We study a discrete-time (s,S) perishable inventory model with geometric inter-demand times and batch demands. With a zero lead time and allowing backlogs, we can construct a multi-dimensional Markov chain to model the inventory-level process and obtain a closed-form cost function. Numerical computation for the discrete-time models is quite manageable. Our numerical results reveal some good properties of the cost function. By comparing our results with results from the corresponding continuous-time models, we may also conclude that discrete-time models may be used to approximate their continuous-time counterparts effectively.
