4 research outputs found
The 0 -1 multiple knapsack problem
In operation research, the Multiple Knapsack Problem (MKP) is classified as a
combinatorial optimization problem. It is a particular case of the Generalized Assignment
Problem. The MKP has been applied to many applications in naval as well as financial
management. There are several methods to solve the Knapsack Problem (KP) and
Multiple Knapsack Problem (MKP); in particular the Bound and Bound Algorithm
(B&B). The bound and bound method is a modification of the Branch and Bound
Algorithm which is defined as a particular tree-search technique for the integer linear
programming. It has been used to obtain an optimal solution. In this research, we provide
a new approach called the Adapted Transportation Algorithm (ATA) to solve the KP and
MKP. The solution results of these methods are presented in this thesis. The Adapted
Transportation Algorithm is applied to solve the Multiple Knapsack Problem where the unit profit of the items is dependent on the knapsack. In addition, we will show the link
between the Multiple Knapsack Problem (MKP) and the multiple Assignment Problem
(MAP). These results open a new field of research in order to solve KP and MKP by
using the algorithms developed in transportation.Master of Science (MSc) in Computational Scienc
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