Multiple subset sum with inclusive assignment set restrictions

Document Type

Article

Publication Date

9-1-2011

Abstract

In a traditional multiple subset sum problem (MSSP), there is a given set of items and a given set of bins (or knapsacks) with identical capacities. The objective is to select a subset of the items and pack them into the bins such that the total weight of the selected items is maximized. However, in many applications of the MSSP, the bins have assignment restrictions. In this article, we study the subset sum problem with inclusive assignment set restrictions, in which the assignment set of one item (i.e., the set of bins that the item may be assigned to) must be either a subset or a superset of the assignment set of another item. We develop an efficient 0.6492-approximation algorithm and test its effectiveness via computational experiments. We also develop a polynomial time approximation scheme for this problem. © 2011 Wiley Periodicals, Inc.

Identifier

80051472379 (Scopus)

Publication Title

Naval Research Logistics

External Full Text Location

https://doi.org/10.1002/nav.20466

e-ISSN

15206750

ISSN

0894069X

First Page

546

Last Page

563

Issue

6

Volume

58

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