Modeling of inventory control with regenerative processes

In this paper we will discuss a general framework for single-item inventory models based on the theory of regenerative processes. After presenting without proof the main theorems for regenerative processes we analyze in detail how the different single-item models can be embedded within this general theory. This facilitates writing down the expressions for the average cost associated with an arbitrary costrate function f. Since these expressions are still complicated, involving convolutions, we use a recently developed numerically stable Laplace inversion algorithm to compute these objective functions in MATLAB©. This enables us to compute the costs instead of using approximations.