Knapsack problems with setups

Knapsack problems with setups find their application in many concrete industrial and financial problems. Moreover, they also arise as subproblems in a Dantzig–Wolfe decomposition approach to more complex combinatorial optimization problems, where they need to be solved repeatedly and therefore effic...

Full description

Saved in:
Bibliographic Details
Published in:European journal of operational research 2009-08, Vol.196 (3), p.909-918
Main Authors: Michel, S., Perrot, N., Vanderbeck, F.
Format: Article
Language:English
Subjects:
Applied sciences
Branch & bound algorithms
Branch-and-bound
Computer Science
Exact sciences and technology
Fixed cost
Fixed costs
Flows in networks. Combinatorial problems
Knapsack problem
Knapsack problem Fixed cost Setup Variable upper bound Branch-and-bound
Operational research and scientific management
Operational research. Management science
Operations Research
Optimization algorithms
Setup
Studies
Variable upper bound
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Knapsack problems with setups find their application in many concrete industrial and financial problems. Moreover, they also arise as subproblems in a Dantzig–Wolfe decomposition approach to more complex combinatorial optimization problems, where they need to be solved repeatedly and therefore efficiently. Here, we consider the multiple-class integer knapsack problem with setups. Items are partitioned into classes whose use implies a setup cost and associated capacity consumption. Item weights are assumed to be a multiple of their class weight. The total weight of selected items and setups is bounded. The objective is to maximize the difference between the profits of selected items and the fixed costs incurred for setting-up classes. A special case is the bounded integer knapsack problem with setups where each class holds a single item and its continuous version where a fraction of an item can be selected while incurring a full setup. The paper shows the extent to which classical results for the knapsack problem can be generalized to these variants with setups. In particular, an extension of the branch-and-bound algorithm of Horowitz and Sahni is developed for problems with positive setup costs. Our direct approach is compared experimentally with the approach proposed in the literature consisting in converting the problem into a multiple choice knapsack with pseudo-polynomial size.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2008.05.001