The discounted continuous-review (R,Q) inventory model with continuous and stochastic demand is investigated.  New optimality conditions are derived, clarifying the difference to the average cost case, also graphically. Supported by depreciation theory, applied to the value of a setup, the results suggest an insightful and very precise approximation – The Shrewd Accountant’s Heuristic – based on a new average-cost model. It deepens and extends the work of Hadley (1964). Three examples are worked out in detail and the model is generalized to Poisson demand and to stochastic lead-times.

The probability distribution of customer waiting times due to stock-outs and backlogging is studied, including mean and variance, when demand follows a compound Poisson process and the inventory is governed by an (nQ,R) inventory policy under continuous review. Existing results are reviewed and new exact contributions are presented, particularly covering the case when R<–1, a case that quite often may be optimal for central warehouses, but is missing in the literature. Waiting times are investigated for two cases: For an average unit of demand, assuming partial deliveries, and for a customer demanding

d units, assuming full deliveries only. Here d may be interpreted as the constant order size from a specific customer/retailer. The results are easily generalized to the waiting time of an average customer. Besides exact formulae, various approximations and simple heuristics are suggested for calculation of means and variances. The results should be valuable for approximately optimal inventory control in distribution