Multi-choice programming problems arise due to diverse needs of people. In this paper, multi-choice optimisation is applied bilevel transportation problem. This problem deals with at both the levels, upper as well lower. There are multiple choices for demand and supply parameters. The parameters respective levels converted into polynomials which transmute defined a mixed integer objective paper...

Bilevel programming problems are hierarchical optimization problems in which the feasible set is determined by the set of optimal solutions of a second, parametric optimization problem. In this paper we consider problems where this second problem is a discrete one. We start with addressing the problem of the existence of optimal solutions. Then, an algorithm is proposed solving these problems. ...

This document discusses the aspects of network design.First a brief introduction of network design will be given.Then various types of assignment techniques will be discussed including the mathematical formulation and numerical illustration of the important ones.Then the concept of bilevel programming and few examples will be presented.Finally one such example, namely the network capacity expan...

In a bilevel decision problem, the leader at the upper level attempts to optimize his/her objective, the follower at the lower level tries to find an optimized strategy according to each of possible decisions made by the leader. A bilevel decision problem may involve fuzzy demands which appear either in the objective functions or constraints of the leader or the follower or both. Furthermore, t...

The paper is devoted to applications of advanced tools of modern variational analysis and generalized differentiation to problems of optimistic bilevel programming. In this way, new necessary optimality conditions are derived for two major classes of bilevel programs: those with partially convex and with fully convex lower-level problems. We provide detailed discussions of the results obtained ...

In this paper we discuss special bilevel optimal control problems where the upper level problem is an optimal control problem of ODEs with control and terminal constraints and the lower level problem is a finite-dimensional parametric optimization problem where the parameter is the final state of the state variable of the upper level. We tackle this problem using tools of nonsmooth analysis, op...

In this note, we analyze a bilevel interdiction problem, where the follower’s program is a parametrized continuous knapsack. Based on the structure of the problem and an inverse optimization strategy, we propose for its solution an algorithm with worst-case complexity O(n). Keywords— Bilevel programming, Continuous knapsack problem, Polynomial time. 1 Model Recently, a number of papers have bee...