BFS 2002

Poster Presentation

Production Planning and Inventory Investment for a Monopolistic Firm

Marie Chazal, Elys Jouini

We consider a monopolistic firm which produces and sells a good that can be stored. It acts in continuous time over a period [0,T] and it plans its production/sales schedule by maximizing dynamically its revenue, entailed by its sales, diminished by its production and storage costs. We assume that the firm faces a nonincreasing marginal revenue and a nondecreasing marginal production cost, but we do not assume that the marginal storage cost is monotone. Therefore the firm problem turns out to be a nonconvex optimal control problem. Yet, we give an existence result and a characterization of the solution (from which we deduce a constructive resolution of the problem when it is convex). The optimal plan consists in getting rid of the starting inventories in the best way, in particular, keeping the marginal revenue and the marginal production cost equal. Hence, if there is no initial inventory, then the firm does not exploit its storage capability.