Optimality of (s,S) Inventory Policies under
Renewal Demand and General Cost Structures
We study a single-stage, continuous-time inventory model where unit-sized
demands arrive according to a renewal process and show that an (s,S)
policy is optimal under minimal assumptions on the ordering/procurement and
holding/backorder cost functions. To our knowledge, the derivation of almost
all existing (s,S)-optimality results for stochastic inventory models
assume that the ordering cost is composed of a fixed setup cost and a
proportional variable cost; in contrast, our formulation allows virtually any
reasonable ordering-cost structure. Thus, our paper demonstrates that
(s,S)-optimality actually holds in an important, primitive stochastic
setting for all other practically interesting ordering cost structures
such as well-known quantity discount schemes (e.g., all-units, incremental and
truckload), multiple setup costs, supplier-imposed size constraints (e.g.,
batch-ordering and minimum-order-quantity), arbitrary increasing and concave
cost, as well as any variants of these. It is noteworthy that our proof only
relies on elementary arguments.