ISM 206 Optimization Theory and Applications

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ISM 206Optimization Theory and Applications

• Spring 2005
• Lecture 1 Introduction

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ISM 206 Lecture 1 Overview

• Some Optimization problem examples
• Topics in this class
• Logistics

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Names

• Kevin Ross
• Assistant Professor, Information Systems and
  Technology Management
• Interests in queueing theory, optimization,
  scheduling, networks
• E2 room 367
• Office hours Tuesday 2-4

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Problem 1 Transportation

• PT 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

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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?

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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?

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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

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Thousand person-years gained
country
No. of teams
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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

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Course Overview

• First graduate class in optimization
• Main topics
• Linear Programming
• Nonlinear programming
• Heuristic Methods
• Integer programming
• Dynamic programming
• Inventory Theory

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Class Schedule
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Class Schedule
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Class Schedule
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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.

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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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Off weeks

• Instructor away 2 weeks of this quarter
• Need to agree on time for make-up classes
• Suggestion Thursday afternoons. Time?

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My request

• Feedback!
• This class is for you

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Optimization Overview

• Variables
• Objective
• Subject to Constraints
• Sometimes additional constraints
• Binary
• Integer
• Sometimes uncertainty in parameters (stochastic
  optimization)

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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

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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

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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

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Software with Text

• Link to software