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
Conceptual Model – Model Building
Model Prototype
– Data Gathering
Runable Model -- Validation,Verification
Correct Model
– Solution Method
Model 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”
Continouos (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)
Examples of Models in OM
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Profitability Analysis (Excel)
Product Mix (LP)
Raw Material Blending (LP)
Aggregate Production Planning (LP)
Lot Sizing (IP, DP, …)
Distribution (Transport)
Facility Location (LP, IP)
Manpower Planning (Simulation)
Examples of Models 2
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Portfolio Selection (NLP)
Investment Planning (IP)
Traffic Guidance (Shortest Route)
Dispatching of Trucks (VRP, TSP)
Communication Cables (Min. Span.)
Bottlenecks in Manuf. (Max Flow)
Container Packing (Heuristics)
Cutting Stock (Heuristics)
Supply Chain Management
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Strategic Planning
Forecasting
Aggregate Plan (AP)
Master Production Schedule (MPS)
Material Req. Planning (MRP, JIT)
Capacity Req. Planning (CRP, TOC)
Scheduling, Sequencing of jobs/lots
Process Control (SPC)
Distribution of Goods
Strategic Planning
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More than one Criteria
Even > 1 Decision Maker
Many Alternatives
Example: Facility Location
MCDM, AHP
Profitability Models (Excel)
Forecasting
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Qualitative Methods:
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Quantitative Models:
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Last Year + x%
Market Survey
Delphi Method
Demand with Trend (+/-)
Seasonal Pattern
Forecasting Error
MA, ES, Regression, …
Products & Raw Materials
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Product Mix
Raw Material Blending
Grading Raw Material
Cutting Stock
Packing, Loading
Optimization Models (LP, IP)
Aggregate Planning (AP)
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Seasonal Peaks (forecasted)
Aggregate Unit
Inventory, Manpower
Overtime, Shift Work
Subcontract, Backlogging
Spreadsheet Modeling
LP, Transportation
Master Prod. Sched. (MPS)
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AP provides the framework
4 – 6 weeks
Orders/Lots for Stocked Items
Freezing Zone
Lot Sizing
IP
Mat. Req. Plan (MRP, JIT)
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Reduces Inventories
Requires:
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Inventory Computer System
Bill of Materials (BOM)
“Frozen” Production Schedules
Discipline
Lot Sizing (IP, DP)
Inventory Control
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Based on Forecasting
Minimizing Total Cost
Order Quantities/Lot Sizes (Q)
Reorder Point (R)
Optimization
Cap. Req. Plan (CRP, TOC)
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Balancing Capacity & Flow
Based on Process Analysis
Find the Bottleneck (TOC)
Simulation
Scheduling, Sequencing
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Keep Due Dates, Reduce Lead Time
SPT, EDD, LPT, …
Combinatorial Problems (nxm)
Min. Setup Times (TSP)
Shift Scheduling
Heuristics (GA, SA, TS)
Process Control (SPC)
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Assignable vs Common Causes
Measurements, samples
Control Charts (XR-, c-, p-charts)
Statistics
Distribution
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Max. Service, Min. Cost
Dispatching Trucks (VRP, TSP)
Transportation Planning
Facility Location
Network Models, LP, IP
Service Systems
 Maintain Service Level
 Design Specifications
 Manpower Planning
 Queuing Theory, Simulation
Reading Material
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Askin & Standridge: Modeling and
Analysis of Manufacturing Systems
Hillier & Lieberman: Introduction to
Operations Research
Winston: Operations Research.
Applications and Algorithms
Law & Kelton: Simulation Modeling and
Analysis