Abstract
This paper proposes two sets of formulas for the sensitivity analysis of the optimal value function of a parametric linear programming problem. The first one evaluates the changes of the optimal value with respect to perturbations of the right-hand side vector in the constraint system and of the cost vector. The second one gives a lower bound and an upper bound for the Dini directional derivative of the optimal value function.
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Acknowledgements
The author would like to thank Professor Nguyen Dong Yen for the problem statement and the guidance.
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Thieu, N.N. Some Differential Estimates in Linear Programming. Acta Math Vietnam 41, 243–249 (2016). https://doi.org/10.1007/s40306-015-0130-3
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DOI: https://doi.org/10.1007/s40306-015-0130-3
Keywords
- Linear programming
- Sensitivity analysis
- Optimal value
- Second-order estimates for the increment
- Dini directional derivative