Production Planning and Inventories Optimization : A Backward Approach in the Convex Storage Cost Case

As in [1], we study the deterministic optimization problem of a profit- maximizing firm which plans its sales/production schedule. The firm knows the revenue associated to a given level of sales, as well as its production and storage costs. The revenue and the production cost are assumed to be respectively concave and convex. Here, we also assume that the storage cost is convex. This allows us to relate the optimal planning problem to the study of an integro-differential backward equation, from which we obtain an explicit construction of the optimal plan.