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Resources in grid systems are heterogeneous, geographically distributed, belong to different administrative domains and apply different management policies. Matchmaking and bidding based are two resource management models in grid systems. This paper presents the evolution of the bidding based grid resource selection mechanisms to illustrate the enhancement occurred in the bidding based process and also to highlight the main aspects and issues related to the area of grid resource management. Moreover, this paper presents a new resource management architecture to optimize the process of resource selection in the grid environment in terms of efficiency and effectiveness.