ISM 206 Optimization Theory and Applications Fall 2011 Lecture 1: Introduction

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

Introductions Kevin Ross Assistant Professor, Technology and Information Management Interests in queueing theory, optimization, scheduling, networks E2 room 559 Office hours: Thursday

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

Problem 5: Digging for Oil As an oil company, you have to decide whether to drill an area or not You have some idea of how likely it is that you will find oil (say 25%) You have to pay for drilling whether it is successful or not (say $100,000) You only get the reward (say $800,000) if you actually find oil Questions: –Should you drill? –Should you pay a geologist to give you better information? –What would that information be worth to you?

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

Class Schedule LectureDateTopicAssessment 1Thu, Sep 22 Introduction and ModelingCh 1&2 2Tue, Sep 27 Intro to Linear Programming Ch 3, 4, 5 3Thu, Sep 29 The simplex methodCh 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 HW1 due HW 2 assigned 7Thu, Oct 13 Nonlinear ProgrammingCh 12

Class Schedule LectureDateTopicAssessment 8Tue, Oct 18Nonlinear Programming 2 9Thu, Oct 20Nonlinear Programming 3 10Tue, Oct 25Dynamic ProgrammingCh 10Homework 2 due Homework 3 assigned 11Thu, Oct 27Integer ProgrammingCh 11 12Tue, Nov 1Midterm ExamCh 13 13Thu, Nov 3MetaheuristicsCh 14 14Tue, Nov 8Game TheoryMidterm Exam Homework 4 assigned

Class Schedule LectureDateTopicAssessment 15Thu, Nov 10 Decision AnalysisCh 15Homework 3 due. 16Tue, Nov 15 Markov ChainsCh 16 17Thu, Nov 17 Queueing TheoryCh 17Homework 4 due. Homework 5 assigned 18Tue, Nov 22 Inventory theoryCh 18 Thu, Nov 24 NO CLASS - THANKSGIVING 19Tue, Nov 29 SimulationCh 20 20Thu, Dec 2ReviewHomework 5 due FINAL EXAM Tue, Dec 6, 8am Final Exam

Assessment Five homework sets, assigned approximately every two weeks. Late assignments will lose 10% per day. Exams Exams will be open book and open notes. You may bring a basic calculator but not a computer. Homework40% Midterm Exam20% Final Exam40%

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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 Demo of OR Tutor

Class recordings Classes are being recorded and should be available on slugtube.soe.ucsc.edu a few days after each class

Website Includes lecture notes (pdf). These will be updated after each lecture if any mistakes are found. Extra credit available for helping me to improve these notes for the class