On some stability notions of multiobjective integer linear fractional programming problem under randomness

In this paper a solution algorithm to chance-constrained multiobjective integer linear fractional programming problem is suggested. We assume that there is randomness in the right-hand side of the constraints only and that the random variables are normally distributed. Some stability notions for the problem of concern are defined and characterized. An illustrative numerical example is provided to clarify the developed theory and the suggested solution algorithm.

[1]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[2]  Omar M. Saad,et al.  On Solving Single-Objective Fuzzy Integer Linear Fractional Programs , 2010 .

[3]  Hamdy A. Taha,et al.  Integer Programming: Theory, Applications, and Computations , 1975 .

[4]  Tawfik R. Mohamed,et al.  • TAYLOR SERIES APPROACH FOR SOLVING CHANCE-CONSTRAIED MULTIOBJECTIVE INTEGER LINEAR FRACTIONAL PROGRAMMING PROBLEM , 2012 .

[5]  Omar M. Saad,et al.  On Stability in Multiobjective Integer Linear Programming: A Stochastic Approach , 2005 .

[6]  Pankaj Gupta,et al.  Sensitivity analysis in fuzzy multiobjective linear fractional programming problem , 2001, Fuzzy Sets Syst..

[7]  Elsaid Ebrahim Ammar,et al.  On some basic notions of fuzzy parametric nonsmooth multiobjective nonlinear fractional programming problems , 1998, Fuzzy Sets Syst..

[8]  Omar M. Saad,et al.  • TAYLOR SERIES APPROACH FOR SOLVING CHANCE- CONSTRAINED BI-LEVEL INTEGER LINEAR FRACTIONAL PROGRAMMING PROBLEM , 2011 .

[9]  Omar M. Saad,et al.  On stability of proper efficient solutions in multiobjective fractional programming problems under fuzziness , 2007, Math. Comput. Model..

[10]  D. Granot,et al.  On Integer and Mixed Integer Fractional Programming Problems , 1977 .

[11]  Omprakash K. Gupta,et al.  Branch and Bound Experiments in Convex Nonlinear Integer Programming , 1985 .

[12]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[13]  Abraham Charnes,et al.  Programming with linear fractional functionals , 1962 .

[14]  M. Balinski An algorithm for finding all vertices of convex polyhedral sets , 1959 .

[15]  G. Nemhauser,et al.  Integer Programming , 2020 .