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ISM 206 Optimization Theory and Applications

ISM 206 Optimization Theory and Applications. Fall 2005 Lecture 1: Introduction. ISM 206 Lecture 1 Overview. Some Optimization problem examples Topics in this class Logistics. Names. Kevin Ross Assistant Professor, Information Systems and Technology Management

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ISM 206 Optimization Theory and Applications

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  1. ISM 206Optimization Theory and Applications Fall 2005 Lecture 1: Introduction

  2. ISM 206 Lecture 1 Overview • Some Optimization problem examples • Topics in this class • Logistics

  3. Names Kevin Ross • Assistant Professor, Information Systems and Technology Management • Interests in queueing theory, optimization, scheduling, networks • E2 room 559 • Office hours: Tuesday 2-4

  4. Problem 1: Transportation • P&T Company makes canned peas • Peas are prepared in 3 canneries • Washington, Oregon, Minnesota • Shipped to 4 distributing warehouses • California, Utah, South Dakota, New Mexico • How much should we ship from each cannery to each warehouse? • Transportation costs are different between each pair of locations • There is a limit on capacity at each plant

  5. Problem 2: Engineering Design Problem • Consider lighting a large area with a number of lamps: • Each lamp has a total power limit • Several points in the room have a ‘desired illumination level’ How much power should be applied to each lamp to get the room as close as possible to desired level?

  6. Problem 2: Engineering Design Problem Now add two more constraints: • No more than half the total power goes to any five lamps • No more than 15 lamps are turned on What effect do (1) and (2) have on the original problem?

  7. Problem 3: Medical Team Distribution • World Health Council is devoted to improving health care in underdeveloped countries: • Need to allocate five teams to three different countries • Each team added gains more person-years of life saved in the country • You cannot assign partial teams or partial people

  8. Thousand person-years gained country No. of teams

  9. Problem 4: Inventory Levels • A wholesale Bicycle Distributor: • Purchases bikes from manufacturer and supplies to many shops • Demand to each shop is uncertain How many bikes should the distributor order from the manufacturer? • Costs: • Ordering cost to manufacturer • Holding cost in factory • Shortage cost due to lack of sales

  10. Course Overview • First graduate class in optimization • Main topics: • Linear Programming • Nonlinear programming • Heuristic Methods • Integer programming • Dynamic programming • Inventory Theory

  11. Class Schedule

  12. Class Schedule

  13. Class Schedule

  14. Assessment • Five homework sets, assigned approximately every two weeks. • Late assignments will lose 10% per day. Lecture Notes • Each lecture one student will act as a scribe for everyone. • They are responsible for typing up the lecture notes using Latex. • The notes are due 1 week after the assigned lecture. • Depending on class size, you will be assigned two or three lectures to write up. Exams • Exams will be open book and open notes. • You may bring a basic calculator but not a computer.

  15. Lecture Notes Schedule • Volunteers for today and Thursday • Each lecture one student will act as a scribe for everyone. • They are responsible for typing up the lecture notes using Latex. • The notes are due 1 week after the assigned lecture. • Schedule to be announced Thursday

  16. My request… • Feedback! • This class is for you

  17. Optimization Overview • Variables: • Objective: • Subject to Constraints: • Sometimes additional constraints: • Binary • Integer • Sometimes uncertainty in parameters (stochastic optimization)

  18. Types of Optimization Problems • Linear: Linear functions for objective and constraints • Nonlinear: Nonlinear functions… • Convex • Integer • Mixed-Integer • Combinatorial • Unconstrained: No constraints • Dynamic: Solved in stages

  19. Optimization terms and Concepts • Variable • Feasible region • Solution (feasible point) • Optimal solution (best point) • Global and local optimality • Optimality conditions • Duality • Direct methods • Numerical methods • Heuristics

  20. Modeling and Optimization Stages • Define problem and gather data • Feasibility check • Formulate mathematical model • Develop computer-based method for finding optimal solution • Design and Software implementation • Test and refine model • Validation • Prepare for ongoing model utilization • Training, installation • Implement • Maintenance, updates, reviews, documentation, dissemination

  21. Software with Text • Link to tutor and software

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