Background: Despite the development of alternative concepts of goods flow management, the inventory management under conditions of random variations of demand is still an important issue, both from the point of view of inventory keeping and replenishment costs and the service level measured as the level of inventory availability. There is a number of inventory replenishment systems used in these conditions, but they are mostly developments of two basic systems: reorder point-based and periodic review-based. The paper deals with the latter system. Numerous researches indicate the need to improve the classical models describing that system, the reason being mainly the necessity to adapt the model better to the actual conditions. This allows a correct selection of parameters that control the used inventory replenishment system and - as a result - to obtain expected economic effects.

Methods: This research aimed at building a model of the periodic review system to reflect the relations (observed during simulation tests) between the volume of inventory shortages and the degree of accounting for so-called deferred demand, and the service level expressed as the probability of satisfying the demand in the review and the inventory replenishment cycle. The following model building and testing method has been applied: numerical simulation of inventory replenishment - detailed analysis of simulation results - construction of the model taking into account the regularities observed during the simulations - determination of principles of solving the system of relations creating the model - verification of the results obtained from the model using the results from simulation.

Results: Presented are selected results of calculations based on classical formulas and using the developed model, which describe the relations between the service level and the parameters controlling the discussed inventory replenishment system. The results are compared to the simulation results which are treated as reference. Determined are the relative errors of calculations based on formulas and the model. It is determined that the results obtained from the model have a significantly better fit.

Conclusions: The model presented in the paper should be a starting point for further works with the purpose to account for other phenomena observed during the simulation of inventory replenishment. This will allow a more accurate determination of the controlling parameters of the tested system, and also using the results to build similar models for other inventory replenishment systems used in practice.