An optimal replenishment policy for an inventory with decaying items and a ramp in demand

We present a model of an order-level inventory system that contains items that deteriorate over time while simultaneously reacting to a ramp in demand. An optimal analytical solution is found for the ordering policy that minimizes the inventory cost. The solution is in terms of the Lambert W function, adding to the list of applications for this recently rediscovered function. The exact solutions confirm numerical approximations derived previously. The analytical solutions allow a detailed sensitivity analysis to be performed, and we present some properties of the optimal solutions in which precision issues emerge.