Regenerative Inventory Systems

This is a renewal-theoretic analysis of a class of single-item inventory systems; included in a unified exposition are both continuous and periodic review systems. The book starts from the derivation of the time-dependent and stationary distributions of basic stochastic processes related to these systems and concludes with the construction and testing of simple, distribution-free approximations for optimal control policies. Its main focus is on systems with full backlogging of unfilled demand and constant lead times. Extensions to two-shipment order arrivals, ordering delays, and random lead times are also considered. The book is written both for researchers and practitioners. It can also be used as a textbook to support a graduate course in inventory theory. The level is intermediate and the style is informal. Some prior knowledge of probability theory and inventory control is assumed on the part of the reader.