Soft Computing

, Volume 23, Issue 21, pp 11055–11061 | Cite as

Bounds on the worst optimal value in interval linear programming

  • Mohsen Mohammadi
  • Monica GentiliEmail author
Methodologies and Application


One of the basic tools to describe uncertainty in a linear programming model is interval linear programming, where parameters are assumed to vary within a priori known intervals. One of the main topics addressed in this context is determining the optimal value range, that is, the best and the worst of all the optimal values of the objective function among all the realizations of the uncertain parameters. For the equality constraint problems, computing the best optimal value is an easy task, but the worst optimal value calculation is known to be NP-hard. In this study, we propose new methods to determine bounds for the worst optimal value, and we evaluate them on a set of randomly generated instances.


Interval linear programming Worst optimal value Bounds 



The authors thank the two anonymous referees for their suggestions and comments which helped improve the quality and clarity of the paper.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversity of LouisvilleLouisvilleUSA
  2. 2.Department of MathematicsUniversity of SalernoFiscianoItaly

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