This paper studies the problem of single machine stochastic scheduling with random processing times, deterministic due dates and an independent setup time. The jobs are also deteriorated based on the position, which their processes are done. The objective function is to find a schedule of jobs, which minimizes the expected value of maximum lateness. A branch and bound scheme is presented to solve the problem analytically and a simulated annealing metaheuristic (SA) is also provided for solving the problem in larger scales. Computational experiments demonstrate that the proposed SA is capable of finding near optimal solutions with very low gap.