The paper is devoted to developed algorithms and methods for managing of objects in solving orthogonal packing problems of any dimensions. For description of packing schemes we use a model of potential containers which allows controlling of all existing free spaces in containers. Fast placement of objects is provided by using of a multilevel linked data structure the depth of which is equal to dimension of a considered packing problem. We propose a method of deleting orthogonal objects in any dimensional orthogonal container which will be used in realization of rearranging packing procedures. All methods and algorithms presented in the paper provide the maximal fast and right formation of placement schemes on decoding solutions obtained with any algorithms used for optimization of the cutting and packing problems. The described algorithms and methods are realized in developed applied software which will be used in future research devoted to analysis of heuristic and metaheuristic algorithms intended for optimization of one-, two- and three-dimensional orthogonal packing and rectangular cutting problems of any types.