CHAPTER 5 Modeling and Analysis Good morning, everybody. Simon and I are going to introduce chapter 5, modeling and analysis. The first major components of DSS was introduced in chapter 4, the database and its management. In this chapter, we will introduce the second major component: the model base and its management.

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 Here is the outline that I’m going to introduce to you. From 5.1 opening vignette to 5.8 optimization via mathematical programming.

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

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

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) (It’s important to analyze the scope of problem domain and dynamics of the environment.) DSS can include several models, which represents a different part of the decision-making problem. Table 5.1 classifies DSS models into seven groups and list several representative techniques for each category.

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 DSS model can be classified as static or dynamic. Static models take a snapshot of a situation. During this snapshot everything occurs in a single interval.For instance, a decision on whether to or buy a product or not.

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 When we build models, any of these conditions can occur. If a decision-making problem is under certainty, we can easily choose the best solution. For uncertainty, we do not know the probabilities of events occurring in the future. More information is unavailable. For risk, sometimes the actual probabilities of events occurring in the future are known, and we have decision-making under risk. Other times, we make estimates of the risk and presume the risk situation occurs.

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) Influence diagrams appear in several formats. Bodily(1985) suggested the following conventions.

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 The tortuous arrow means uncertainty relationship. And we have to put a tilde above the risk variable’s name.

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

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 The spreadsheet is the most popular end-user modeling tool because it incorporates many powerful functions. Add-ins were developed for structuring and solving specific model classes.

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) We can do what-if analysis because it’s easy to change a cell’s value and immediately see the result. Goal seeking is performed by indicating a target cell, and a changing cell. Database management can be performed, or parts of a database can be imported for analysis. The programming productivity of building DSS can be enhanced with the use of macros. Microsoft Excel, Lotus1-2-3 Two most important popular spreadsheet package

5.6 MSS Modeling in Spreadsheets Excel spreadsheet static model example

5.6 MSS Modeling in Spreadsheets Excel spreadsheet dynamic model example

5.7 Decision Analysis of Few Alternatives (Decision Tables and Trees) Finite and not too large number of alternatives Single-goal situations Decision situations that involve a finite and not too large number of alternatives are modeled by an approach called decision analysis. The can be evaluated to select the best alternative. Single-goal situation can be modeled with decision tables or decision trees.Multiple goals can be modeled with several other technique described later.

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 An investment company is considering investing in one of three alternatives: bonds, stocks, or certificates of deposit. The company is interested in one goal: maximizing the yield on the investment after 1 year. The word stagnation means the economy is not prosperity.

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% The alternatives are the decision variables. The states of nature are uncontrollable variables. And the yield is the result variable. Decision Variables

Treating Uncertainty Optimistic approach Assume that the best 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 There are several methods of handling uncertainty. For example, the optimistic approach assumes that the best possible outcome of each alternative will occur and then selects the best of the best. The pessimistic approach assumes that the worst possible outcome for each alternative will occur and selects the best one of those.

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 The most common method for solving this risk analysis problem is to use known probabilities to compute the expected values, and then select the alternative with the largest expected value. For example, in table5.3, investing in bonds yields an expected return of 8.4%.

Decision Trees Graphically show the relationship of the problem Can handle complex situations in a compact form The word compact here means something not complicated.

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 There are many decision analysis and multicriteria decision-making software packages. Analytic Hierarchy Process is a leading one to solve multicriteria decision-making problem.

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

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

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

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 The value of decision variables are unknown and are searched for.

Lindo LP Product-Mix Model DSS 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 Input-output coefficients indicate resource utilization for a decision variable.(300,500) You can see the detail information, like solution report of this problem on page 184. Thank you for your listening. Capacities

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.

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.

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.

Heuristic Programming (4) 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.

Methodology (1) Searching Learning Evaluating Judging Knowledge

Methodology (2) Tabu search Genetic algorithms “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.

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.

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.

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

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.

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.

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.

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.

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.

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

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.

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

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

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.

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

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.

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.

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.

Visual Interactive Modeling & Visual Interactive Simulation (3) Is one of the most exciting dynamic VIMs. VIS allows the end user to watch the progress of the simulation model in a animated form. Basic philosophy of VIS is that decision makers can interact with the simulated model and watch the results develop over time.

Visual Interactive Modeling & Visual Interactive Simulation (4) VIMs and DSS VIM in DSS has used in several operations management decisions. Waiting-line management (queuing) VIM approach can be used in conjunction with artificial intelligence. General-purpose commercial dynamic VIM software is readily available.

5.13 Quantitative Software Packages - OLAP Some DSS tools offer several subroutines for constructing quantitative models. Statistics, financial analysis, accounting, and management science. In addition, many DSS tools can easily interface with powerful standard quantitative software packages.

Quantitative Software Packages Statistical packages Typical functions：mean, median, variance, standard deviation, t-test, various types of regression correlations. Excel, SPSS, Minitab, SAS. Now statistical software is considered a decision-making tool. It’s embedded in data mining and OLAP tools.

Quantitative Software Packages Management science packages There are several hundred management science packages on the market for models ranging from inventory control to project management.

Quantitative Software Packages Revenue management Involves models that attempt to stratify an organization’s customers, estimate demands, establish prices for each category of customer, and dynamically model all. Other specific DSS applications P.203

5.14 Model Base Management (1) Model base management system (MBMS) is a software package with capabilities similar to DBMS. There are no standardized MBMS： There are too many standard model classes. Each model class have several approaches for solving problems, depending on problem. Each organization uses models differently MBMS capabilities require expertise and reasoning capabilities.

Model Base Management (2) Some desirable MBMS capabilities： Control Flexibility Feedback Interface Redundancy reduction Increased consistency

Model Base Management (3) Modeling languages Some popular mathematical programming model languages include Lingo, AMPL, and GAMS. Relational model base management system Object-oriented model base and its management Models for database and MIS design and their management