# Optimal value bounds in interval fractional linear programming and revenue efficiency measuring

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## Abstract

This paper deals with the fractional linear programming problem in which input data can vary in some given real compact intervals. The aim is to compute the exact range of the optimal value function. A method is provided for the situation in which the feasible set is described by a linear interval system. Moreover, certain dependencies between the coefficients in the nominators and denominators can be involved. Also, we extend this approach for situations in which the same vector appears in different terms in nominators and denominators. The applicability of the approaches developed is illustrated in the context of the analysis of hospital performance.

## Keywords

Linear interval systems Fractional linear programming Optimal value range Interval matrix Dependent data## Mathematics Subject Classification

90C31 90B50 65G40## Notes

### Acknowledgements

M. Hladík was supported by the Czech Science Foundation under Grant P403-18-04735S.

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