This paper attempts to determine the maximum number of storage and retrieval requests that can be handled by automated warehousing systems under physical and operational constraints. The system is formulated as a stochastic constrained optimization problem and an algorithm is developed for its solution. Due to the stochastic nature of the operation of the system, a simulation model is constructed to evaluate the system for various values of its parameters. The optimization routine interacts with the simulation model and systematically moves towards the optimum solution. The problem is studied under various levels of constraints. Also several levels of the risk of violation of constraints are examined.