Date
2008
Notes
La version attachée à cette notice est la version soumise à publication.
Dewey
Economie financière
Sujet
Production Planning; Inventory Management; Integro-differential Equations
JEL code
D21; D42
Journal issue
Journal of Mathematical Economics
Volume
44
Number
9-10
Publication date
09-2008
Article pages
997-1023
Publisher
Elsevier
Author
Jouini, Elyès
Chazal, Marie
Tahraoui, Rabah
Type
Article accepté pour publication ou publié
Abstract (EN)
We study the deterministic optimization problem of a profit-maximizing firm which plans its sales/production schedule. The firm controls both its production and sales rates and 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. In Chazal et al. [Chazal, M., Jouini, E., Tahraoui, R., 2003. Production planning and inventories optimization with a general storage cost function. Nonlinear Analysis 54, 1365–1395], we provide an existence result and derive some necessary conditions of optimality. Here, we further assume that the storage cost is convex. This allows us to relate the optimal planning problem to the study of a backward integro-differential equation, from which we obtain an explicit construction of the optimal plan.