Production planning and inventories optimization with a general storage cost function

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 whereas the cost of storage has no particular properties of convexity. First, in spite of this non-convexity, we give an existence result. Second, from the necessary conditions, we derive some precise qualitative description of the optimal plan. In particular, we obtain that inventory accumulation is not optimal.