We analyse an (s, Q) inventory model with unit Poisson demand, several demand classes and lost sales. When dealing with different demand classes the usual approach is to control the inventory by critical levels at which stock is reserved for demand of higher priority. We focus on time-remembering policies where the critical levels are allowed to depend on the time since the actual outstanding order (if any) was issued. In particular, we introduce a new class of policies called restricted time-remembering (RTR) policies. We divide the lead time in m intervals of time and restrict the critical levels of the RTR policy to be constant over each interval of time. This policy is much easier to implement than the optimal rationing policy, where the critical levels can change continuously over time, and in a numerical study we show that the performance of the RTR policy is close to that of the optimal policy, even when the number of intervals is 2 or 3.
