Download Model Building

Models
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Physical: Scale, Analog
Symbolic:
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Drawings
Computer Programs
Mathematical:
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Analytical (Deduction)
Experimental (Induction)
Why use Models
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Optimize or Satisfice
Prediction (Forecasting, Simulation)
Control (SPC, Sequencing SPT, EDD,..)
Insight, Understanding (the model
building process itself)
Justification, sales tool (Simulation)
Model Building
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Real World Problem – Systems Analysis
Model Prototype
– Data Gathering
Conceptual Model – Model Building
Runable Model -- Validation,Verification
Correct Model
– Solution Method
Model Solution -- Present Results
Ready Solution
– Implementation
Problem Solution
Math. Model Categories
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Prescriptive vs Descriptive
Static vs Dynamic
Continouos vs Discrete
Stochastic vs Deterministic
Linear vs Nonlinear
Prescriptive Models
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Objective Function, Goal (Max, Min)
Decision Variables (Cont., Integer)
Constraints (Feasible Solution Space)
Parameters, Coefficients (Data)
Solution Method (Analytic, Numeric)
Solution (Optimal Values of Variables)
Sensitivity Analysis
Prescriptive Model Types
 Optimization
 Mathematical Programming
 Network Models (some)
 Heuristics
 Decision Analysis Models
 Inventory Control
Example of Optimization: EOQ
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Objective: minTC(Q) = S*D/Q + H*Q/2
Variable:
Q
Constraints: Qmin < Q < Qmax
Data:
D, P, S, H, Qmin, Qmax
Solution Method: Differentiation
Solution:
EOQ = sqrt(2*D*S/H)
Sensitivity: TC(Q)/TC(EOQ)
Descriptive Model Types
 Simulation
 Queuing (Waiting Line) Theory
 Forecasting
 Some Network Models
 Game Theory
 Profitability Analysis
Simulation
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“When all else fails”!
Descriptive, “What-if”
Continuous (Predator-Prey)
Discrete:
Time-Step vs Event-Driven
Monte Carlo, Pseudo Random Numbers
Profitability Model
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Model of an Investment and Operations
during the Planning Horizon
Descriptive, Dynamic Model
Discrete Simulation
Time Step (year by year)
Usually Deterministic
Mathematical Programming
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Linear Programming (LP)
Integer Programming (IP, MIP)
Nonlinear Programming (NLP)
Dynamic Programming (DP)
Stochastic Programming (SP)
Transportation Model
Assignment Model
Network Models
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Minimal Spanning
Shortest Path
Maximal Flow
CPM/PERT (Longest Path)
Vehicle Routing Problem (VRP)
Traveling Salesman Problem (TSP)
Heuristics
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Evolutionary Search Methods:
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Genetic Algorithm (GA)
Simulated Annealing (SA)
Tabu Search (TS)
Other Heuristics
Decision Analysis Models
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Decision Trees
Newsboy Problem
Multi Criteria Decision Making
Analytic Hierarchy Process (AHP)
Goal Programming (GP)