Integer Programming Formulation of the Bilevel Knapsack Problem
نویسندگان
چکیده
منابع مشابه
Integer Programming Formulation of the Bilevel Knapsack Problem
The Bilevel Knapsack Problem (BKP) is a hierarchical optimization problem in which the feasible set is determined by the set of optimal solutions of parametric Knapsack Problem. In this paper, we propose two stages exact method for solving the BKP. In the first stage, a dynamic programming algorithm is used to compute the set of reactions of the follower. The second stage consists in solving an...
متن کاملBilevel Programming with Knapsack Constraints
A special class of bilevel programming problems with discrete para-metric lower level problems is considered. First, necessary and suucient conditions for the existence of optimal solutions are given. Then, a pseu-dopolynomial exact and a polynomial approximate algorithms for solving the bilevel problem are proposed.
متن کاملOn a Stochastic Bilevel Programming Problem with Knapsack Constraints
In this paper we propose a mixed integer bilevel problem having a probabilistic knapsack constraint in the first level. The problem formulation is mainly motivated by practical pricing and service provision problems as it can be interpreted as a model for the interaction between a service provider and clients. We assume the probability space to be discrete which allows us to reformulate the pro...
متن کاملDynamic programming algorithms for the bi-objective integer knapsack problem
This paper presents two new dynamic programming (DP) algorithms to find the exact Pareto frontier for the bi-objective integer knapsack problem. First, a property of the traditional DP algorithm for the multiobjective integer knapsack problem is identified. The first algorithm is developed by directly using the property. The second algorithm is a hybrid DP approach using the concept of the boun...
متن کاملDynamic-Programming-Based Inequalities for the Unbounded Integer Knapsack Problem
We propose a new hybrid approach to solve the unbounded integer knapsack problem (UKP), where valid inequalities are generated based on intermediate solutions of an equivalent forward dynamic programming formulation. These inequalities help tighten the initial LP relaxation of the UKP, and therefore improve the overall computational efficiency. We also extended this approach to solve the multi-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Modelling of Natural Phenomena
سال: 2010
ISSN: 0973-5348,1760-6101
DOI: 10.1051/mmnp/20105719