This paper considers the problem of grid scheduling in which different jobs are assigned to different processors, and a scheduling algorithm is devised, using tabu search, to find optimal solutions in order to maximize the number of scheduled jobs. However, inherent in the nature of the application, the processing times of jobs are not precise but are estimates that vary between minimal values, in case of premature failure of jobs, to maximal values as specified 'a priori' by well-experienced users. Fuzzy methodology becomes instrumental in this application as it allows the use of fuzzy sets to represent the processing times of jobs, modelling their uncertainty. This work presents the implementation of a tabu search algorithm to create good schedules and explores the robustness of the schedule when processing times do vary by assessing its performance in both fuzzy and crisp modes. Finally, the impact of changing the shapes of fuzzy completion times and the average job length on the schedule performance is discussed.