In this paper, we examine the problem of choosing discriminatory prices for customers with probabilistic valuations and a seller with indistinguishable copies of a good. We show that under certain assumptions this problem can be reduced to the continuous knapsack problem (CKP). We present a new fast ǫ-optimal algorithm for solving CKP instances with asymmetric concave reward functions. We also ...

In this paper we propose an approach for solving problems of optimal resource capacity allocation to a collection of stochastic dynamic competitors. In particular, we introduce the knapsack problem for perishable items, which concerns the optimal dynamic allocation of a limited knapsack to a collection of perishable or non-perishable items. We formulate the problem in the framework of Markov de...

We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly hard) instance of the knapsack problem. We provide both complexity results (size of the key, time needed to encypher/decypher...) and experimental results. Sec...

Online knapsack problem is considered, where items arrive in a sequential fashion that have two attributes; value and weight. Each arriving item has to be accepted or rejected on its arrival irrevocably. The objective is to maximize the sum of the value of the accepted items such that the sum of their weights is below a budget/capacity. Conventionally a hard budget/capacity constraint is consid...

In this paper we introduce the knapsack problem for perishable inventories concerning the optimal dynamic allocation of a collection of products to a limited knapsack. The motivation for designing such a problem comes from retail revenue management, where different products often have an associated lifetime during which they can only be sold, and the managers can regularly select some products ...

In this paper we study a particular version of the stochastic knapsack problem with normally distributed weights: the two-stage stochastic knapsack problem. In contrary to the single-stage knapsack problem, items can be added to or removed from the knapsack at the moment the actual weights come to be known (second stage). In addition, a probability constraint is introduced in the first stage in...

Many combinatorial problems involving weights can be formulated as a so-called ranged problem. That is, their input consists of a universe U , a (succinctly-represented) set family F ⊆ 2 , a weight function ω : U → {1, . . . , N}, and integers 0 ≤ l ≤ u ≤ ∞. Then the problem is to decide whether there is an X ∈ F such that l ≤ ∑ e∈X ω(e) ≤ u. Well-known examples of such problems include Knapsac...

Myasnikov et al. have introduced the knapsack problem for arbitrary finitely generated groups. In [24] the authors proved that for each graph group, the knapsack problem can be solved in NP. Here, we determine the exact complexity of the problem for every graph group. While the problem is TCcomplete for complete graphs, it is LogCFL-complete for each (non-complete) transitive forest. For every ...

In this paper, we propose the assignment problem of resources humans’ methodology by using the multiple knapsack approach to formulate the studied problem, and solve it by using the genetic algorithm for obtaining the optimal assignment of the new qualified employees that ensures the maximization the productivity by introducing constraints corresponding to the cost of each posts, and capacity o...