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Improved dynamic programming and approximation results for the knapsack problem with setups
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DOI：10.1111/itor.12381.png)
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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.
Keyword:
0-1 knapsack problem with setups
approximation scheme
dynamic programming
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