This paper tackles a stochastic version of single machine scheduling with random processing times, deterministic due dates, independent setup times and precedence constraints. The jobs are also deteriorated based on the position at which their processes are done. The objective function is to find a schedule of jobs which minimizes the expected value of total weighted tardiness. A branch and bound scheme is presented to solve the problem analytically. Since the problem is NP-hard, it is not possible to find global optimum values for larger scales of the problem in a reasonable run time, therefore, a simulated annealing meta-heuristic (SA) is also provided to solve the larger scale problems. Computational experiments demonstrate that the proposed SA is strongly capable of finding near optimal solutions with a very low gap.