Efficient model for interval goal programming with arbitrary penalty function

Hao Chun Lu, Tzu Li Chen*

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

5 Scopus citations


Penalty function is a key factor in interval goal programming (IGP), especially for decision makers weighing resources vis-à-vis goals. Many approaches (Chang et al. J Oper Res Soc 57:469-473, 2006; Chang and Lin Eur J Oper Res 199, 9-20, 2009; Jones et al. Omega 23, 41-48, 1995; Romero Eur J Oper Res 153, 675-686, 2004; Vitoriano and Romero J Oper Res Soc 50, 1280-1283, 1999)have been proposed for treating several types of penalty functions in the past several decades. The recent approach of Chang and Lin (Eur J Oper Res 199, 9-20, 2009) considers the S-shaped penalty function. Although there are many approaches cited in literature, all are complicated and inefficient. The current paper proposes a novel and concise uniform model to treat any arbitrary penalty function in IGP. The efficiency and usefulness of the proposed model are demonstrated in several numeric examples.

Original languageEnglish
Pages (from-to)325-341
Number of pages17
JournalOptimization Letters
Issue number2
StatePublished - 02 2013
Externally publishedYes


  • Interval goal programming
  • Penalty function


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