Production planning and inventories optimization: A backward approach in the convex storage cost case. (English) Zbl 1142.90302

Summary: 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 an earlier paper [Nonlinear Anal., Theory Methods Appl. 54A, No. 8, 1365–1395 (2003; Zbl 1064.90013)], we provided 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.


90B05 Inventory, storage, reservoirs
90B30 Production models
91B38 Production theory, theory of the firm


Zbl 1064.90013
Full Text: DOI Link


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