Perishable inventories and queues with impatience

Excerpt

The literature about perishable inventory systems (PISs) is comprehensive and rich. This direction of research is a mainstream of inventory theory in operations management (OM). In the last four decades, hundreds of studies were published on this stream of research; many of them are reviewed in several review papers, but our attention is restricted to two comprehensive monographs—Nahmias [6] and Karaesmen et al. [5]. The author of Nahmias [6] distinguishes between two research trends of PIS: (i) models of OM in which a controller has to decide when to place an order and for how much and (ii) stochastic models of performance analysis without a controller at all. He states that from an OM point of view, only category (i) is of interest and publications like the pioneering study—Kaspi and Perry [4] and all the extensions (25–30) that stem from it, belong to category (ii) above. He claims that studies of category (ii) are queueing models with impatience. Indeed, in publications of category (ii) about PIS no controller is involved, since the input (in addition to the output) into the shelf is also random. The motivation of Kaspi and Perry [4] (and its extensions) stems from the blood bank system in which the supply of blood portions, whose shelf life is bounded, is random. The second monograph—Karaesmen et al. [5] is based on the PhD dissertation of the third author. The authors devote a comprehensive section to studies of category (ii). They review many extensions of Kaspi and Perry [4] until 2011, though, some extensions are not mentioned. In the last 15 years, the 3 coauthors (O.J. Boxma, D. Perry and W. Stadje) have been involved in research of category (ii). It is worth noting that more extensions of Kaspi and Perry [4] were published after 2011 and ongoing research is now under investigation by them. …