Optimization of inventory control systems under uncertainty

Ills paper illustrates the fact that it is often desirable to have statistical tolerance limits for the distributions used to describe demand data in inventory control problems. We present an invariant embedding technique based on the constructive use of tile invariance principle in mathematical statistics. This technique allows one to solve many problems of the theory of statistical inferences in a simple way. The aim of the present paper is to show how the invariance principle may be employed in the particular case of finding a lower tolerance limit for the size of the stock in order to ensure an adequate service level. The illustrative examples are given.