Stochastic leadtimes in continuous‐time inventory models

Abstract

This paper shows that one of the fundamental results of inventory theory is valid under conditions much broader than those treated previously. The result characterizes the distributions of inventory level and inventory position in the standard, continuous‐time model with backorders, and leads to the relatively easy calculation of key performance measures. We treat both fixed and random leadtimes, and we examine both stationary and limiting distributions under different assumptions. We consider demand processes described by several general classes of compound‐counting processes and a variety of order policies. For the stochastic‐leadtime case we provide the first explicit proof of the result, assuming the leadtimes are generated according to a specific, but plausible, scenario.