All right reserved, YAO Zhong, School of E&M, BUAA

  32. 5.7 Decision Analysis of Few Alternatives(Treating Risk) • Use known probabilities (Table 5.3) • Risk analysis: compute expected values EV=(probabilityResults) Can be dangerous:for example, Financial advisor presents you with an “almost sure” investment of $1,000 that will double your money in one day. Then he says, “well, there is a 0.999 probability that you will double your money, but unfortunatively there is a 0.0001 probability that you would be liable for a $500,000 out-of-pocket loss”. The expected value of this investment is 0.9999($2,000-$1,000)+0.0001(-$500,000-$1,000)=$949.8 All right reserved, YAO Zhong, School of E&M, BUAA

  33. Table 5.3: Decision Under Risk and Its Solution Solid Stagnation Inflation Expected Growth Value Alternatives .5 .3 .2 Bonds 12% 6% 3% 8.4% * Stocks 15% 3% -2% 8.0% CDs 6.5% 6.5% 6.5% 6.5% All right reserved, YAO Zhong, School of E&M, BUAA

  34. Decision Trees • Other methods of treating risk • Simulation • Certainty factors • Fuzzy logic • Multiple goals AHP approach: Saaty: Analytic Hierarchy Process • Yield, safety, and liquidity (Table 5.4) All right reserved, YAO Zhong, School of E&M, BUAA

  35. Table 5.4: Multiple Goals Alternatives Yield Safety Liquidity Bonds 8.4% High High Stocks 8.0% Low High CDs 6.5% Very High High All right reserved, YAO Zhong, School of E&M, BUAA

  36. 5.8 Optimization via Mathematical Programming • Linear programming (LP) 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 All right reserved, YAO Zhong, School of E&M, BUAA

  37. LP Allocation 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 All right reserved, YAO Zhong, School of E&M, BUAA

  38. LP Allocation Model • Rational economic assumptions 1. Returns from allocations can be compared in a common unit 2. Independent returns 3. Total return is the sum of different activities’ returns 4. All data are known with certainty 5. The resources are to be used in the most economical manner • Optimal solution: the best, found algorithmically Allocation problem typically have a number of possible alternative solutions. Depending on the underlying assumptions, the number of solutions can either be infinite or finite. Of the available solutions, one (sometimes more than one) is best. In the sense that the degree of goal attainment associated with it is the highest (total reward is maximized). This is called an optimal solution, which can be found by algorithm. All right reserved, YAO Zhong, School of E&M, BUAA

  39. Linear Programming • Decision variables • Objective function • Objective function coefficients • Constraints • Capacities • Input-output (technology) coefficients All right reserved, YAO Zhong, School of E&M, BUAA

  40. Lindo LP Product-Mix ModelDSS in Focus 5.4 << 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 All right reserved, YAO Zhong, School of E&M, BUAA

  41. << Generated Solution Report >> LP OPTIMUM FOUND AT STEP 3 OBJECTIVE FUNCTION VALUE 1) 5066667.00 VARIABLE VALUE REDUCED COST X1 333.333300 .000000 X2 200.000000 .000000 All right reserved, YAO Zhong, School of E&M, BUAA

  42. ROW SLACK OR SURPLUS DUAL PRICES LABOR) .000000 26.666670 BUDGET) 1666667.000000 .000000 MARKET1) 233.333300 .000000 MARKET2) .000000 -1333.333000 NO. ITERATIONS= 3 All right reserved, YAO Zhong, School of E&M, BUAA

  43. RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 8000.000 INFINITY 799.9998 X2 12000.000 1333.333 INFINITY RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE LABOR 200000.000 50000.000 70000.000 BUDGET 8000000.000 INFINITY 1666667.000 MARKET1 100.000 233.333 INFINITY MARKET2 200.000 140.000 200.000 All right reserved, YAO Zhong, School of E&M, BUAA

