Optimisation of Inventory Levels as Logistics Challenge

Inventory ensures stability of the production technical system. Production facilities have warehouses for workpieces to create final output parts, and warehouses for finished products to meet customer demand. Stocks of workpieces avoid manufacturing downtime. Stocks of finished products make it possible to meet demand in a timely manner and avoid penalties for late deliveries of finished products to consumers. On the other hand, the objects that make up the inventory are «dead» material resources that do not bring profit and negatively affect economic efficiency and competitiveness. According to published data, in economically developed countries, such as the USA, Japan, Germany and others, up to 30–40 % of production is in stocks. All this indicates the relevance of the issue of optimising the level of reserves, of solving the problem of establishing and maintaining the optimal level of the stock, its timely replenishment, considering time required for execution of applications of end users. The objective of the work is to propose a solution to a stochastic logistic problem of inventory management with a random time delay and random demand, obtained by the authors using the methods of mathematical statistics, mathematical modelling, and production logistics for unknown and arbitrary form of distribution functions of demand and time delay. The work provides specific examples of approaches to implementation of suggested solution.