Chapter 4: Modeling and Analysis Decision Support and Business Intelligence Systems (8th 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 user Understand some different, well-known model classes Understand how to structure 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, and when to use them 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: Background: problem situation Proposed solution Results Answer and discuss the case questions

Opening Vignette: “Lessons Learned Form Modeling” DuPont learned how different approaches to rail transportation would work out. Procter & Gamble learned the best shipping options from product sources to distribution centers. American Airlines learned the optimum ascent and descent profiles for its aircraft.

Major Modeling Issues problem identification and environmental analysis: scanning the environment to figure out what problems exist and can be solved via a model variable identification: identifying the critical factors in a model and their relationships ex: Influence diagram : Graphical representations of a model 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)

Major Modeling Issues forecasting: predicting the future It is essential for construction models because when a decision implemented, the results occur in the future. E-Commerce ( Information about purchases should be analyzed to predict demand) 5 Rights (How to get the right product(s) to the right customer at the right price at the right time in the right format CRM and RMS rely heavily on forecasting techniques Predict the most profitable customers use of multiple models: combining them to solve many parts of a complex problem Each of which represents a different part of the decision – making problem E.g., the Procter and Gamble supply chain DSS include: Location model to locate distribution centre , a product strategy model, a demand- forecasting model, cost generation model ,….

Major Modeling Issues use of multiple models Types of models: Standard : built in to DSS or freestanding soft ware that can interface with a DSS Nonstandard : constructed from scratch. model categories: selecting the right type of model for the problem or sub-problem (table 4.1) model management: coordinating a firm’s models and their use Models like data, must be managed to maintain their integrity and their applicability Management is done by MBMS knowledge-based modeling: how to take advantage of human knowledge in modeling DSS use mostly quantitive models, wheres Expert systems use qualitiative

Categories of Models Table 4.1 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, every thing occurs in a single interval describes relationships among parts of a system at a point in time. Ex: A decision about buy a product , Annual income statement. Dynamic Analysis Evaluate scenarios that change over time Time dependent Ex: In determining how many checkout points should be open in a supermarket. A 5 year Profit and Loss projection in which input data (costs, prices, and quantities ) change from year to year

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

MSS Modeling with Spreadsheets Spreadsheet: most popular end-user modeling tool Flexible and easy to use Powerful functions Add-in functions and solvers (small programs designed to extend the capabilities of a spreadsheet package) Programmability (via macros) What-if analysis Goal seeking Simple database management Incorporates both static and dynamic models Examples: Microsoft Excel, Lotus 1-2-3

Types of Decision Making Environments Decision Making under Certainty Decision Making under Risk (Decision making with probability) Decision Making Under Uncertainty (Decision making without probability)

The Six Steps in Decision Theory Clearly define the problem at hand List all the possible alternatives (decisions to be made) Identify the possible outcomes (state of nature) of each alternative List the payoff or the profit of each combination of alternatives and outcomes Select one of the mathematical decision theory models (e.g. Decision Making under Risk) Apply the model and make your decision

Certainty, Uncertainty and Risk The Zones of Decision Making

Decision Making:Treating Certainty Certainty Models Assume complete knowledge All potential outcomes are known May yield optimal solution The decision maker knows exactly what the outcome of each course of action will be. decision maker is to compute the optimal alternative or outcome with some optimization criterion in mind. Ex: if the optimization criterion is least cost and you are considering two different brands of a product, which appear to be equal in value to you, one costing 20% less than the other, then, all other things being equal, you will choose the less expensive brand. decision making under certainty is rare because all other things are rarely equal. Linear programming is one of the techniques for finding an optimal solution under certainty

Decision Making: Uncertainty and Risk Several outcomes for each decision Probability of each outcome is unknown Knowledge would lead to less uncertainty Decision under uncertainty is very difficult Managers attempt to avoid uncertainty. Instead they attempt to obtain more information so it can be treated under certainty Or Some estimated probabilities are assigned to the outcomes and the decision making is done as if it is decision making under risk.

