

				620-361 Operations Research Techniques and Algorithms Semester 1, 2002

Subject Coordinator: Dr Natashia Boland, Room 148 Richard Berry Building, 8344-5547

Class SSLC Representative: Daniella Barros, dabarr@ecr.mu.oz.au - thank you Daniella for a great job!

GOOD LUCK TO YOU ALL IN THE EXAM!!!!

View the exam cover page.

PAST EXAMS

The 2000 and 2001 exam are duplicated at the back of the Notes. Solutions to the 2000 exam were worked through in Monday and Tuesday practice classes. In Wednesday 5th June practice classes, solutions to the 2001 exam question 7, the 1999 exam questions 5, 6, 7 and 1, and Exercise 2 from Chance-Constrained Optimization were worked through. Please note that the last five slides got shuffled in scanning, so you should read them in order 1,..,10,11, 14, 13, 12, 15.

1999 exam - note the last part of question 3(ii) regarding the BFGS method is not relevant, and in questions 7(ii) and 7(iii), you can replace "Wolfe dual" with "Lagrangian dual". Also note that for question 3(ii) you should assume that the Hessian matrix of the function at the point x^0 is positive definite.

All past exams from 1996 onwards are available on closed reserve in the Maths Sciences library - just ask at the desk. Relevant subject code and exam questions for years 1996-1998 are as follows. Papers are also available on the web from the Buddy Science site. Just follow the link to Exam Papers. (Note that for some reason I can't find the 620-361 papers before 1999 at this site - but they are definitely in the Maths Sciences library. You might find this site useful for other subjects.)
1998 exam - all questions except 7 and 3(c) are relevant, for 6(ii), replace "(Wolfe)" with "(Lagrangian)"
1997 exam - code 618-361, question 3, 4, 5 and 6 are relevant
1996 exam - code 618-362, questions 1, 2 and 3 are relevant

All project teams need to submit a Team Feedback Form. If your team cannot agree on the split of marks, each team member must fill out and submit privately an Individual Feedback Form. If your team has forgotten to do this, and getting together is difficult, then I will accept the same information by email, or by separate forms, but I must receive something from every team member. Please note that a plagiarism sheet must be signed for the project reports, by every person. Team members can sign together on a single sheet, or hand them in separately, whichever is more convenient.

Project marks are now available. Detailed feedback on project reports will be emailed to all team members, where email addresses are available. Feedback from official markers on final talks can be collected from Natashia.

Solutions to Assignment 1 are now available, as are marks.

Solutions to Assignment 2 are now available, as are marks.

Solutions to Assignment 3 are now available, as are marks.

Tips for report writing now available - workshop on Business Writing in practice class on Tuesday 7th May included more materials - get the handout!

View errata in notes - list updated as errors found.

View the first quick quiz questions and answers.

Download the week-by-week subject breakdown and assessment plan here.

Download tips for presentations here.

Practice Class 1: exercises on background mathematics

Practice Class 2: teams worked on projects, some exercises on background mathematics set

Practice Class 3: did exercises on background mathematics set in Prac Class 2

Practice Class 4: assorted exercises on unconstrained optimization

Lecture 8th April: introduction to KKT conditions

Practice Class 5: exercises on KKT conditions

Lecture 12th April: example of second order sufficiency condition. Important note: before concluding that a KKT point for which a second order sufficiency condition holds yields a local minimum of the NLP, you need to check that a constraint qualification (CQ) holds at the stationary point, since this is a condition of Theorem 9. In this example, the CQ is easily shown to hold, and the conclusion given follows; as an exersise you should check a CQ does indeed hold.

Lecture 15th April: examples penalty functions and proof of differentiability of l2 penalty function.

Practice Class 6: exercises on second order sufficiency conditions for NLP

Practice Class 8: Exercise 51 on SPLPT

Lecture 13th May: Exercise on inventory proving solution in case of uniform replenishment with limited capacity is optimal

Extension to Theorem 13 for use in inventory.

Lecture 17th May: Extra examples on Lagrangian duality and convex NLPs.

Lecture 22th May: Extra examples on Lagrangian duality, SPLPT and SQP methods.

All work submitted for assessment must now have the plagiarism cover sheet attached. Please make sure you also write your student number on the assignment itself, as cover sheets are detached from the assignment after submission.

Lectures and Practice Classes

All classes are in the Richard Berry Building.

Monday	3:15pm-4:15pm	Lecture	Russell Love Theatre
Tuesday	2:15pm-3:15pm	Practice Class	Classroom 213
Wednesday	3:15pm-4:15pm	Lecture	Russell Love Theatre
Friday	3:15pm-4:15pm	Lecture	Russell Love Theatre

Practice classes will usually be unstructured, providing opportunities for project teams to meet. They will also be times that individuals can work on exercises and get help from the lecturer. On occasion, they may be used for some project team presentations, or other scheduled activity. Most classes will be held in Classroom 213, but on occasion may be held in the Small iMac Lab.

SWOTVAC Office Hours: Monday 3rd 1:30-2:30pm, Wednesday 5th 12-1pm and 3-4pm.

SWOTVAC Practice Classes: Monday 3rd 12-1pm and 2:30-3:30pm, Tuesday 4th 12-1pm, Wednesday 5th 10-11am and 2-3pm. All classes will be in the Russell Love Theatre.

Assessment:

65% Exam (3 hours)

24% Group project

11% Assignments

There will be 3 assignments spread evenly across the subject material. They will be due in approximately Weeks 5, 8 and 11 of semester.

All assignments are to be entirely individual work: no collaboration, consultation or discussion of assignment questions with others is permitted. For clarification of assignment questions, see the lecturer.

Group Projects

Assessment of group projects totals 24%:

3% Introductory talk (5 minutes, in Week 3).

