Scheduling problems have been widely investigated over the last five decades. Production scheduling problem is an extensive problem in industrial production processes and more effective on human resource effectively, efficiency, corporations competitiveness. Most of the research has been concentrated on deterministic scheduling problems in which all problem parameters such as processing times, duedate are predetermined. In real world, however, nondeterministic and probabilistic phenomena such as machine breakdowns, prolonged jobs processing time, worker illnesses, delays in raw material delivery, and new work-in-process jobs during the execution of the scheduling plan may cause deterministic scheduling solution efficiency to loss. Several methods such as robust scheduling to solve such problems is developed. A new approach to dealing with uncertain data in a scheduling problem is the robust scheduling approach which allows one to arrange an initial schedule in such a way that any variation during the implementation of the schedule will cause the least possible changes in the initial schedule. Several types of robust scheduling problem solution approach are scenario based approach, surrogate measures, stability measures. Another one is ? - robust method which has been used probabilistic approach. Result of ? - robust approach is establishinig a schedule that maximize the probability of not exceeding objective function from deterministic amount usually determined by manager. In this thesis, we concentrate on the problem of maximizing the probability of having the total jobs processing time on identical parallel machines not exceeding a predefined value. We also assume the processing times to be probabilistic, e.g., the problem . In order to solve the problem optimally, we present several theorems whereby the search space is drastically reduced. A Branch and Bound (B am) method is also proposed whose branching procedure is particularly designed for the problem considered. A number of lemmas to determine dominant sets, a number of dominance rules, and efficient lower and upper bounds are presented to solve optimally problems with 45 jobs on 5 machines. Finally, comparisons will be made to demonstrate that the proposed method, which is especially designed to deal with several machines, is much more efficient than those designed for handling single machines.