Sensitivity of the Optimum to Perturbations of the Profit or Weight of an Item in the Binary Knapsack Problem

Mhand Hifi, Hedi Mhalla and Slim Sadfi
Additional contact information
Mhand Hifi: Université de Picardie Jules Verne
Hedi Mhalla: Université de Picardie Jules Verne
Slim Sadfi: Université de Picardie Jules Verne

Journal of Combinatorial Optimization, 2005, vol. 10, issue 3, No 3, 239-260

Abstract: Abstract In the binary single constraint Knapsack Problem, denoted KP, we are given a knapsack of fixed capacity c and a set of n items. Each item j, j = 1,...,n, has an associated size or weight w j and a profit p j . The goal is to determine whether or not item j, j = 1,...,n, should be included in the knapsack. The objective is to maximize the total profit without exceeding the capacity c of the knapsack. In this paper, we study the sensitivity of the optimum of the KP to perturbations of either the profit or the weight of an item. We give approximate and exact interval limits for both cases (profit and weight) and propose several polynomial time algorithms able to reach these interval limits. The performance of the proposed algorithms are evaluated on a large number of problem instances.

Keywords: combinatorial optimization; knapsacks; optimality; sensitivity analysis (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10878-005-4105-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:10:y:2005:i:3:d:10.1007_s10878-005-4105-5

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-005-4105-5

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().