This paper presents a fuzzy goal programming methodology for solving bilevel programming problems having quadratic fractional form of objectives of the decision makers. In the proposed procedure, the membership functions for the defined fuzzy goals of objective of the decision makers at both levels are developed first. Then a fuzzy goal programming model is developed to minimize the group regre...

In this paper, we consider the bilevel linear programming problem (BLPP) where all coefficients in are interval type-2 triangular fuzzy numbers (IT2TFNs). First, convert a BLPP with IT2TFN parameters to an BLPP. next step, solve BLPPs and obtain optimal solution as IT2TFN.

In recent years, branch-and-cut algorithms have become firmly established as the most effective method for solving generic mixed integer linear programs (MIPs). Methods for automatically generating inequalities valid for the convex hull of solutions to such MIPs are a critical element of branch-and-cut. This paper examines the nature of the so-called separation problem, which is that of generat...

Bilevel scheduling problems constitute a hardly studied area of scheduling theory. In this paper we summarise the basic concepts of bilevel optimisation, and discuss two problem classes for which we establish various complexity and algorithmic results. The first one is the bilevel total weighted completion time problem in which the leader assigns the jobs to parallel machines and the follower s...

For a long time, the bilevel programming problem has essentially been considered as a special case of mathematical programs with equilibrium constraints (MPECs), in particular when the so-called KKT reformulation is in question. Recently though, this widespread believe was shown to be false in general. In this paper, other aspects of the difference between both problems are revealed as we consi...

A very general optimization problem with a variational inequality constraint, inequality constraints, and an abstract constraint are studied. Fritz John type and Kuhn–Tucker type necessary optimality conditions involving Mordukhovich coderivatives are derived. Several constraint qualifications for the Kuhn–Tucker type necessary optimality conditions involving Mordukhovich coderivatives are intr...