The two-dimensional knapsack problem consists in packing rectangular items into a single box such that the total value of packed is maximized. In this article, we restrict to 2-stage non-exact guillotine cut packings and consider variant with splittable items: each item can be horizontally as many times needed, may contain only portion an item. This arises semifluid items, like tubes small radi...

The maximum profit twoor three-dimensional knapsack packing problem asks to pack a maximum profit subset of some given rectangles or boxes into a larger rectangle or box of fixed dimensions. Items must be orthogonally packed, but no other restrictions are imposed to the problem. The problem could also be considered as a knapsack problem generalized to two or three dimensions. In this paper we p...

Orthogonal packing problems are natural multidimensional generalizations of the classical bin packing problem and knapsack problem and occur in many different settings. The input consists of a set I = {r1, . . . , rn} of d-dimensional rectangular items ri = (ai,1, . . . , ai,d) and a space Q. The task is to pack the items in an orthogonal and non-overlapping manner without using rotations into ...

This paper describes a new technique for solving the duration minimization in a resourceconstrained network. It is based on a transformation of the resource-constrained project scheduling problem (RCPSP) to a sequence of (multi)knapsack problem (MKP) solutions. In the first part, three deterministic approaches are summarized and their time complexity is discussed. Due to the combinatorial natur...

In this paper, we consider the multi-band robust knapsack problem which generalizes the Γ-robust knapsack problem by subdividing the single deviation band into several smaller bands. We state a compact ILP formulation and develop two dynamic programming algorithms based on the presented model where the first has a complexity linear in the number of items and the second has a complexity linear i...

We examine a situation in which a decision-maker executes a sequence of resource allocation decisions over time, but the availability of the indivisible resources at future epochs is uncertain due to actions of competitors. We cast this problem as a specialized type of stochastic knapsack problem in which the uncertainty of item (resource) availability is induced by competitors concurrently fil...