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Operations Research, 1979
The knapsack sharing problem has a utility or tradeoff function for each variable and seeks to maximize the value of the smallest tradeoff function (a maximin objective function). A single constraint places an upper bound on the sum of the non-negative variables.
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The knapsack sharing problem has a utility or tradeoff function for each variable and seeks to maximize the value of the smallest tradeoff function (a maximin objective function). A single constraint places an upper bound on the sum of the non-negative variables.
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The Unbounded Knapsack Problem
2008This paper presents a survey of the unbounded knapsack problem. We focus on the techniques for obtaining the optimal solutions, particularly those using the periodic structure of the optimal solutions when the knapsack weight-carrying capacity b is sufficiently large.
T. C. Hu, Leo Landa, Man-tak Shing
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The Multiple-Choice Knapsack Problem
Operations Research, 1979The multiple-choice knapsack problem is defined as a binary knapsack problem with the addition of disjoint multiple-choice constraints. The strength of the branch-and-bound algorithm we present for this problem resides with the quick solution of the linear programming relaxation and its efficient, subsequent reoptimization as a result of branching. An
Prabhakant Sinha, Andris A. Zoltners
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Information Processing Letters, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Stochastic Knapsack Problem
1988In the literature various stochastic versions of NP-hard scheduling problems have been shown to be solvable in polynomial time by simple list scheduling rules [Weiss 1982], [Pinedo 1982], [Derman et al. 1978] and [Pinedo 1983]. Here we will show that the same phenomenon occurs for the knapsack problem, the deterministic model of which is binary NP-hard.
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On the two-dimensional Knapsack Problem
Operations Research Letters, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alberto Caprara, Michele Monaci
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2016
We now turn to the subject of integer linear programming, or integer programming for short. integer programming, which permits non-integer values of the solution variables, is known to be “easy” in the sense of having known algorithms with worst-case runtime that is polynomial in the size of the problem instance.
T. C. Hu, Andrew B. Kahng
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We now turn to the subject of integer linear programming, or integer programming for short. integer programming, which permits non-integer values of the solution variables, is known to be “easy” in the sense of having known algorithms with worst-case runtime that is polynomial in the size of the problem instance.
T. C. Hu, Andrew B. Kahng
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The continuous collapsing Knapsack problem
Mathematical Programming, 1983A Collapsing Knapsack is a container whose capacity diminishes as the number of items it must hold is increased. This paper focuses on those cases in which the decision variables are continuous, i.e., can take any non-negative value. It is demonstrated that the problem can be reduced to a set of two dimensional subproblems.
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An Enumeration Algorithm for Knapsack Problems
Operations Research, 1970Enumeration techniques have been shown to be successful for solving integer linear programming problems. The purpose of this paper is to apply the enumeration philosophy to the classical knapsack problem; it shows that this approach applies quite naturally to this type of integer linear program when combined with the Fourier-Motzkin elimination method
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