A Survey of Stochastic Inventory Models with Fixed Costs : Optimality of (s, S) and (s, S)-Type Policies

Fixed costs of ordering items or setting up a process arise in many real-life scenarios. In their presence, the most widely used ordering policy in the stochastic inventory literature is the (s, S) policy. Optimality of (s, S) policies and (s, S)-type policies have been investigated for various inventory models, including those with discrete- and continuous-time reviews, finite- and infinite-time horizons, discounted- and average-cost objectives, backlogging and lost-sales settings, standard and generalized demand and cost structures, deterministic and stochastic lead times, single- and multi-product settings, and coordinated pricing-inventory decisions. This survey provides a comprehensive review of this highly mature literature dating back to 1951. We discuss model specifications, proof techniques, specific results, and limitations of the papers published on the topic. We conclude the survey by providing suggestions for extensions and directions for future research