Application of Operations Research has traditionally arisen in response to solve the complex nature problems due to change in structure of human organizations, specialization in various fields and introduction of division of labour concept in each organization. In view of this, a variant Assignment Problem with the introduction of third dimension is studied in this paper. The problem is more versatile which influences the objective function. It is a mini-max combinatorial programming problem. A Lexi-Search exact algorithm based on the pattern recognition technique is developed to obtain an optimal solution and is illustrated with a numerical example. Lexi-Search method is an implicit enumeration method where it eliminates subsets of solutions called blocks which are not having an optimal feasible solution and converge fast to an optimum solution