This work presents column generation methods for two important assignment problems: the Generalized Assignment Problem (GAP) and the problem of assigning cells to switches in cellular mobile networks (PACS). GAP is one of the most representative combinatorial optimisation problems and can be stated as the problem of optimising the assignment of n jobs to m agents, such that each job is assigned to exactly one agent and the resource capacity of each agent is not violated. PACS consists of determining a cell assignment pattern which minimizes cabling costs between a cell and a switch and transfer costs between cells assigned to different switches, while respecting certain constraints, especially those related to limited switch's capacity. The traditional column generation process is compared with the proposed algorithms that combine the column generation and lagrangean/surrogate relaxation. Computational experiments are presented in order to confirm the effectiveness of the proposed algorithms.
Combinatorial optimization; assignment problems; lagrangean; column generation
