## 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.

Original language | English (US) |
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Pages (from-to) | 546-563 |

Number of pages | 18 |

Journal | Naval Research Logistics |

Volume | 58 |

Issue number | 6 |

DOIs | |

State | Published - Sep 1 2011 |

## All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Ocean Engineering
- Management Science and Operations Research

## Keywords

- inclusive assignment sets
- polynomial time approximation scheme
- subset sum
- worst case analysis