Исследование потоковых моделей управления запасами методом R-аппроксимации

Abstract

Purpose: It is difficult to study mathematical models of inventory management systems with on/off control when the demand has an arbitrary distribution function. The difficulty is the integral-differential equation whose solution is the probability density function of the inventory levels. Purpose: The idea is to develop methods for studying mathematical models of inventory management with an approximation of the demand distribution function. Methods: For the research of inventory control models, we build an R-approximation of the demand distribution function, similar to the hyper-exponential approximation. Results: We have built a mathematical model for the inventory management with on/off control when the rate of the product flow is continuous and the demand has an arbitrary distribution function. We have obtained a function which approximates the demand distribution. This function can be a hyper-exponential distribution, otherwise it can be a distribution but not hyper-exponential; in the third case, this function is not a distribution but still can be used. Using R-approximation, we have also obtained the probability density of the inventory levels. The simulation results showed that this method can be applied in a fairly wide area for gamma- and lognormal distribution of the demand. Practical relevance: The results can be used for modeling real inventory management systems, such as insurance companies, reservoirs, warehouses, etc. when we can estimate the three moments of the demands distribution using real data about the demand.