Derivation of confidence intervals of service measures in a base-stock inventory control system with low-frequent demand

We explore a base-stock system with backlogging where the demand process is a compound renewal process and the compound element is a delayed geometric distribution. For this setting it holds that the long-run average service measures order fill rate (OFR) and volume fill rate (VFR) are equal in values. However, though equal ex ante one will ex post observe differences as actual sample paths are different. By including a low-frequency assumption in the model, we are able to derive mathematical expressions of the confidence intervals one will get if OFR and VFR are estimated in a simulation using the regenerative method. Through numerical examples we show that of the two service measures it is OFR that in general can be estimated most accurately. However, simulation results show that the opposite conclusion holds if we instead consider finite-horizon service measures, namely per-cycle variants of OFR and VFR.