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,..) Insight, Understanding (the model building process itself) Justification, sales tool (Simulation)

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

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

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

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

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)

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

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

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

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

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

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

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