Abstract
We consider three new knapsack problems with variable weights or profits of items, where the weight or profit of an item depends on the position of the item in the sequence of items packed in the knapsack. We show how to solve the problems exactly using dynamic programming algorithms with pseudo-polynomial running times and propose fully polynomial-time approximation schemes for their approximate solution.
Original language | English |
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Pages (from-to) | 137-156 |
Number of pages | 20 |
Journal | Annals of Operations Research |
Volume | 326 |
Issue number | 1 |
DOIs | |
State | Published - Jul 2023 |
Keywords
- Approximation schemes
- Dynamic programming
- Knapsack problem
All Science Journal Classification (ASJC) codes
- General Decision Sciences
- Management Science and Operations Research