The solution of the problem of managing the inventory of an enterprise whose activities are related to the purchase and sale of gas cylinders is considered. To solve the problem, it was necessary to investigate and choose the best inventory management strategy that provides the minimum value of the average inventory balance in the warehouse with the established upper limit of the average deficit. The problem of determining the best strategy is presented as a discrete programming problem, the required variables of which depend on the replenishment method. With a periodic replenishment strategy, the controlled variables are the volume of the delivery line and the delivery interval, with a threshold one, the minimum inventory level and the volume of the delivery line. Let’s also consider replenishment with a predicted inventory level, where the delivery level and the minimum inventory level are used as control variables. Three tabular simulation models with a given delivery time and random demand are proposed. Using the Chi-square test, it was found that the quantity demanded has a normal distribution law. By carrying out computational experiments, the optimal values of controlled variables were determined. The best objective function values were obtained using a model with a predicted inventory level and a threshold replenishment strategy. Experiments conducted on the basis of historical data have shown the advantage of the two model strategies compared to the strategy currently used in the enterprise. The use of a model with a predictable inventory level would reduce the average inventory balance by 46 %, and, consequently, save working capital. The results of the study can be useful for managers of enterprises whose activities are related to inventory management