6% Final talk (10-15 minutes, in Week 12), a typeset presentation of transparencies or electronic slides is required.

15% Written report (due Week 12).

The first Wednesday class will be used to select projects and team members (teams should be preferably of size 4). If you cannot attend the class, 3:15pm, Wednesday March 6th, please speak to Natashia Boland.

The third Monday class, on March 18th, will include 5 minute talks, introducing projects, by group representatives. If needed, additional presentations will be made in the practice class on Tuesday March 19th. A role will be taken at all project presentation occasions, and any student not participating sufficiently in project activities, which includes attending presentations, risks having project marks deducted.

All classes in Week 12 will be used for final project presentations.

Subject Description

This subject develops problem-solving skills and sharpens analytical skills. You will work in groups, tackling unfamiliar problems, based on real business and industry case studies. Each team will plan their project work and deliver both oral and written presentations.

This subject introduces a number of basic techniques of operations research. It develops the formulation of operations research models and algorithms with application in production planning, scheduling, inventory management and capital budgeting. You should develop skills in setting up and analysing operations research models for a number of planning problems; and competence in the use of computer packages for the solution of operations research problems. This subject demonstrates the factors and restrictions involved in building and using models for planning and management problems.

Topics are selected from operations research models; formulation of planning and management problems, including linear programming models, scheduling models, inventory management, capital budgeting, and chance-constrained optimisation; and linear and nonlinear techniques, decision tree models, parametric optimisation, simulation. Use of computer packages and internet resources is examined.

In addition to learning specific technical skills that will assist you in your future careers in science, engineering, commerce, education or elsewhere, you will have the opportunity to develop in this subject generic skills that will assist you whatever your future career path.

· Through practice exercises, assignments and in particular through project work, you will develop problem-solving skills including engaging with unfamiliar problems, and identifying relevant strategies.

· The project and assignment work will encourage you to research and make creative use of widely-used computer software resources.

· You will develop analytical skills - the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of the analysis – through practice exercises, assignments and project work.

· You will develop your oral presentation skills, practicing presentation of technical solutions to problems based on real case studies. This practice will assist you in learning how to present material in a well-organized, well-structured, lucid and persuasive fashion.

· Professional report writing skills will be developed through the team project, for which a written report is required.

· Through the team project, you will develop the ability to participate effectively in a team. The department distinguishes between ethical collaboration, which is strongly encouraged, and plagiarism, which is prohibited.

· With both team-based and individually assessable material to be submitted throughout the semester, you will learn to manage your time, balance competing commitments and meet regular deadlines.

Textbooks

Subject notes will be available for purchase from the University Bookroom. There is no single recommended text, but a number of books have sections relevant to some parts of the material. Some examples are listed below.

HA Taha, Operations Research: An Introduction, McMillan (5^th edition 1992).

HP Williams, Model Solving in Mathematical Programming, John Wiley & Sons (1993).

WL Winston, Operations Research: Applications and Algorithms, PWS-Kent (1987).

MW Carter and CC Price, Operations Research: a Practical Introduction, CRC Press LLC (2000).

R Fletcher, Practical Methods of Optimization, 2^nd Edition, John Wiley & Sons, NY (1987).

FS Hillier and GJ Lieberman, Introduction to Mathematical Programming, McGraw-Hill (1995).

Past Exams

Copies of the 2000 and 2001 exams are included in the subject notes. All past exams from 1996 onwards are available on closed reserve in the Maths Sciences library - just ask at the desk. Relevant subject code and exam questions for years 1996-1998 are as follows. Papers are also available on the web from the Buddy Science site. Just follow the link to Exam Papers. (Note that for some reason I can't find the 620-361 paper at this site - but it is definitely in the Maths Sciences library.)

1998 exam - all questions except 7 and 3(c) are relevant, for 6(ii), replace "(Wolfe)" with "(Lagrangian)"
1997 exam - code 618-361, question 3, 4, 5 and 6 are relevant
1996 exam - code 618-362, questions 1, 2 and 3 are relevant

Links to solvers

LINDO - download free trial versions of LINDO solver for linear and integer programming or LINGO for nonlinear programming.

AMPL - follow "Try AMPL" links or go direct to AMPL start-up page . If you want to enter your problem on-line instead of uploading a file you have already prepared, just hit the "Submit" button half-way down this page.

tutOR - follow links to Simplex solvers, or go direct to the Simplex Place and select "Simplex Engine" in the left-hand frame.

Links to interesting places

Have a look at some ideas on team management and team roles at the Belbin site.

A great web site, with interactive case studies in linear programming, quadratic programming, stochastic programming and integer programming is the NEOS Guide: Case Studies site. (Note you may find the material here on the Quadratic Assignment Problem relevant to your project!) The parent site Optimization Technology Center also has lots of interesting stuff, with background notes and references on many areas of operations research (see, in particular, the "Optimization Tree" link).

ASOR has a monthly seminar series, with slides and summaries of past lectures available at this website. Students are WELCOME to attend seminars, and also to join ASOR. A half-day workshop on "Global Optimization" presented by an international researcher is being given on July 9th. Email Natashia for details.

Price-Waterhouse-Coopers Decision Advisory Centre is using Operations Research to help companies in various ways. There is an on-line case study for a production-distribution "value chain", or "supply chain".

Berkeley has an interactive OR site.

The CSIRO Operations Research Group has lots of interesting stuff happening – they also have vacation scholarships on occasion.

INFORMS – the International Society for Operations Research and Management Sciences - student services!

Panorama - recreational OR - have fun!

Created: 1 August 2001

Last modified: 27 February 2002

Authorised by: Natashia Boland, Department of Mathematics and Statistics.

Maintained by: Natashia Boland, Department of Mathematics and Statistics.
Email: natashia@unimelb.edu.au