© 2001

Linear Optimization and Extensions

Problems and Solutions


Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Dimitris Alevras, Manfred W. Padberg
    Pages 1-37
  3. Dimitres Alevras, Manfred W. Padberg
    Pages 39-45
  4. Dimitres Alevras, Manfred W. Padberg
    Pages 47-54
  5. Dimitri Alevras, Manfred W.Padberg
    Pages 55-61
  6. Dimitris Alevras, Manfred W. Padberg
    Pages 63-92
  7. Dimitris Alevras, Manfred W. Padberg
    Pages 93-123
  8. Dimitris Alevras, Manfred W. Padberg
    Pages 125-200
  9. Dimitris Alevras, Manfred W. Padberg
    Pages 201-261
  10. Dimitris Alevras, Manfred W. Padberg
    Pages 263-321
  11. Dimitres Alevras, Manfred W.Padberg
    Pages 323-358
  12. Back Matter
    Pages 359-451

About this book


Books on a technical topic - like linear programming - without exercises ignore the principal beneficiary of the endeavor of writing a book, namely the student - who learns best by doing course. Books with exercises - if they are challenging or at least to some extent so exercises, of - need a solutions manual so that students can have recourse to it when they need it. Here we give solutions to all exercises and case studies of M. Padberg's Linear Optimization and Exten­ sions (second edition, Springer-Verlag, Berlin, 1999). In addition we have included several new exercises and taken the opportunity to correct and change some of the exercises of the book. Here and in the main text of the present volume the terms "book", "text" etc. designate the second edition of Padberg's LPbook and the page and formula references refer to that edition as well. All new and changed exercises are marked by a star * in this volume. The changes that we have made in the original exercises are inconsequential for the main part of the original text where several ofthe exercises (especiallyin Chapter 9) are used on several occasions in the proof arguments. None of the exercises that are used in the estimations, etc. have been changed.


Analysis Graph Matrix Polyhedral Theory Sim algorithms combinatorial optimization complexity linear optimization optimization programming

Authors and affiliations

  1. 1.IBM Corp.West ChesterUSA
  2. 2.Department of Operations Research Stern School of BusinessNew York UniversityNew YorkUSA

Bibliographic information

Industry Sectors
Finance, Business & Banking


From the reviews of the first edition:

"... This book is a useful supplement to the textbook [W.Padberg, Linear Optimization and Extensions, 2nd ed., Springer, Berlin 1999]. It serves the purpose well to train MATHEMATICAL optimizers, but has little impact on the education of mathematical OPTIMIZERS, i.e. it concentrates on mathematics, but not on problem solving in reality. It is a valuable contribution for students in mathematics, but may be less suitable for students of economics or business administration."

OR-Spektrum, Issue 14, p.37, 2002 

"Die in diesem Werk präsentierten Übungsaufgaben wurden überarbeitet, ergänzt, und werden im vorliegenden Text samt Lösungen und geraffter Zusammenfassung der notwendigen theoretischen Resultate präsentiert. ... Bemerkenswert ist weiters, daß auch Programmieraufgaben gestellt und gelöst werden. ... Insgesamt ist das Buch sowohl als Quelle für Übungsaufgaben zu Vorlesungen über Lineare Optimierung als auch zum Selbststudieum sehr gut geeignet."

F.Rendl (Klagenfurt), IMN - Internationale Mathematische Nachrichten 190, 2002, S. 76-77

"Do you know M. Padberg’s Linear Optimization and Extensions (second edition, Springer-Verlag, Berlin, 1999)? If you teach a course on linear programming then you should know it. ... Now here is the continuation of it, discussing the solutions of all its exercises and with detailed analysis of the applications mentioned. … For those who cherish the original textbook (students and lecturers) this is an extremely valuable sequel. For those who strive for good exercises and case studies for LP this is an excellent volume." (Péter Hajnal, Acta Scientiarum Mathematicarum, Vol.69, 2003)