Applied Mathematical Programming Bradley Solution Manual Pdf

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

The following two softwares implement approximately the same modelling language:

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

Course materials

Some solved exercises are courtesy of Prof. Stefano Coniglio. Please point out any mistake or obscurity in the materials writing to me: I will take care of the correction as soon as possible.

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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