(S − 1, S) Policies for Perishable Inventory - Schmidt, Charles P.; Nahmias, Steven (Management Science, 1985)
We consider (S − 1, S) policies for a single item whose lifetime is fixed and known with certainty. Demands are generated by a stationary Poisson process and there is a positive leadtime for replenishment. We believe this study gives the only analysis for perishables with a positive order leadtime. The analysis involves the derivation of the stationary distribution of the S-dimensional stochastic process corresponding to the time elapsed since the last S orders were placed. This distribution is then used to obtain an expression for the expected cost rate of operating the system in steady state as a function of S. A computer program has been developed to compute optimal S values and expected annual costs. We report a computation for a variety of system parameters which show some of the unusual features of the problem. Finally, we show how this model can be used in the context of a problem of optimizing availability of operating equipment subject to scheduled maintenance as well as random failure.