While lost sales systems are very relevant in practice, most scientific papers on stochastic inventory models assume backordering.
The reason for the limited attention for lost sales
systems in the scientific literature is the fact that discrete-time
inventory models with stochastic demands, a constant lead-time
and lost sales are notoriously difficult (Zipkin, 2008). The first
structural results were derived by Karlin and Scarf (1958) and