Reliability type inventory models based on stochastic programming

The models discussed in the present paper are generalizations of the models introduced previously by A. Prékopa [6] and M. Ziermann [13]. In the mentioned papers the initial stock level of one basic commodity is determined provided that the delivery and demand process allow certain homogeneity (in time) assumptions if they are random. Here we are dealing with more than one basic commodity and drop the time homogeneity assumption. Only the delivery processes will be assumed to be random. They will be supposed to be stochastically independent. The first model discussed in this paper was already introduced in [9]. All these models are stochastic programming models and algorithms are used to determine the initial stock levels rather than simple formulas. We have to solve nonlinear programming problems where one of the constraints is probabilistic. The function and gradient values of the corresponding constraining function are determined by simulation. A numerical example is detailed.