Solutions in Hadley-Whitin Q-r Models

Abstract

The Hadley-Whitin approximate Q-r models have been in existence for nearly fifteen years now and are rather Widely used by practitioners because of their simplicity and rather general applicability. There are, however, some questions regarding the characterization of solutions in these models due to the fact that the objective function is not always convex as asserted by the authors. This paper gives a complete characterization of the solutions in both the backorders model and the lost sales case for normal leadtime demand. It brings out the fact that the solution always exists in both cases but may in fact be different from the published one. A simple scheme is provided for isolating the solution in terms of the given values of the parameters for any particular application.