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Models

Models. Physical: Scale, Analog Symbolic: Drawings Computer Programs Mathematical: Analytical (Deduction) Experimental (Induction). Why use Models. Optimize or Satisfice Prediction (Forecasting, Simulation) Control (SPC, Sequencing SPT, EDD,..)

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Models

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  1. Models • Physical: Scale, Analog • Symbolic: • Drawings • Computer Programs • Mathematical: • Analytical (Deduction) • Experimental (Induction)

  2. Why use Models • Optimize or Satisfice • Prediction (Forecasting, Simulation) • Control (SPC, Sequencing SPT, EDD,..) • Insight, Understanding (the model building process itself) • Justification, sales tool (Simulation)

  3. Model Building • 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

  4. Math. Model Categories • Prescriptive vs Descriptive • Static vs Dynamic • Continouos vs Discrete • Stochastic vs Deterministic • Linear vs Nonlinear

  5. Prescriptive Models • 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

  6. Prescriptive Model Types • Optimization • Mathematical Programming • Network Models (some) • Heuristics • Decision Analysis Models • Inventory Control

  7. Example of Optimization: EOQ • 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)

  8. Descriptive Model Types • Simulation • Queuing (Waiting Line) Theory • Forecasting • Some Network Models • Game Theory • Profitability Analysis

  9. Simulation • “When all else fails”! • Descriptive, “What-if” • Continuous (Predator-Prey) • Discrete: • Time-Step vs Event-Driven • Monte Carlo, Pseudo Random Numbers

  10. Profitability Model • Model of an Investment and Operations during the Planning Horizon • Descriptive, Dynamic Model • Discrete Simulation • Time Step (year by year) • Usually Deterministic

  11. Mathematical Programming • Linear Programming (LP) • Integer Programming (IP, MIP) • Nonlinear Programming (NLP) • Dynamic Programming (DP) • Stochastic Programming (SP) • Transportation Model • Assignment Model

  12. Network Models • Minimal Spanning • Shortest Path • Maximal Flow • CPM/PERT (Longest Path) • Vehicle Routing Problem (VRP) • Traveling Salesman Problem (TSP)

  13. Heuristics • Evolutionary Search Methods: • Genetic Algorithm (GA) • Simulated Annealing (SA) • Tabu Search (TS) • Other Heuristics

  14. Decision Analysis Models • Decision Trees • Newsboy Problem • Multi Criteria Decision Making • Analytic Hierarchy Process (AHP) • Goal Programming (GP)

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