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

Elyès Jouini (1) , Marie Chazal (2) , Rabah Tahraoui (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 D-MATH - Department of Mathematics

As in [3], 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-di_erential backward equation, from which we obtain
an explicit construction of the optimal plan.

Mots clés: integro-dfferential backward<br />equations; Production planning; inventory management; integro-dfferential backward<br />equations.

Domaines: Economies et finances

Elyès Jouini, Marie Chazal, Rabah Tahraoui. Production Planning and Inventories Optimization: A Backward Approach in the Convex Storage Cost Case. 2007. ⟨halshs-00167156⟩