Modeling

Models

• Iconic model (scale models)― The least abstract type of model― physical replica of a system Ex: scale model of F16

Models

• Analog model– An abstract, symbolic model of a system that

behaves like the system but looks different– More abstract than iconic models.

Ex: blueprint of a house or machine.

Models

• Mental model– The mechanisms or images through which a

human mind performs sense-making in decision making.

– Used when there are qualitative factors.– ex: when airplane pilots consider whether to fly.

• Mathematical (quantitative) modelA system of symbols and expressions that represent a real situation

Models

• The benefits of models – Model manipulation is much easier than

manipulating a real system – Models enable the compression of time – The cost of modeling analysis is much lower – The cost of making mistakes during a trial-and-

error experiment is much lower when models are used than with real systems

Models

The benefits of models (cont.)

– With modeling, a manager can estimate the risks resulting from specific actions within the uncertainty of the business environment

– Mathematical models enable the analysis of a very large number of possible solutions

– Models enhance and reinforce learning and training – Models and solution methods are readily available on

the Web

DSS Modeling

• Current trends– Multidimensional analysis (modeling)

A modeling method that involves data analysis in several dimensions

– Influence diagramA diagram that shows the various types of variables in a problem (e.g., decision, independent, result) and how they are related to each other

Static and Dynamic Models

• Static modelsModels that describe a single interval of a situation

• Dynamic modelsModels whose input data are changed over time (e.g., a five-year profit or loss projection)

MSS Modeling with Spreadsheets

• Models can be developed and implemented in a variety of programming languages and systems

• The spreadsheet is clearly the most popular end-user modeling tool because it incorporates many powerful financial, statistical, mathematical, and other functions

MSS Modeling with Spreadsheets

MSS Modeling with Spreadsheets

– Other important spreadsheet features include what-if analysis, goal seeking, trial and error, optimization , data management, and programmability

– Most spreadsheet packages provide fairly seamless integration because they read and write common file structures and easily interface with databases and other tools

– Static or dynamic models can be built in a spreadsheet

MSS Modeling with Spreadsheets

Optimization via Mathematical Programming

• 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

LP Problem Characteristics

1. Limited quantity of economic resources2. Resources are used in the production of products or

services3. Two or more ways (solutions, programs) to use the

resources4. Each activity (product or service) yields a return in

terms of the goal5. Allocation is usually restricted by constraints

LineLine

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

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 LimitLabor (days) 300 500 <= 200,000 /moMaterials ($) 10,000 15,000 <= 8,000,000 /moUnits 1 >= 100Units 1 >= 200Profit ($) 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 To300X1 + 500X2 200K

10000X1 + 15000X2 8000K

X1 100

X2 200

Sensitivity, What-if, and Goal Seeking Analysis

• Sensitivity– Assesses impact of change in inputs on outputs– Eliminates or reduces variables– Can be automatic or trial and error

• What-if– Assesses solutions based on changes in variables or

assumptions (scenario analysis)• Goal seeking– Backwards approach, starts with goal– Determines values of inputs needed to achieve goal– Example is break-even point determination

Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

– Sensitivity analysis tests relationships such as: • The impact of changes in external (uncontrollable)

variables and parameters on the outcome variable(s)• The impact of changes in decision variables on the

outcome variable(s)• The effect of uncertainty in estimating external

variables• The effects of different dependent interactions among

variables• The robustness of decisions under changing conditions

Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

– Sensitivity analyses are used for:• Revising models to eliminate too-large sensitivities• Adding details about sensitive variables or scenarios• Obtaining better estimates of sensitive external variables• Altering a real-world system to reduce actual sensitivities• Accepting and using the sensitive (and hence vulnerable)

real world, leading to the continuous and close monitoring of actual results

– The two types of sensitivity analyses are automatic and trial-and-error

Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

• Automatic sensitivity analysis – Automatic sensitivity analysis is performed in

standard quantitative model implementations such as LP (Linear Programming)

• Trial-and-error sensitivity analysis – The impact of changes in any variable, or in several

variables, can be determined through a simple trial-and-error approach

Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

• What-If Analysis A process that involves asking a computer what the effect of changing some of the input data or parameters would be

Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

• Goal seekingAsking a computer what values certain variables must have in order to attain desired goals

Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking

• Computing a break-even point by using goal seeking – Involves determining the value of the decision

variables that generate zero profit