Decision Making Under Uncertainty Four Criteria MAXIMAX - find the alternative that maximizes the maximum outcome for every alternative (Optimistic approach ) Ex: stocks MAXIMIN - find the alternative that maximizes the minimum outcomes for every alternative (Pessimistic approach ) Ex : CDs EQUALLY LIKELY- find the alternative with the highest average outcome MINIMAX REGRET- minimizes the maximum regret (regret is the difference between the payoff from the best decision and all the other decision payoffs)

Decision Analysis: A Few Alternatives Single Goal Situations Decision tables :organize information and knowledge in a systmatic ,tabular manner to prepare it for analysis Multiple criteria decision analysis Features include : Decision variables: describe alternatives course of variable), Uncontrollable variables, Parameters : factors that effect the result variables nut not under control of decision maker Result variables: reflect intermediate outcomes in mathematical models.

Decision Tables Investment example: An investment company investing in one of the three alternatives :bonds stock or CDs 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%; CDs 6.5% 2. If stagnation, bonds yield 6%; stocks 3%; CDs 6.5% 3. If inflation, bonds yield 3%; stocks lose 2%; CDs yield 6.5%

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

Investment Example Decision Making Under Uncertainty MAXIMAX State of nature Alternative Solid Growth Stagnation Inflation Maximum Bonds 12 6 3 Stocks 15 -2 CDs 6.5 Max

Investment Example Decision Making Under Uncertainty MaxiMin State of nature Alternative Solid Growth Stagnation Inflation Minimum Bonds 12 6 3 Stocks 15 -2 CDs 6.5 Max

Decision Making Under Uncertainty Equally Likely State of nature Alternative Solid Growth Stagnation Inflation Row Avg. Bonds 12 6 3 7 Stocks 15 -2 5.3 CDs 6.5 Highest Avg.

Investment Example Decision Making Under Uncertainty The Minimax Regret Construct a regret table : Find the best payoff for that state of nature. State of nature Alternative Solid Growth Stagnation Inflation Bonds 12 6 3 Stocks 15 -2 CDs 6.5

Decision Making Under Uncertainty The Minimax Regret calculate for each state of nature the difference between each payoff and the best payoff for that state of nature. Find the maximum regret for each alternative. Select the alternative with the minimum of these values State of nature Alternative Solid Growth Stagnation Inflation Maximum Regret Bonds 3 .5 3.5 Stocks 8.5 CDs Min

Decision Making: Risk Risk analysis (probabilistic decision making) Several outcomes for each decision Probability of each outcome is known Instead of optimizing the outcomes, the general rule is to optimize the expected outcome. As an example: if you are faced with a choice between two actions one offering a 1% probability of a gain of $10000 and the other a 50% probability of a gain of $400, you as a rational decision maker will choose the second alternative.

Investment Example Decision Making Under Risk Let us suppose that based on several economic forecasts, the investor is able to estimate 0.50% Solid Growth 0.30% Stagnation 0.20% Inflation State of nature Alternative Solid Growth .50% Stagnation .30% Inflation .20% Bonds 12 6 3 Stocks 15 -2 CDs 6.5

Investment Example Decision Making Under Risk Risk analysis Compute expected values or Expected payoff (EP) (outcome of first state of nature)*(its prob.) + (outcome of second state of nature)*(its prob.)+…+ (outcome of last state of nature) * (its prob.) E.g. , In bonds yield = 12(.5)+6(.3)+3(.2) = 8.4 percent The Best decision is the one with the greatest EP If the payoffs were in terms of costs, the best decision would be the one with the lowest EP

Investment Example Decision Making Under Risk Alternative approach in decision making under risk is to minimize expected opportunity loss (EOL). Opportunity loss, also called regret EOL for an alternative is sum of all possible regrets of alternative, each weighted by probability of state of nature for that regret occurring. EOL (alternative i ) = (regret of first state of nature) x (probability of first state of nature) + (regret of second state of nature) x (probability of second state of nature) + . . . + (regret of last state of nature) x (probability of last state of nature)

