Model of Optimizing the Delivery Moment Taking Into Account the Uncertainty of Demand

The majority of trade enterprises in Russia are guided by the average demand and delivery time indicators in stock management, and only a few large companies use simulation of logistics processes, which improves the efficiency and performance by reducing costs of storage and shortages. The article presents a model of stock management, or a model of determining the optimal delivery moment with due account for the uncertainty of demand. The criterion of minimizing the integral costs, with due account for the costs of excess stocks and the costs of the lack of goods in stock, is an efficiency criterion. The triangular distribution is considered as a law of random demand distribution, being one of the most appropriate in the context of insufficient statistical data. The economic mathematical model under consideration allows to optimize the delivery moment if risks are minimized, based on statistical data on the demand for goods in the previous period, or to use expert estimates if such data are not available. These data are sufficient for building a probability distribution for a random variable of demand. The model allows to determine the day of delivery for a certain amount of goods in the case of random demand if risks are minimized. In the case of a triangular distribution, this optimization problem has an analytical solution, which is reduced to formula evaluation.