Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Polyhedral results for the precedence-constrained knapsack problem
Discrete Applied Mathematics
Lifting cover inequalities for the precedence-constrained knapsack problem
Discrete Applied Mathematics
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Algorithms for the Longest Common Subsequence Problem
Journal of the ACM (JACM)
Dynamic programming revisited: improving knapsack algorithms
Computing - Special issue on combinatorial optimization
A Minimal Algorithm for the Bounded Knapsack Problem
INFORMS Journal on Computing
Integer knapsack problems with set-up weights
Computational Optimization and Applications
Lot-sizing on a single imperfect machine: ILP models and FPTAS extensions
Computers and Industrial Engineering
Generalized quadratic multiple knapsack problem and two solution approaches
Computers and Operations Research
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The Bounded Set-up Knapsack Problem (BSKP) is a generalization of the Bounded Knapsack Problem (BKP), where each item type has a set-up weight and a set-up value that are included in the knapsack and the objective function value, respectively, if any copies of that item type are in the knapsack. This paper provides three dynamic programming algorithms that solve BSKP in pseudo-polynomial time and a fully polynomial-time approximation scheme (FPTAS). A key implication from these results is that the dynamic programming algorithms and the FPTAS can also be applied to BKP. One of the dynamic programming algorithms presented solves BKP with the same time and space bounds of the best known dynamic programming algorithm for BKP. Moreover, the FPTAS improves the worst-case time bound for obtaining approximate solutions to BKP as compared to using FPTASs designed for BKP or the 0-1 Knapsack Problem.