Investment Example Decision Making Under Risk EOL: Opportunity loss table (=regret table) State of nature Alternative Solid Growth .50% Stagnation .30% Inflation .20% EOL $ Bonds 3 .5 3.5 2.35 Stocks 8.5 2.75 CDs 4.25 Min

Investment Example Decision Making Under Risk The Maximum Likelihood Criterion Identify the state of nature with the largest Probability. 2. Choose the decisions alternative that has the largest Payoff State of nature Alternative Solid Growth .50% Stagnation .30% Inflation .20% Bonds 12 6 3 Stocks 15 -2 CDs 6.5

Investment Example Decision Making Under Risk Expected Value of Perfect Information (EVPI) Is used to place an upper limit on what you should pay for information that will aid in making a better decision. Is the increase in the EP that could be obtained if it were possible to learn the true state of nature before making the decision Is the difference between the expected value under certainty and the expected value under risk

Investment Example Decision Making Under Risk Expected Value of Perfect Information (EVPI) EVPI = A – B A = expected value with perfect information B = expected value without perfect information For A: The optimal values for each value are: Max Value (A)= 15*.5 +6.5*.3 +6.5*.2 =10.75 State of nature Alternative Solid Growth .50% Stagnation .30% Inflation .20% Bonds 12 6 3 Stocks 15 -2 CDs 6.5

Investment Example Decision Making Under Risk Expected Value of Perfect Information (EVPI) B = expected value without perfect information For B: we compute the expected values for each column first, and then select the max as below: EVPI = 10.75-8.4 = 2.55 $

Decision Analysis: A Few Alternatives Multiple goals : Having multiple goals means that a decision maker hopes to obtain the best possible combination of several factors, all of which depend on the decision to be made. Ex: Yield, safety, and liquidity

Decision Analysis: A Few Alternatives Single Goal Situations Decision trees Graphical representation of relationships Multiple criteria approach Demonstrates complex relationships Cumbersome, if many alternatives exists How can a decision tree be used in decision making? By showing the decision maker the possible outcomes that could result from a given choice, the tree gives the decision maker information by which to compare choices

Decision trees The Five Steps 1. Define the problem 2. Structure or draw the decision tree 3. Assign probabilities to the states of nature 4. Estimate the payoffs for each possible combination of alternative and state of nature  Solve the problem by computing expected payoff (EP) for each state of nature node 5. Make your decision

Decision Tree Example (Self Study) This is just a beginning of ADM2302 course and Andrew does not know if he should attend all classes. He consulted some other students and came to the following conclusions: • chances of passing a course while attending all classes are 80% • chances of passing a course while attending randomly are 50%. It is well known that professor who is teaching that course is giving second chance to the students who failed. They have to solve a pretty nasty case study. Again, Andrew estimates that chances of solving this case if he would go to all the classes are 60%, while they drop to just 10% if he would attend classes randomly. Andrew would be very happy if he passes the course (5 on a happiness scale of 0 - 5). Clearly, he would be very disappointed if he fails (0 on a happiness scale). Going to a classroom requires an effort and diminished happiness associated with passing the course. It goes down by 3 points (happiness scale) for attending all classes and 1 point for 39 random attendance.

