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Mathematical Programming, 1977
The fractional knapsack problem to obtain an integer solution that maximizes a linear fractional objective function under the constraint of one linear inequality is considered. A modification of the Dinkelbach's algorithm [3] is proposed to exploit the fact that good feasible solutions are easily obtained for both the fractional knapsack problem and ...
Ishii, Hiroaki +2 more
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The fractional knapsack problem to obtain an integer solution that maximizes a linear fractional objective function under the constraint of one linear inequality is considered. A modification of the Dinkelbach's algorithm [3] is proposed to exploit the fact that good feasible solutions are easily obtained for both the fractional knapsack problem and ...
Ishii, Hiroaki +2 more
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2021
The text of this chapter is based on [1, 2, 3]. The Multiple Knapsack problem (MKP) is a hard combinatorial optimization problem with large application, which embraces many practical problems from different domains, including transport, cargo loading, cutting stock, bin-packing, financial management, etc.
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The text of this chapter is based on [1, 2, 3]. The Multiple Knapsack problem (MKP) is a hard combinatorial optimization problem with large application, which embraces many practical problems from different domains, including transport, cargo loading, cutting stock, bin-packing, financial management, etc.
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Operations Research Letters, 1995
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1980
The quadratic knapsack (QK) model naturally arises in a variety of problems in operations research, statistics and combinatorics. Some “upper planes” for the QK problem are derived, and their different uses in a branch-and-bound scheme for solving such a problem are discussed.
Gallo, G., Hammer, P. L., Simeone, B.
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The quadratic knapsack (QK) model naturally arises in a variety of problems in operations research, statistics and combinatorics. Some “upper planes” for the QK problem are derived, and their different uses in a branch-and-bound scheme for solving such a problem are discussed.
Gallo, G., Hammer, P. L., Simeone, B.
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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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2011
For many important optimization problems no efficient solution algorithm is yet known – the only way to find the optimal solution is to compare all possible solutions. The time requirement for this simple procedure is of course dependent on the number of solutions, and hence in general it is very large.
Beier, R., Vöcking, B.
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For many important optimization problems no efficient solution algorithm is yet known – the only way to find the optimal solution is to compare all possible solutions. The time requirement for this simple procedure is of course dependent on the number of solutions, and hence in general it is very large.
Beier, R., Vöcking, B.
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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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2004
The multiple knapsack problem is a generalization of the standard knapsack problem (KP) from a single knapsack to m knapsacks with (possibly) different capacities. The objective is to assign each item to at most one of the knapsacks such that none of the capacity constraints are violated and the total profit of the items put into knapsacks is maximized.
Hans Kellerer +2 more
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The multiple knapsack problem is a generalization of the standard knapsack problem (KP) from a single knapsack to m knapsacks with (possibly) different capacities. The objective is to assign each item to at most one of the knapsacks such that none of the capacity constraints are violated and the total profit of the items put into knapsacks is maximized.
Hans Kellerer +2 more
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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
Sinha, Prabhakant, Zoltners, Andris A.
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