Upload
myron-knight
View
228
Download
7
Tags:
Embed Size (px)
Citation preview
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
– 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
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
• 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
• Goal seekingAsking a computer what values certain variables must have in order to attain desired goals