A variant of the Hungarian inventory control model

The 'Hungarian inventory control model' was initiated by Prékopa [1965. Reliability equation for an inventory problem and its asymptotic solutions. In: Prékopa, A. (Ed.), Application of the Mathematics to Economics. Publication House of the Hungarian Academy of Science, pp. 317-327] and Ziermann [1964. Application of Smirnov's theorems for an inventory control problem. Publications of the Mathematical Institute of the Hungarian Academy of Science Series B 8, 509-518 (in Hungarian)], where the ordered amount is delivered in an interval, rather than at a time epoch according to some stochastic process and consumption takes place in the same interval. The problem is to determine the minimum level of initial safety stock that ensures continuous consumption, without disruption, in the whole time interval with a prescribed high probability. Prékopa [2006. On the Hungarian inventory control model. European Journal of Operational Research 171, 894-914] has formulated a two-stage model with such interval type processes and probabilistic constraints. In this paper we modify the assumptions of those models and formulate simpler, numerically more tractable models. We also present numerical examples.