This work tackles the problem of task allocation in heterogeneous distributed computing systems with the goal of maximizing the system reliability. It first develops a mathematical model for reliability based on a cost function representing the unreliability caused by the execution of tasks on the system processors and the unreliability caused by the interprocessor communication costs subject to constraints imposed by both the application and the system resources. It then proposes an optimal, memory efficient, hybrid algorithm to this problem. The algorithm first finds a near optimal allocation by applying the well known simulated annealing (SA) and then finds an optimal distribution by applying the branch-and-bound (BB) technique considering the solution of the SA as the initial solution. The proposed algorithm overcomes the low solutions quality that may be obtained by using heuristics. It also overcomes the computational time complexity of the exact algorithms.