ABOUT PROBABILISTIC ANALOGUE OF WILSON'S MODEL FOR DETERMINING THE OPTIMAL SIZE OF DELIVERY OF A GOODS PARTY

Introduction. Wilson's classical model in the theory of inventory management and its various generalizations still continues to play an important role in the theory and practice of logistics management. In particular, its development in the following areas is of great theoretical and practical interest: taking into account possible risks associated with a variation in the timing of deliveries of ordered consignments of goods to a supply company, as well as a random fluctuation in demand for goods; joint planning by a supply company for the purchase of goods and their delivery to consumers by vehicles; study the impact of the firm's procurement policy on the organization of the production process at consumer enterprises. This paper is devoted to the analysis of possible approaches to solving the problem related to the first of the above directions and based on the application of queuing theory methods. Goal. The construction and analysis of a generalized Wilson model for the case when the length of time from the moment of placing the order for the delivery of goods to the delivery itself is a random variable with an arbitrary distribution function. Results. The stochastic model is proposed for lot size of good optimization which supply firm orders at a vendor taking into account a random time of good delivery. The model generalizes the classic Wilson formula for determination of optimal lot size. The model is built with the help of storage and queueing theories methods. The inventory control system is analyzed in steady-state regime of functioning. The objective function is total mean current costs of supply firm for order of good, its storage, and for market losses because of temporal absence of good in warehouse. For the case one kind of good the generalized Wilson formula is obtained. For the case of several kinds of good the corresponding optimization problem for optimal lot sizes determination has been formulated. Conclusions. The paper shows that to take into account the randomness of the lead time for the delivery of a consignment, you can use a combination of the stock theory apparatus and queue theory. Moreover, the Wilson formula for one type of product has the same simple form as for the case of zero lead time. The approach used above can be used to analyze a more general situation, when the demand for goods is also a random variable, which is more consistent with logistic practice.