In this paper we consider the multiple knapsack problem which is deened as follows: given a set N of items with weights f i , i 2 N, a set M of knapsacks with capacities F k , k 2 M, and a proot function c ik ; i 2 N; k 2 M; nd an assignment of a subset of the set of items to the set of knapsacks that yields maximum proot (or minimum cost). With every instance of this problem we associate a pol...

We consider a version of the knapsack problem in which an item size is random and revealedonly when the decision maker attempts to insert it. After every successful insertion the decisionmaker can dynamically choose the next item based on the remaining capacity and available items,while an unsuccessful insertion terminates the process. We build on a semi-infinite relaxationi...

Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in multi-agent systems and distributed systems, and can also be found as subproblems of scheduling problems. We propose bin completion, a branch-and-bound stra...

The most e¢cient algorithms for solving single criterion {0,1}-knapsack problems are based on the core concept and the core problem. However, those concepts remain unnoticed in the multiple criteria case. In this paper we bring them to this topic. A large amount of e¢cient solutions are considered for analysing the importance of the core itself and the core problem. The results show that the pr...

An employee transporting problem is described and a set partitioning model is developed. An investigation of the model leads to a knapsack problem as a surrogate problem. Finding a partition corresponding to the knapsack problem provides a solution to the problem. An exact algorithm is proposed to obtain a partition (subset-vehicle combination) corresponding to the knapsack solution. It require...

2. A teacher finds Garret, a freshman, smoking in the boys’ locker room. In accordance with school policy, the teacher completes a discipline notice and sends Garret to the principal’s office. Mr. Rodriquez, the principal, informs Garret that he has been accused of smoking in the locker room. He tells Garret that because this is his first offense, he will be suspended for three days. Mr. Rodriq...

In this paper, we study the set of 0−1 integer solutions to a single knapsack constraint and a set of non-overlapping cardinality constraints (MCKP). This set is a generalization of the traditional 0− 1 knapsack polytope and the 0− 1 knapsack polytope with generalized upper bounds. We derive strong valid inequalities for the convex hull of its feasible solutions by lifting the generalized cover...