This paper addresses the problem of profit-oriented disassembly line design and balancing considering partial disassembly, presence of hazardous parts and uncertainty of task processing times. Few papers have studied the stochastic disassembly line balancing problem and existing approaches have focused on heuristic and metaheuristic methods. Most existing work has concentrated on complete disassembly where task times are assumed to be normal random variables and where AND/OR graphs are not considered. The objective of this paper is the design of a serial line that obtains the maximum revenue and then balances the workload under uncertainty. The processing time of a disassembly task is assumed to be a random variable with any known probability distribution. An AND/OR graph is used to model the precedence relationships among tasks. Stochastic programming models and exact-based solution approaches combining the L-shaped algorithm and Monte Carlo sampling techniques are proposed. The relevance and applicability of the proposed models and solution methods are shown by solving efficiently a set of disassembly problem instances from the literature.