### Abstract

We introduce the following network optimization problem: given a directed graph with a cost function on the arcs, demands at the nodes, and a single source s, find the minimum cost connected subgraph from s such that its total demand is no less than lower bound D. We describe applications of this problem to disaster relief and media broadcasting, and show that it generalizes several well-known models including the knapsack problem, the partially ordered knapsack problem, the minimum branching problem, and certain scheduling problems. We prove that our problem is strongly NP-complete and give an integer programming formulation. We also provide five heuristic approaches, illustrate them with a numerical example, and provide a computational study on both small and large sized, randomly generated problems. The heuristics run efficiently on the tested problems and provide solutions that, on average, are fairly close to optimal.

Original language | English |
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Pages (from-to) | 1793-1799 |

Number of pages | 7 |

Journal | Computers and Operations Research |

Volume | 39 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2012 Aug 1 |

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### Keywords

- Distribution
- Graph theory
- Logistics
- Network flows

### ASJC Scopus subject areas

- Computer Science(all)
- Management Science and Operations Research
- Modelling and Simulation

### Cite this

*Computers and Operations Research*,

*39*(8), 1793-1799. https://doi.org/10.1016/j.cor.2011.06.001