This paper considers online stochastic reservation problems, where requests come online and must be dynamically allocated to limited resources in order to maximize profit. Multi-knapsack problems with or without overbooking are examples of such online stochastic reservations. The paper studies how to adapt the online stochastic framework and the consensus and regret algorithms proposed earlier ...

& is called a knapsack constraint. The special case of the MKP01 with %*!) is the classical knapsack problem (KP01), whose usual statement is the following. Given a knapsack of capacity and objects, each being associated a profit (gain) and a volume occupation, one wants to select + ( +, and + not fixed) objects such that the total profit is maximized and the capacity of the knapsack is not exc...

Efficient hardware/software partitioning is crucial towards realizing optimal solutions for constraint driven embedded systems. The size of the total solution space is typically quite large for this problem. In this paper, we show that the knapsack model could be employed for the rapid identification of hardware components that provide for time efficient implementations. In particular, we propo...

In this thesis a method for solving the Generalized Assignment Problem (GAP) is described. It is based on a reformulation of the original problem into a Set Partitioning Problem (SPP), in which the columns represent partial solutions to the original problem. For solving this problem, column generation, with systematic overgeneration of columns, is used. Conditions that guarantee that an optimal...

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...

Knapsack problems and variants thereof arise in several different fields from operations research to cryptography to really, really serious problems for hard−core puzzle enthusiasts. We discuss some of these and show ways in which one might formulate and solve them using Mathematica.

This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0– 1 problems. Furthermore, its tractability is highlighted. Then, an op...

A class of knapsack problems which generalizes the classical ones is studied. Algorithms based on the dynamical programming and Branch and Bound methods are proposed. The correctness and time estimation of the algorithm are given. 1 Problem formulation We study a class of knapsack problems which generalizes problems from [1-2]. The main mathematical model we shall use is formulated as follows. ...

The Lasserre/Sum-of-Squares hierarchy is a systematic procedure to strengthen LP relaxations by constructing a sequence of increasingly tight formulations. For a wide variety of optimization problems, this approach captures the convex relaxations used in the best available approximation algorithms. The capacitated covering IP is an integer program of the form min{cx : Ux ≥ d, 0 ≤ x ≤ b, x ∈ Z+}...

Abstract We consider three new knapsack problems with variable weights or profits of items, where the weight profit an item depends on position in sequence items packed knapsack. show how to solve exactly using dynamic programming algorithms pseudo-polynomial running times and propose fully polynomial-time approximation schemes for their approximate solution.