Improved dynamic programming and approximation results for the knapsack problem with setups
In this paper, we consider the 0–1 knapsack problem with setups. Items are grouped into families and if any items of a family are packed, this induces a setup cost as well as a setup resource consumption. We introduce a new dynamic programming algorithm that performs much better than a previous dyna...
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| Veröffentlicht in: | International transactions in operational research 2018-03, Vol.25 (2), p.667-682 |
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| container_title | International transactions in operational research |
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| creator | Pferschy, Ulrich Scatamacchia, Rosario |
| description | In this paper, we consider the 0–1 knapsack problem with setups. Items are grouped into families and if any items of a family are packed, this induces a setup cost as well as a setup resource consumption. We introduce a new dynamic programming algorithm that performs much better than a previous dynamic program and turns out to be also a valid alternative to an exact approach based on the use of an Integer Linear Programming (ILP) solver. Then we present a general inapproximability result. Furthermore, we investigate several relevant special cases that still permit fully polynomial‐time approximation schemes and others where the problem remains hard to approximate. |
| doi_str_mv | 10.1111/itor.12381 |
| format | Article |
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| ispartof | International transactions in operational research, 2018-03, Vol.25 (2), p.667-682 |
| issn | 0969-6016 1475-3995 |
| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete; Business Source Complete |
| subjects | 0–1 knapsack problem with setups Approximation approximation scheme Dynamic programming Integer programming Knapsack problem Linear programming Mathematical analysis Operations research |
| title | Improved dynamic programming and approximation results for the knapsack problem with setups |
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