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

Marie Chazal (marie.chazal@yahoo.fr), Elyès Jouini (jouini@ceremade.dauphine.fr) and Rabah Tahraoui
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Rabah Tahraoui: Crest

No 2003-45, Working Papers from Center for Research in Economics and Statistics

Abstract: We study the deterministic optimization problem of a profit-maximizing firmwhich plans its sales/production schedule. The firm controls both its productionand sales rates and knows the revenue associated to a given level of sales, aswell as its production and storage costs. The revenue and the production cost areassumed to be respectively concave and convex. In [4], we provide an existence resultand derive some necessary conditions of optimality. Here, we further assumethat the storage cost is convex. This allows us to relate the optimal planningproblem to the study of a backward integro-differential equation, from which weobtain an explicit construction of the optimal plan.

Date: 2003
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Related works:
Journal Article: Production planning and inventories optimization: A backward approach in the convex storage cost case (2008)
Working Paper: Production Planning and Inventories Optimization: A Backward Approach in the Convex Storage Cost Case (2007)
Working Paper: Production Planning and Inventories Optimization: A Backward Approach in the Convex Storage Cost Case (2003)
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