  44. Lingo LP Product-Mix Model DSS in Focus 5.5 << The Model >>> MODEL: ! The Product-Mix Example; SETS: COMPUTERS /CC7, CC8/ : PROFIT, QUANTITY, MARKETLIM ; RESOURCES /LABOR, BUDGET/ : AVAILABLE ; RESBYCOMP(RESOURCES, COMPUTERS) : UNITCONSUMPTION ; ENDSETS DATA: PROFIT MARKETLIM = 8000, 100, 12000, 200; AVAILABLE = 200000, 8000000 ; All right reserved, YAO Zhong, School of E&M, BUAA

  45. UNITCONSUMPTION = 300, 500, 10000, 15000 ; ENDDATA MAX = @SUM(COMPUTERS: PROFIT * QUANTITY) ; @FOR( RESOURCES( I): @SUM( COMPUTERS( J): UNITCONSUMPTION( I,J) * QUANTITY(J)) <= AVAILABLE( I)); @FOR( COMPUTERS( J): QUANTITY(J) >= MARKETLIM( J)); ! Alternative @FOR( COMPUTERS( J): @BND(MARKETLIM(J), QUANTITY(J),1000000)); All right reserved, YAO Zhong, School of E&M, BUAA

  46. << (Partial ) Solution Report >> Global optimal solution found at step: 2 Objective value: 5066667. Variable Value Reduced Cost PROFIT( CC7) 8000.000 0.0000 PROFIT( CC8) 12000.00 0.0000 QUANTITY( CC7) 333.3333 0.0000 QUANTITY( CC8) 200.0000 0.0000 MARKETLIM( CC7) 100.0000 0.0000 MARKETLIM( CC8) 200.0000 0.0000 AVAILABLE( LABOR) 200000.0 0.0000 AVAILABLE( BUDGET) 8000000. 0.0000 All right reserved, YAO Zhong, School of E&M, BUAA

  47. UNITCONSUMPTION( LABOR, CC7) 300.00 0.00 UNITCONSUMPTION( LABOR, CC8) 500.00 0.00 UNITCONSUMPTION( BUDGET, CC7) 10000. 0.00 UNITCONSUMPTION( BUDGET, CC8) 15000. 0.00 Row Slack or Surplus Dual Price 1 5066667. 1.000000 2 0.0000000 26.66667 3 1666667. 0.0000000 4 233.3333 0.0000000 5 0.0000000 -1333.333 All right reserved, YAO Zhong, School of E&M, BUAA

  48. 5.9 Heuristic Programming • The determination of optimal solutions to some complex decision problems could involves a prohibitive amount of time and cost or may be impossible. Alternatively, the simulation approach may be lengthy, complex, and even inaccurate. In such situations, it is sometimes possible to arrive at satisfying solutions more quickly and less expensively by using heuristics. • Heuristic procedure can be described as finding rules that help to solve complex problems (or intermediate sub-problems to discover how to set up these sub-problem for final solution by finding the most promising paths in the search for solutions), finding ways to retrieve and interpret information on each experience, and then finding the methods that lead to a computational algorithm or general solution. All right reserved, YAO Zhong, School of E&M, BUAA

  49. 5.9 Heuristic Programming • Heuristic programming (definition)is the approach of using heuristics to arrive at feasible and “good enough” solutions to some complex problems. “good enough” is usually in the range of 90-99.9 percent of the objective value of an optimal solution. • Heuristics can be • Quantitative • Qualitative (in ES) All right reserved, YAO Zhong, School of E&M, BUAA

  50. 5.9 Heuristic Programming • Methodology Heuristic thinking does not necessarily proceed in a direct manner. It involves searching, learning, evaluating, judging, and then again searching, relearning, reappraisal as exploring and probing take place. The knowledge gained from success or failure at some point is feedback and modifies the search process. More often than not, it is necessary to redefine either objective or the problem, or solve related or simplified problems before the primary one can be solved. Tabu search heuristics are based on intelligent search strategies to reduce the search for high-quality solutions in computer problem solving. Essentially, the methods “remembers” what All right reserved, YAO Zhong, School of E&M, BUAA

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