Management of critical resources having uncertain consumption rates is perhaps the most common challenge encountered by businesses in discharging their numerous functions, e.g., inventory distribution, marketing, finance, production, personnel, etc. It involves making two key decisions optimally: (1) How much of each critical resource must be procured (replenishment quantity decision), and, having procured, (2) How much of each resource should be allocated among the competing entities (allocation decision). The finance/inventory literature thus far has addressed the allocation decision in an optimal fashion using certain ranking algorithms. However, the optimal replenishment decisions have not yet been addressed optimally except under a restrictive assumption called the allocation assumption. Using the illustration of a periodic-review, stochastic-demand, fixed-route, centralized, multi-echelon distribution system in this paper, we propose a non-ranking allocation policy that is faster than those existing in the literature and also develop an optimal replenishment algorithm that is independent of the allocation assumption. Furthermore, we allow our distribution system a greater flexibility than that allowed in the literature thus far--we explicitly permit fixed delivery routes, arbitrary demand distribution parameters, non-identical delivery leadtimes simultaneously with a positive order leadtime. The major empirical contribution of this work is to demonstrate, through an extensive simulation study, that computationally efficient heuristic, called the hybrid heuristic, performs close to optimal, even for the systems with high demand uncertainty. Intriguingly, the bottom line finding of our computational experiments is that while the probability of violation of the allocation assumption itself is very sensitive to the system demand uncertainty, it is relatively insensitive to the expected system inventory costs in the vicinity of the optimal region. We also develop hand- computable theoretical lower and upper bounds on system replenishment quantity and expected system cost per period that require a single Normal distribution table look-up
