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Production planning and inventories optimization: A backward approach in the convex storage cost case

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  • Chazal, Marie
  • Jouini, Elyès
  • Tahraoui, Rabah

Abstract

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.

Suggested Citation

  • Chazal, Marie & Jouini, Elyès & Tahraoui, Rabah, 2008. "Production planning and inventories optimization: A backward approach in the convex storage cost case," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 997-1023, September.
  • Handle: RePEc:eee:mateco:v:44:y:2008:i:9-10:p:997-1023
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    1. repec:dau:papers:123456789/360 is not listed on IDEAS
    2. Feichtinger, Gustav & Hartl, Richard, 1985. "Optimal pricing and production in an inventory model," European Journal of Operational Research, Elsevier, vol. 19(1), pages 45-56, January.
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    Cited by:

    1. Du, Juan & Liang, Liang & Chen, Yao & Bi, Gong-bing, 2010. "DEA-based production planning," Omega, Elsevier, vol. 38(1-2), pages 105-112, February.
    2. Amirteimoori, Alireza & Kordrostami, Sohrab, 2012. "Production planning in data envelopment analysis," International Journal of Production Economics, Elsevier, vol. 140(1), pages 212-218.

    More about this item

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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