Polyhedral results for the precedence-constrained knapsack problem
نویسندگان
چکیده
منابع مشابه
Lifting valid inequalities for the precedence constrained knapsack problem
This paper considers the precedence constrained knapsack problem. More speci cally, we are interested in classes of valid inequalities which are facet-de ning for the precedence constrained knapsack polytope. We study the complexity of obtaining these facets using the standard sequential lifting procedure. Applying this procedure requires solving a combinatorial problem. For valid inequalities ...
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We consider the polyhedral structure of the precedence constrained knapsack (PCK) problem, also known as the partially ordered knapsack problem. A set of items N is given, along with a partial order, or set of precedence relationships, on the items, denoted by S ⊆ N × N. A precedence relationship (i, j) ∈ S exists if item i can be placed in the knapsack only if item j is in the knapsack. Each i...
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We consider a knapsack problem with precedence constraints imposed on pairs of items, known as the precedence constrained knapsack problem (PCKP). This problem has applications in manufacturing and mining, and also appears as a subproblem in decomposition techniques for network design and related problems. We present a new approach for determining facets of the PCKP polyhedron based on clique i...
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This paper considers the polyhedral structure of the precedence-constrained knapsack problem, which is a knapsack problem with precedence constraints imposed on the set of variables. The problem itself appears in many applications. Moreover, since the precedence constraints appear in many important integer programming problems, the polyhedral results can be used to develop cutting-plane algorit...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1993
ISSN: 0166-218X
DOI: 10.1016/0166-218x(90)90053-f