Foundations of Operations Research
(Prof. Roberto Cordone)

You can have also a look at last year's webpage.

Lesson schedule

• Tuesday: 13.30-15.15 in classroom V07
• Thursday: 10.15-12.45 in classroom 3.8 or in laboratory 3.1

Adviced textbooks

• Hillier and Lieberman, Introduction to Operations Research (have a look on the web)
• Bradley, Hax and Magnanti, Applied Mathematical Programming (have a look on the web)
• Fischetti, Lezioni di Ricerca Operativa (the closest to our program, but only available in Italian)

If you have doubts on the exercises provided with these textbooks, please send your solution by e-mail: the correct commented solutions might be published to everybody's benefit.

Laboratory software

• AMPL Student Edition (commercial software, restricted size, downloadable book)
• GLPK (free software, unrestricted size, good manual included)

Course materials

• Introduction (October 8th, 2013)
• Modelling (October 10th, 2013) (cfr. Chapter 2 of Hillier-Liebermann, Chapter 1 of Bradley-Hax-Magnanti)
  • solved exercises
• Fundamentals on graphs (October 15th, 2013)
  (cfr. Chapter 9.1-9.2 of Hillier-Liebermann, unavailable in Bradley-Hax-Magnanti, Chapter 6.1-6.2-6.3 of Fischetti)
• First laboratory session (October 17th, 2013): AMPL modelling language, linear programming examples
  • How to run AMPL from the command line
  • The AMPL book (free download)
• Optimal spanning trees (October 22nd-29th, 2013)
  (cfr. Chapter 9.4 of Hillier-Liebermann, unavailable in Bradley-Hax-Magnanti, Chapter 6.5 of Fischetti)
  • solved exercises
  • partly solved exercises
  • solved exercises
• Second laboratory session (October 24th, 2013):
  Other linear programming examples
  • A Linear Programming model
  • The associated data
• Shortest path problem with nonnegative costs (October 31th, 2013)
  (cfr. Chapter 9.3 of Hillier-Liebermann, unavailable in Bradley-Hax-Magnanti, Chapter 6.6 of Fischetti)
  • solved exercise with the efficient version of Dijkstra's algorithm
  • solved exercises (Note: for the exercise on project planning see below: the solution given here uses the activity on arc model, whereas our course adopts the activity on node model)
• Shortest path problem with general costs and on acyclic graphs (November 5th, 2013)
  (cfr. Chapter 9.3 of Hillier-Liebermann, unavailable in Bradley-Hax-Magnanti, Chapter 6.6 of Fischetti)
  • solved exercises
• Project planning (November 7th, 2012)
  (cfr. Chapter 10.1-10.3 of Hillier-Liebermann, unavailable in Bradley-Hax-Magnanti, Chapter 6.6.5 of Fischetti)
  • solved exercise
• Maximum flow problem (November 12th, 2013)
  (cfr. Chapter 9.5 of Hillier-Liebermann, Appendix C in Bradley-Hax-Magnanti, Chapter 6.7 of Fischetti)
  • solved exercise (positive and negative labelling method)
  • solved exercises (residual network method)
• Third laboratory session (November 14th, 2013)
• Computational complexity (November 21st, 2013)
• Introduction to Linear Programming (November 26st, 2013)
  (cfr. Chapter 3 of Hillier-Liebermann, part of Chapter 1.4 of Bradley-Hax-Magnanti, Chapter 1.2 of Fischetti)
  • solved exercise
• Geometry of Linear Programming (November 26th, 2012)
  (cfr. Chapter 3.1 of Hillier-Liebermann, part of Chapter 2.1-2.2 of Bradley-Hax-Magnanti, Chapter 3.1 of Fischetti)
  • solved exercise
• Bases and basic solutions (November 28th, 2013)
  (cfr. Chapter 5.1 of Hillier-Liebermann, Chapter 3.1.1 of Fischetti)
• The simplex method (December 3rd, 2013)
  (cfr. Chapter 4.1-4.5 and 5.3 of Hillier-Liebermann, Chapter 3.2.1-3.2.4 of Fischetti)
  • solved exercise
• Fourth laboratory session (December 5th, 2013)
  (cfr. Chapter 3.1-3.6 of Bradley, Hax, Magnanti)
• The simplex method: special cases (December 10th, 2012)
  (cfr. Chapter 4.1-4.5 of Hillier-Liebermann, Chapter 3.2.5-3.2.6 of Fischetti, Chapter 2.1-2.5 of Bradley, Hax, Magnanti)
  • solved exercise (there is a mistake at page 6 and following; I will post a corrected version as soon as possible)
  • solved exercises
• Duality in Linear Programming (December 12th, 2012)
  (cfr. Chapter 6 of Hillier-Liebermann, Chapter 4.1-4.6 of Bradley, Hax, Magnanti, Chapter 4 of Fischetti, excluding Section 4.7)
  • solved exercise
  • solved exercise
  • solved exercises
• Integer Linear Programming models (skipped lesson, useful for modelling)
  (cfr. Chapter 12.1-12.4 of Hillier-Liebermann, Chapters 9.1-9.4 of Bradley, Hax, Magnanti, Chapters 2 and 7 of Fischetti)
• Introduction to Integer Linear Programming (December 17th, 2012)
  (cfr. Chapter 12.5 of Hillier-Liebermann, Chapter 5.1-5.2 of Fischetti)
• Cutting planes (December 19th, 2013)
  (cfr. Chapter 12.8 of Hillier-Liebermann, Chapter 9.8 of Bradley, Hax, Magnanti, Chapter ?.? of Fischetti)
  • solved exercise on the dual simplex
  • solved exercise on Gomory cuts
• Branch-and-bound for ILP (January 7th, 2013)
  (cfr. Chapter 12.6-12.7 of Hillier-Liebermann, Chapters 9.5-9.6 of Bradley, Hax, Magnanti, Chapter ?.? of Fischetti)
  • solved exercise on branch-and-bound for ILP
  • solved exercises (ignore the exercise on knapsack
    and remark that the exercise on branch-and-bound adopts a visit strategy more refined than depth-first)
• Exercises, nearly all solved (January 9th, 2012)
• samples of exam exercises
  The latter is a work in progress: ExamSamples.pdf is absorbing exercises in Italian (the other PDF files) and raw translations (the text file)
  No solution is presently available: send your own solutions to make them available sooner.

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