The Structure of MSS Mathematical Models A very simple Financial model is : P= R – C Where P= profit, R=revenue, and C=cost R=unit sold X unit price C=unit cost X unit sold + fixed cost Present -value cash flow model Pv= ___CFn__ (1+r)n Where CFn = Future cash flow , r= interest rate and n= # of years The Present value of a payment of $100,000 to be made five years from today, at a 10 percent (0.1) interest rate : Pv=100,000/(1+0.1)5

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 Limited quantity of economic resources 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, which manufactures special-purpose computers, needs to make a decision: How many computers should it produce next month at the Boston plant? MBI is considering two types of computers: the CC–7 which requires 300 days of labor and $10,000 in materials, and the CC–8, which requires 500 days of labor and $15,000 in materials. The profit contribution of each CC–7 is $8000 whereas that of each CC–8 is $12,000. The plant has a capacity of 200,000 working days per month, and the material budget is $8 million per month. Marketing requires that at least 100 units of the CC–7 and at least 200 units of the CC–8 be produced each month. The problem is to maximize the company's profits by determining how many units of the CC–7 and how many units of the CC–8 should be produced each month.

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

Linear Programming (Self Study) You need to buy some filing cabinets. You know that Cabinet X costs $10 per unit, requires six square feet of floor space, and holds eight cubic feet of files. Cabinet Y costs $20 per unit, requires eight square feet of floor space, and holds twelve cubic feet of files. You have been given $140 for this purchase, though you don't have to spend that much. The office has room for no more than 72 square feet of cabinets. How many of which model should you buy, in order to maximize storage volume? Objective Function Volume: V = 8x + 12y Subject To Cost: 10x + 20y < 140 Space: 6x + 8y < 72

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 Automatic Sensitivity analysis is performed in standard quantitative model implementation such as LP Trial and Error Change in any variable or in several Two approaches: What-if and Goal Seeking

Sensitivity, What-if, and Goal Seeking Analysis Assesses solutions based on changes in variables or assumptions (scenario analysis) Ex: What will happen to the total inventory cost if the cost of carrying inventories increases by 10 percent?

Sensitivity, What-if, and Goal Seeking Analysis Backwards approach, starts with goal Determines values of inputs needed to achieve goal Ex: what annual R&D budget is needed for an annual growth rate of 15 percent by 2014?

Sensitivity, What-if, and Goal Seeking Analysis Computing a Break-Even Point Using Goal Seeking Values that generate zero profit Break –Even= Fixed cost / (selling cost – variable cost) Where : fixed cost =cost that not change such as tax, insurance ,.. Selling price: the price that a unit sold for Variable cost : related to production unit.

Problem –Solving Search Methods Search methods used in the choice phase of problem solving includes: Analytical techniques , algorithms , blind searching and heuristic searching For normative models (Comparing all the outcomes of alternative) : analytical approach is used For descriptive models(a comparison of a limited number of alternatives is used) : blindly or heuristic s are used.

Problem –Solving Search Methods

Problem –Solving Search Methods Analytical Techniques Use mathematical formulas to derive optimal solution Solving structured problems (tactical or operational) Ex: inventory management, resource allocation. Analytical Techniques may use Algorithms Algorithms Step by step search process Obtaining an optimal solution Web search engines use algorithms To speed searches and produces accurate results

Problem –Solving Search Methods Blind Searching Problem solving is done by searching through the possible solutions The first search methods of problem solving Arbitrary search approaches that are not guided Two types: A complete enumeration : all alternatives are considered to find an optimal solution. Incomplete (Partial) : continues until a good –enough solution is found Heuristic Searching Informal judgmental knowledge of an application area that constitute the rules of the good judgment in the field.

Traveling Salesman Problem The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization 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

Simulation Simulation is a process of designing a model of real system a model of real system purpose of understanding the behavior for the operation of the behavior for the operation of the system. Frequently used in DSS tools

Simulation System: State: System can be Discrete Collection of entities, ex: people machines that act and interact towards the accomplishment. State: Collection of variables necessary to describe a system at a particular time relative to the objective of study Bank model: Could include number of busy tellers, time of arrival of each customer, etc System can be Discrete State variables change instantaneously at separated points in time Bank model: State changes occur only when a customer arrives or departs

Continuous State variables change that continuously tracks system response over time Airplane flight: State variables like position, velocity change continuously

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) 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

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

End of the Chapter Questions / Comments…

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