@conference{Imeri2026,
  author       = {A. Imeri and S.M. Disney and G. Reiner},
  title        = {Reperceiving state representation in lost-sales inventory systems},
  booktitle    = {Pre-prints of the 24th International Working Seminar of Production Economics},
  year         = {2026},
  pages        = {10 pages},
  address      = {Innsbruck, AUSTRIA},
  month        = {23th-27th February},
  url          = {xxx},
  abstract     = {We provide an explainable, demand-independent approach for solving a periodic-review inventory problem with positive lead time and lost sales. Inventory models with lost sales are challenging to optimise, especially since the current order shapes subsequent ones. This is the case when planning over a finite rolling horizon. Dynamic programming facilitates planning where problems have a sequential nature by defining state-dependent policies. In finite-horizon problems, the state is represented as the inventory level and the forecasted demand. The biggest challenge in deriving an inventory policy from such a state vector is that the number of future states increases exponentially with the possible demand, the lead time, and the planning horizon. As long as the expected costs and inventory distributions from the conditional transitions can be extracted, an explicit enumeration of all future states becomes unnecessary. We pinpoint that the number of unique inventory distributions does not necessarily grow exponentially with decision epochs and lead time. Furthermore, we propose an approach to track how the inventory distributions evolve throughout the planning horizon, along with a solution procedure for a discrete-demand setting. The procedure builds on dynamic programming. It leverages unique inventory distributions to increase the computational efficiency and is suitable for instances where demand is modelled as a non-stationary process. Since the procedure is based on enumeration, no gradient-based cost optimisation is used. This makes the approach flexible for evaluating different cost structures.}
  }