Chapter 4 MODELING AND ANALYSIS

Model component Data component provides input data User interface displays solution It is the model component of a DSS that actually solves the problem – it is the heart of any DSS

Modeling Steps Determine the Principle of Choice (or Result / Dependent variable) Eg. Profit Perform Environmental Scanning & Analysis to identify all Decision / independent variables For this, –one can use Influence diagrams (Cognitive modeling) –how did you model the car loan payment ? (assignment #2) Identify an existing model that relate the dependent and independent variables If needed, develop a new model from scratch –Eg. Factor analysis Multiple models: If needed divide the problem into sub- problems and fit a model for each sub-problem –Eg. Factor analysis, followed by Regression

Eg. Economy

Static, Dynamic, Multi-Dimensional Models Static models Models describing a single interval (Fig 4.2). Parameter values may be considered stable (eg. Interest rate) Dynamic models Models whose input data are changed over time. E.g., a five-year profit or loss projection; a spreadsheet model may capture inflation, business cycle of economy; see also Fig 4.3. Multidimensional models A modeling method that involves data analysis in several dimensions

Multi-dimensional modeling in Excel

Multi-dimensional view Vendor Warranty type Equipment type (ABC Hardware, Laptop, Full warranty)=1000 units

Model Categories Optimization –Algorithms (Simplex in LP) Decision Analysis – Decision-Table/Tree Simulation –Uses experimentation, random generator Predictive –Forecasting using regression, time-series analysis Heuristics –Logical deduction using if-then rules (eg. Expert Systems) –This is a qualitative model Other –What if, goal-seeking, multiple goals

Optimization Every LP problem is composed of: –Decision variables –Objective function –Constraints –Capacities

Optimization Do Exercise #7

Sensitivity analysis A study of the effect of a change in an input variable on the overall solution By studying each variable in turn, one can identify the ‘sensitive’ variables Helps evaluate robustness of decisions under changing conditions Revising models to eliminate too-large sensitivities

Matching model & decision environments Certainty A condition under which it is assumed that only one result is associated with a decision (easier to model) Uncertainty For a given decision, possible outcomes are unknown; even if known, probabilities cannot be calculated due to lack of data. (most difficult to model) Eg. Testing a new rocket / product Risk Possible outcomes are known & data is available to calculate probabilities of occurrence of each outcome for a given decision

Decision Tables under Risk/Uncertainty Choose Decision D3 since it has the largest Expected Monetary Value.

Decision Trees under risk/uncertainty

Decision trees in Excel using Precision-Tree Add-in

Simulation An imitation of reality (eg. market fluctuations) Creates random scenarios Major characteristics –Simulation is a technique for conducting experiments –Simulation is a descriptive rather than a normative/prescriptive method –Simulation is normally used only when a problem is too unstructured to be treated using numerical optimization techniques

Simulation Advantages –A great amount of time compression can be attained –Simulation can handle an extremely wide variety of problem types (eg. queuing, inventory, market returns, product demand variations) –Simulation produces many important performance measures Disadvantages –An optimal solution cannot be guaranteed –Simulation model construction can be a slow and costly process –Solutions and inferences from a simulation study are usually not transferable to other problems

Simulation

Simulation Exercise Enter this data as shown. Select cell C20. Type, =RAND(), Enter. Copy C20 all the way down to C34. Select D20. Type, VLOOKUP(C20,$C$7:$D$16,2). Copy cell D20 all the way down to D34. Select F24. Type, =Average(D20:D34). Select F25. Calculate SD.

What-if, Goal-seek, Multiple goals What-if: Similar to sensitivity analysis, but focus is on generating the revised solution when an input value is changed. Goal-seek: Calculates the value of an input necessary to achieve a desired level of output (goal). Eg. How many hours to study to get an A? Multiple goals: Finds a compromise solution. Eg. Group decision environments, usually based on utility analysis (Analytical Hierarchy Process-Chapter 10)

Goal-seek Exercise

Scenarios A statement of assumptions about the operating environment of a particular system at a given time; a narrative description of the decision-situation setting Scenarios are especially helpful in simulations and what-if analyses Possible scenarios –The worst possible scenario –The best possible scenario –The most likely scenario –The average scenario Do Exercise #8

Problem solving search methods DSS uses these in the Design & Choice phases Eg. LP Eg. Chess (large RAM) Eg. Chess Eg. Med diagnosis