CO 370 Deterministic OR Models - Lecture 1 - PowerPoint

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					    CO 370/CM 443
Deterministic Operations
   Research Models
    Chaitanya Swamy
cswamy@math.uwaterloo.ca
     Office: MC 4033
            Today’s lecture
• What is Operations Research (OR)?
  – Examples and success stories

• What you will learn in this course
  – Course outline

• Administrivia
• A little LP review + LP formulations
    What is Operations Research?
•   Enterprises typically consist of various units whose
    operations need to be coordinated
     – A typical problem: how to distribute resources across units
       so as to maximize efficiency
•   OR is the discipline of applying analytical tools based on
    mathematical models to help take better decisions in
    managing these operations (the “science of better”)
•   Typical decision-making process in OR entails:
     1.   Gathering available data                   Feedback: may
     2.   Building an abstract mathematical model    need to enhance
     3.   Solving the mathematical problem           data or model
     4.   Supplying the results to management
          A Brief History of OR
World War II led to the birth of OR
• Scientists and engineers used mathematical tools single
                                       Perhaps the to
 deploy, manage, and analyze military operations, e.g.,
                                        most important
   – deployment of the radar             catalyst in the
                                         advancement of OR
   – management of convoy and submarine operations

• Many important developments took place in this period.
 Most notably George Dantzig invented the simplex
 method for solving linear programs (LPs) in 1947
   – One of the first applications was the diet problem:
     given foods with varying nutrient amounts, plan a diet
     that satisfies the desired nutrient requirements + the
     food-amount constraints, and minimizes cost
                       Brief History (contd.)
After the War:
•   Industrial boom led to rapid increase in size of
    corporations – growing need for systematic decision-
    making tools
•   Managers began to realize both, the modeling power of
    LPs and OR tools, and their potency in improving
    efficiency even under existing technology; applications
    increased manifold
•   Serendipitously, great advances were made in
    computational technology, which allowed one to solve
    problems of ever-increasing size via OR tools
            Where is OR Today?
•   Immense computing power available readily and fairly
    cheaply, e.g., PCs
•   A half-century of research in OR has led to:
    – very good theoretical understanding
    – various software packages, e.g., CPLEX, LINDO,
      XPRESS-MP, being available that can be used “off-the
      shelf”
•   OR is everywhere – from booking an airline ticket, to
    checking into your hotel
•   By the end of this course, you will be able to solve real-
    world problems on your PC using these OR tools!
        OR in action:
Optimizing Harbor Operations
                Picture of container
                terminal Altenwerder in
                Hamburg
                One of the most modern
                terminals: handles ~ 2.4
                million containers yearly
                All internal traffic and
                storage cranes are
                automated.
        Harbor Operations (contd.)
•    Overall objective: minimize vessel waiting time
•    Containers are transported between vessels and storage area
     via automated guided vehicles (AGVs)

                                         Moehring et al. 2004
                                         give a fast algorithm
                                         based on shortest-path
                                         computations that
                                         works much better than
                                         previous adhoc methods

    Subproblem: compute AGV routes that are free of conflicts
    and jams while maximizing container throughput.
    Also routes have to be computed in real-time.
      Some other success stories
•   Continental Airlines saves ~ $40 million by using OR tools
    to near-optimally reassign crews after disruptions
•   Texas Children’s Hospital used nonlinear optimization to
    monitor healthcare contract negotiations
•   Athens Olympic Organizing Committee used logistics,
    optimization tools to manage its resources and plan the
    2004 Olympics; estimated savings: $70 million
•   Philips Semiconductors saves ~ $5 million by using
    stochastic multiperiod inventory theory to handle demand
    uncertainty
•   Many more applications on “The Science of Better”
    website on Syllabus page
Yet, it is always surprising (to me) that there are many
applications out there that are tailor-made for the use
of OR tools that are still tackled by adhoc methods.
Article in ScienceDaily titled
   “Techniques for making Barbie Dolls can Improve
                     Health Care”
talks about how OR tools will soon come to be adopted
to improve health care delivery
Researchers working on optimizing Air New Zealand’s
crew scheduling reported that “many airlines still use
heuristic or manual methods”
          What you will learn
• Mathematical Modeling
  – learn a variety of ways of modeling real-world
    problems as structured mathematical
    problems
• Solution Methods
  – learn to use powerful optimization tools to
    solve the problems arising in your
    mathematical models
              Course Outline
• Linear Optimization Models
  – Formulations, Sensitivity analysis
• Stochastic and Robust Optimization
  – Decision-making under uncertainty
• Integer Optimization
  – Formulations, Solution methods
• Network models and algorithms
  – Max-flow, min-cut, shortest paths
• Dynamic Programming
  – Formulations
                 Administrivia
•   Course webpage:
    www.student.math.uwaterloo.ca/~co370
    – Check here for announcements, assignments,
      lecture notes, important dates, …
    – Some material will be password protected
      username: co370         password:
    – Email: co370@student.math.uwaterloo.ca
•   Reading material: CO 370 course notes; highly
    recommended
•   Software: AMPL; trial version from course
    homepage; full version in MC 3006, MC 3009
                       Administrivia (contd.)
•   Grading
    –   Prerequisite-quiz: 5%
    –   Assignments: 10%        5 assignments
    –   Projects: 10%           2 projects
    –   Midterm: 30%,           Final: 45%
•   Prerequisite-quiz will test knowledge of a few
    topics from linear programming
    – will be easy – goal: recall relevant CO350 material.
    – will be held in second-week of classes – on Thursday,
      Sep. 22
    – Syllabus: simplex method and duality (without Farkas
      lemma)
                    Administrivia (contd.)
• Cheating policy
  – students caught cheating will be reported to assoc.
    dean, get no credit for that assignment/project and
    any penalty prescribed by assoc. dean
  – you may discuss the assignment with others, but must
    write up your own solutions

• Feedback, comments, suggestions, questions
 are always most welcome.
  – Come see me at MC 4033
  – Office hours: Mondays, Wednesdays 4:30-5:30pm
  – Office hours of TAs: see course website
        LP review: Definitions
Linear programming problem:
– problem of maximizing or minimizing a linear function of a
  finite number of variables
– subject to a finite number of linear constraints:
  £, ³ or = constraints

max/min       f(x) = c1x1 + c2x2 + … + cnxn
                                       £
subject to ai1x1 + ai2x2 + … + ainxn ³ bi "i=1,…,m
                                       =
Feasible point: xÎRn s.t. x satisfies all constraints
Feasible region: set of all feasible points
                 P = {xÎRn: x satisfies all constraints}
       LP review: more definitions
                                               Decision variables:
                                               should completely
Objective function
                                               describe all decisions
                                               to be made
 max/min      f(x) = c1x1 + c2x2 + … + cnxn
 subject to   a11x1 + a12x2 + … + a1nxn £ b1
              a21x1 + a22x2 + … + a2nxn ³ b2
                                                 Constraints
              a31x1 + a32x2 + … + a3nxn = b3

  Optimal solution: feasible solution with best (max/min)
  objective-function value
  Optimal value: objective-f’n. value at an optimal solution

				
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