The precedence constrained knapsack problem: Separating maximally violated inequalities

Daniel Espinoza, Marcos Goycoolea, Eduardo Moreno

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We consider the problem of separating maximally violated inequalities for the precedence constrained knapsack problem. Though we consider maximally violated constraints in a very general way, special emphasis is placed on induced cover inequalities and induced clique inequalities. Our contributions include a new partial characterization of maximally violated inequalities, a new safe shrinking technique, and new insights on strengthening and lifting. This work follows on the work of Boyd (1993), Park and Park (1997), van de Leensel et al. (1999) and Boland et al. (2011). Computational experiments show that our new techniques and insights can be used to significantly improve the performance of cutting plane algorithms for this problem.

Original languageEnglish
Pages (from-to)65-80
Number of pages16
JournalDiscrete Applied Mathematics
StatePublished - 30 Oct 2015


  • Induced clique inequality
  • Induced cover inequality
  • Lifting
  • Precedence-constrained knapsack problem
  • Separation problem
  • Shrinking


Dive into the research topics of 'The precedence constrained knapsack problem: Separating maximally violated inequalities'. Together they form a unique fingerprint.

Cite this