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 Interests in queueing theory, optimization, scheduling, networks E2 room 559 Office hours: Tuesday 2-4

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

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?

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

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

Thousand person-years gained country No. of teams

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

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

Class Schedule LectureDateTopicReadi ng ScribeAssessment 1Thu, Sep 22 Introduction and Modeling Ch 1&2 2Tue, Sep 27 Intro to Linear Programming Ch 3, 4, 5 3Thu, Sep 29 The simplex method Ch 6Homework 1 assigned 4Tue, Oct 4 Duality and Sensitivity Analysis Ch 7 5Thu, Oct 6 Other LP Methods. Transportation, Assignment and Network Optimization Problems Ch 8 &9 6Tue, Oct 11 Unconstrained Nonlinear Optimization Homework 1 due Homework 2 assigned 7Thu, Oct 13 Nonlinear Programming Ch 12 8Tue, Oct 18 Nonlinear Programming 2

Class Schedule LectureDateTopicReadingScribeAssessment 9Thu, Oct 20 Nonlinear Programming 3 Homework 2 due Homework 3 assigned 10Tue, Oct 25 Dynamic Programming Ch 10 11Thu, Oct 27 Integer Programming Ch 11 12Tue, Nov 1 Metaheuristics Ch 13Homework 3 due. 13Thu, Nov 3 Midterm Exam 14Tue, Nov 8 Game Theory Ch 14Homework 4 assigned 15Thu, Nov 10 Decision Analysis Ch 15 16Tue, Nov 15 Markov Chains Ch 16Homework 4 due. Homework 5 assigned

Class Schedule LectureDateTopicReadingScribeAssessment 17Thu, Nov 17 Queueing Theory Ch 17 18Tue, Nov 22 Inventory theory Thu, Nov 24 No class Thanksgiving Break. Ch 18Homework 5 due 19Tue, Nov 29 Simulation Ch 20 20Thu, Dec 1 Review 8-11am, Wed Dec 7Final Exam

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. Homework35% Lecture Notes5% Midterm Exam20% Final Exam40%

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

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

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

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

Modeling and Optimization Stages 1.Define problem and gather data Feasibility check 2.Formulate mathematical model 3.Develop computer-based method for finding optimal solution Design and Software implementation 4.Test and refine model Validation 5.Prepare for ongoing model utilization Training, installation 6.Implement Maintenance, updates, reviews, documentation, dissemination

Software with Text Link to tutor and softwaretutor software