Continuous-review inventory models with exponential random yield

Two continuous-review inventory systems with exponential random yields are motivated and analyzed. Both systems are characterized by jump processes of order replenishment with uniform demand rates. For the first system, exponential lead times are assumed. The strong Markov property of the inventory level process enables us to structure and then solve the model directly. In the second system, constant lead times are assumed. Here the inventory level process is not a Markov process. Thus, a dual strong Markov process with the same stationary law as that of the primal non-Markov process is constructed, and then solved. The technique used to solve the models is based on level-crossing theory. Other variants of the models are also considered.