# Complexity of necessary efficiency in interval linear programming and multiobjective linear programming

@article{Hladk2012ComplexityON, title={Complexity of necessary efficiency in interval linear programming and multiobjective linear programming}, author={Milan Hlad{\'i}k}, journal={Optimization Letters}, year={2012}, volume={6}, pages={893-899} }

We present some complexity results on checking necessary efficiency in interval multiobjective linear programming. Supposing that objective function coefficients perturb within prescribed intervals, a feasible point x* is called necessarily efficient if it is efficient for all instances of interval data. We show that the problem of checking necessary efficiency is co-NP-complete even for the case of only one objective. Provided that x* is a non-degenerate basic solution, the problem is…

## 33 Citations

### On Relation of Possibly Efficiency and Robust Counterparts in Interval Multiobjective Linear Programming

- Economics, Mathematics
- 2017

We investigate multiobjective linear programming with uncertain cost coefficients. We assume that lower and upper bounds for uncertain values are known, no other assumption on uncertain costs is…

### How to determine basis stability in interval linear programming

- Computer ScienceOptim. Lett.
- 2014

This paper proposes a method for testing basis stability and even though the method is exponential in the worst case (not surprisingly due to NP-hardness of the problem), it is fast in many cases.

### New conditions for testing necessarily/possibly efficiency of non-degenerate basic solutions based on the tolerance approach

- Mathematics, EconomicsEur. J. Oper. Res.
- 2020

### Maximal and supremal tolerances in multiobjective linear programming

- MathematicsEur. J. Oper. Res.
- 2013

### On strong optimality of interval linear programming

- Mathematics, Computer ScienceOptim. Lett.
- 2017

A related optimality concept of semi-strong optimality is investigated, showing its characterization and complexity in a linear programming problem with interval data.

### Obtaining Efficient Solutions of Interval Multi-objective Linear Programming Problems

- MathematicsInt. J. Fuzzy Syst.
- 2020

The proposed method solves the IMOLP model corresponding to the problem of the facilities and non-return funds in a bank and generalizes the $$\varepsilon$$ ε -constraint and lexicographic methods which are used for obtaining ESs of the multi-objective linear programming (MOLP) models which are applicable for large-scale problems.

### Some results in interval multiobjective linear programming for recognizing different solutions

- Mathematics
- 2015

Based on the concepts of efficiency and weak efficiency, different solutions are defined to multiobjective linear programming problems with interval objective functions coefficients. This paper…

### Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem

- MathematicsFuzzy Optim. Decis. Mak.
- 2016

This paper attempts to propose a new model with interesting properties by considering the minimax regret criterion and suggests an algorithm to obtain an optimal solution of the new model.

### Multiobjective interval linear programming in admissible-order vector space

- MathematicsInf. Sci.
- 2019

### Robust optimal solutions in interval linear programming with forall-exists quantifiers

- Mathematics, Computer ScienceEur. J. Oper. Res.
- 2016

## References

SHOWING 1-10 OF 30 REFERENCES

### On necessarily efficient solutions in interval multiobjective linear programming

- Mathematics
- 2010

We investigate multiobjective linear programming problems with objective coefficients varying inside given intervals. A feasible solution x ∗ is called necessarily efficient if it is efficient for…

### Computing the tolerances in multiobjective linear programming

- MathematicsOptim. Methods Softw.
- 2008

A procedure computing a tolerance for each objective function coefficient, such that all these coefficients may simultaneously and independently vary within their tolerances while preserving the efficiency of x*.

### Possible and necessary optimality tests in possibilistic linear programming problems

- Computer Science
- 1994

### Possible and necessary efficiency in possibilistic multiobjective linear programming problems and possible efficiency test

- Computer Science, EconomicsFuzzy Sets Syst.
- 1996

### Linear Multiple Objective Problems with Interval Coefficients

- Mathematics
- 1980

In this paper we consider linear multiple objective programs with coefficients of the criteria given by intervals. This class of problems is of practical interest since in many instances it is…

### Strong Unboundedness of Interval Linear Programming Problems

- Mathematics12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)
- 2006

A linear programming problem whose coefficients are prescribed by intervals is called strongly unbounded if each linear programming problem obtained by fixing coefficients in these intervals is…

### An interactive method of tackling uncertainty in interval multiple objective linear programming

- Computer Science
- 2009

The presented procedures provide a global view of the solutions in the best and worst case coefficient scenarios and allow performing the search for new solutions according to the achievement rates of the objective functions regarding both the upper and lower bounds.

### Decision Analysis of the Interval-Valued Multiobjective Linear Programming Problems

- Economics, Business
- 2001

Giving a Multiobjective linear program with the interval-valued cost coefficients, this study proposed a decision procedure to support finding a final efficient decision. After defining the complete…

### Multiple objective linear programming models with interval coefficients - an illustrated overview

- Computer ScienceEur. J. Oper. Res.
- 2007

### Solutions for the Portfolio Selection Problem with Interval and Fuzzy Coefficients

- MathematicsReliab. Comput.
- 2004

Investigating the properties of two efficiency conditions by means of preference cones and feasible region, it is discussed that the two kinds of solutions can be identified with the sets of combinations of lower or upper bounds of intervals.