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


  • Marie Chazal
  • Elyès Jouini
  • Rabah Tahraoui


As in [1], 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-differential backward equation, from which we obtain an explicit construction of the optimal plan.

Suggested Citation

  • Marie Chazal & Elyès Jouini & Rabah Tahraoui, 2003. "Production Planning and Inventories Optimization : A Backward Approach in the Convex Storage Cost Case," GE, Growth, Math methods 0312002, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpge:0312002
    Note: Type of Document - pdf; prepared on Win98; pages: 36

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    References listed on IDEAS

    1. repec:dau:papers:123456789/360 is not listed on IDEAS
    2. Arvan, Lanny & Moses, Leon N, 1982. "Inventory Investment and the Theory of the Firm," American Economic Review, American Economic Association, vol. 72(1), pages 186-193, March.
    3. Agnès Sulem, 1986. "A Solvable One-Dimensional Model of a Diffusion Inventory System," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 125-133, February.
    4. 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.
    5. Elyès Jouini & Marie Chazal & Rabah Tharaoui, 2003. "Production planning and inventories optimization with a general storage cost function," Post-Print halshs-00167148, HAL.
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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


    Production planning; inventory management; integro- differential backward equations;

    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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