On the Hungarian inventory control model

In this paper we recall and further develop an inventory model formulated by the author [Prékopa, A., 1965. Reliability equation for an inventory problem and its asymptotic solutions. In: Prékopa, A. (Ed.), Colloquia Applied Mathematics in Economics. Publ. House of the Hung. Acad. Sci., Budapest, pp. 317–327; Prékopa, A., 1973. Generalizations of the theorems of Smirnov with application to a reliability type inventory problem. Math. Operationsforschung und Stat. 4, 283–297] and Ziermann [Ziermann, M., 1964. Application of Smirnov’s theorems for an inventory control problem. Publications of the Mathematical Institute of the Hungarian Academy of Sciences Ser. B 8, 509–518] that has had wide application in Hungary and elsewhere. The basic assumption made in connection with this model is that the delivery of the ordered amount takes place in an interval, according to some random process, rather than at one time epoch. The problem is to determine that minimum level of safety stock, that ensures continuous production, without disruption, by a prescribed high probability. The model is further developed first by its combination with another inventory control model, the order up to S model and then, by the formulations of a static and a dynamic type stochastic programming models.