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...

• Studies a novel educational context problem of personalized learning environments. Presents new precedence-constrained knapsack model with uncertain item weights. Provides efficient approximate cutting plane methods Taylor approximations. effective pre-processing procedures and cover cuts. This paper studies unique precedence constrained in which there are two available to place an the knapsa...

In this paper we adress a new cyclic problem: finding periodic schedules for unitary resource constrained cyclic scheduling problem. Such resource constraints are characterized by k, the number of types of functional units employed and mx the maximal number of processors of the same type. The main problem is to cope with both precedence delays and resources which make the problem NP-complete in...

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...

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 ...

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...

in this paper, a fully informed particle swarm (fips) algorithm is proposed for solving the multi-mode resource-constrained project scheduling problem (mrcpsp) with minimization of project makespan as the objective subject to resource and precedence constraints. in the proposed fips, a random key and the related mode list (ml) representation scheme are used as encoding schemes and the multi-mod...

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...

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...