This paper considers the total weighted tardiness minimization in a single machineenvironment (1|| wj Tj ) a scheduling problem which has been proved to be NP-Hard. The solution approach uses the Greedy Randomized Adaptive Search Procedure (GRASP) meta-heuristic known for the quality of the solutions it can generate and the selective ability of its utility function during the construction phase. This work proposes and analyses three different utility functions for the problem in question. A statistical study showed significant differences between the mean values obtained from the proposed utility functions. The computational experiments were carried out using problems instances found in the OR-LIBRARY, and the outcome of these experiments were competitive solutions compared to the best known values of the instances involved. This work also shows the ease of developing GRASP methods for solving scheduling problems in a simple spreadsheet software such as MS Excel.