EOQ under exogenous and periodic demand

In this paper we give a sufficient condition for the existence of the economic batch to a Wilson-type inventory model loaded by a fully exogenous continuous demand function of time. After some cases solvable in closed form, the computational problem is introduced of inverting the reordering time versus the ordered quantity as necessary step to obtain the cost function to be minimized. Such a mixed (theoretical/numerical) approach is applied to a demand consisting of three different behaviors: growth, decrease and prolonged zero. Such a wave-form is assumed to iterate itself periodically and the relevant seasonal demand is expanded in a Fourier series of time. Performing the integration and reverting the reordering time, the cost function is computed and its minimizing EOQ detected. Finally an example shows that the above conditions guarantee the existence but not uniqueness to solution.