Exact methods for the knapsack problem and its generalizations

A unified approach and a summary of the most important results concerned with exact methods for solving the (binary) knapsack problem and its generalizations are given. We stress the importance of dual methods for solving linear programming relaxations of the considered problems. Two ways of general...

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Veröffentlicht in:	European Journal of Operational Research 1987, Vol.28 (1), p.3-21
Hauptverfasser:	Dudziński, Krzysztof, Walukiewicz, Stanisław
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Applied sciences branch-and-bound Dynamic programming Exact sciences and technology Integer programming Knapsack problem Lagrangean relaxation Linear programming linear programming relaxation Mail order Mathematical analysis Mathematical programming Operational research and scientific management Operational research. Management science Optimization reduction
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Zusammenfassung:	A unified approach and a summary of the most important results concerned with exact methods for solving the (binary) knapsack problem and its generalizations are given. We stress the importance of dual methods for solving linear programming relaxations of the considered problems. Two ways of generalization of the knapsack problem are described. If the special ordered sets are added, then the multiple-choice knapsack problem is obtained. If the constraints have the nested structure, then we get the nested knapsack problem. Also the multiple-choice nested knapsack problem is discussed.
ISSN:	0377-2217 1872-6860
DOI:	10.1016/0377-2217(87)90165-2