Investing in reducing lead-time randomness in continuous-review inventory models

We consider the selection of optimal lead time variability in continuous review inventory models. The variability level is optimized jointly with the lot size and reorder point, where lower variability can be achieved at an extra cost. Low variabilities may correspond to more reliable sources or production processes, and their attainment is one of the implicit goals of JIT logistics. We analyze the resulting tri-variate models, providing sufficient conditions for joint convexity, and hence unique optimum, an algorithm and illustrative examples.