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 Conceptual Model – Model Building Model Prototype – Data Gathering Runable Model -- Validation,Verification Correct Model – Solution Method Model 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” Continouos (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)

15. Examples of Models in OM 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)

16. Examples of Models 2 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)

17. Supply Chain Management 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

18. Strategic Planning More than one Criteria Even > 1 Decision Maker Many Alternatives Example: Facility Location MCDM, AHP Profitability Models (Excel)

19. Forecasting Qualitative Methods: Last Year + x% Market Survey Delphi Method Quantitative Models: Demand with Trend (+/-) Seasonal Pattern Forecasting Error MA, ES, Regression, …

20. Products & Raw Materials Product Mix Raw Material Blending Grading Raw Material Cutting Stock Packing, Loading Optimization Models (LP, IP)

21. Aggregate Planning (AP) Seasonal Peaks (forecasted) Aggregate Unit Inventory, Manpower Overtime, Shift Work Subcontract, Backlogging Spreadsheet Modeling LP, Transportation

22. Master Prod. Sched. (MPS) AP provides the framework 4 – 6 weeks Orders/Lots for Stocked Items Freezing Zone Lot Sizing IP

23. Mat. Req. Plan (MRP, JIT) Reduces Inventories Requires: Inventory Computer System Bill of Materials (BOM) “Frozen” Production Schedules Discipline Lot Sizing (IP, DP)

24. Inventory Control Based on Forecasting Minimizing Total Cost Order Quantities/Lot Sizes (Q) Reorder Point (R) Optimization

25. Cap. Req. Plan (CRP, TOC) Balancing Capacity & Flow Based on Process Analysis Find the Bottleneck (TOC) Simulation

26. Scheduling, Sequencing Keep Due Dates, Reduce Lead Time SPT, EDD, LPT, … Combinatorial Problems (nxm) Min. Setup Times (TSP) Shift Scheduling Heuristics (GA, SA, TS)

27. Process Control (SPC) Assignable vs Common Causes Measurements, samples Control Charts (XR-, c-, p-charts) Statistics

28. Distribution Max. Service, Min. Cost Dispatching Trucks (VRP, TSP) Transportation Planning Facility Location Network Models, LP, IP

29. Service Systems  Maintain Service Level  Design Specifications  Manpower Planning  Queuing Theory, Simulation

30. Reading Material 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