A pegging approach to the precedence-constrained knapsack problem
نویسندگان
چکیده
منابع مشابه
A pegging approach to the precedence-constrained knapsack problem
The knapsack problem (KP) is generalized to the case where items are partially ordered through a set of precedence relations. As in ordinary KPs, each item is associated with profit and weight, the knapsack has a fixed capacity, and the problem is to determine the set of items to be packed in the knapsack. However, each item can be accepted only when all the preceding items have been included i...
متن کاملA Transitive Reduction Approach to the Precedence-Constrained Knapsack Problem
We are concerned with the precedence-constrained knapsack problem (PCKP), which is a knapsack problem defined on a directed acyclic graph (DAG). It is often the case that the original problem includes redundant constraints, and by eliminating these we obtain a PCKP of (much) smaller size. We show that such a reduction can be explained in terms of the ‘transitive reduction’ of the DAG associated...
متن کاملThe precedence constrained knapsack problem: Separating maximally violated inequalities
We consider the problem of separating maximally violated inequalities for the precedence constrained knapsack problem. Though we consider maximally violated constraints in general, special emphasis is placed on induced cover inequalities and induced clique inequalities. Our contributions include a new partial characterization of maximally violated inequalities, a new safe shrinking technique, a...
متن کاملLifting 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 ...
متن کاملExamples of new facets for the precedence constrained knapsack problem
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Operational Research
سال: 2007
ISSN: 0377-2217
DOI: 10.1016/j.ejor.2006.10.031