Models

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