Lifting cover inequalities for the precedence-constrained knapsack problem
نویسندگان
چکیده
منابع مشابه
Lifting Cover Inequalities for the Precedence-constrained Knapsack Problem
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...
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 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 Cover Inequalities for the Binary Knapsack Polytope
We consider the family of facets of the binary knapsack polytope from minimal covers. We study previous results on sequential lifting in a unifying framework and explore a class of most violated fractional lifted cover inequalities, defined by Balas and Zemel, which are more general than traditional simple lifted cover inequalities. We investigate some theoretical properties of these inequaliti...
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: Discrete Applied Mathematics
سال: 1997
ISSN: 0166-218X
DOI: 10.1016/0166-218x(95)00113-6