Standard sensitivity analysis and additive tolerance approach in MOLP
Tóm tắt
We consider sensitivity analysis of the objective function coefficients in multiple objective linear programming (MOLP). We focus on the properties of the parameters set for which a given extreme solution is efficient. Moreover, we compare two approaches: the standard sensitivity analysis (changing only one coefficient) and the additive tolerance approach (changing all coefficients). We find the connections between these two approaches by giving a theorem describing the upper bound on the maximal additive tolerance.
Tài liệu tham khảo
Benson, H. P., & Sun, E. (2002). A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of a multiple objective linear program. European Journal of Operational Research, 139(1), 26–41.
Borges, A. R., & Antunes, C. H. (2002). A visual interactive tolerance approach to sensitivity analysis in MOLP. European Journal of Operational Research, 142(2), 357–381.
Dauer, J., & Liu, Y. H. (1997). Multiple-criteria and goal programming. In T. Gal & H. J. Greenberg (Eds.), Advances in sensitivity analysis and parametric programming. Boston: Kluwer Academic. Section 11.
Gal, T. (1997). A historical sketch on sensitivity analysis and parametric programming. In T. Gal & H. J. Greenberg (Eds.), Advances in sensitivity analysis and parametric programming. Boston: Kluwer Academic.
Gal, T., & Wolf, K. (1986). Stability in vector maximization—a survey. European Journal of Operational Research, 25, 169–182.
Hansen, P., Labbe, M., & Wendell, R. E. (1989). Sensitivity analysis in multiple objective linear programming: the tolerance approach. European Journal of Operational Research, 38, 63–69.
Hladik, M. (2008). Additive and multiplicative tolerance in multiobjective linear programming. Operations Research Letters, 36, 393–396.
Oliveira, C., & Antunes, C. H. (2007). Multiple objective linear programming models with interval coefficients—an illustrated overview. European Journal of Operational Research, 181(3), 1434–1463.
Sitarz, S. (2008). Postoptimal analysis in multicriteria linear programming. European Journal of Operational Research, 191, 7–18.
Steuer, R. (1986). Multiple criteria optimization theory: computation and application. New York: Willey.
Wendell, R. E. (1982). A preview of a tolerance approach to sensitivity analysis in linear programming. Discrete Mathematics, 38, 121–124.