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

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  • Marie Chazal

    (Crest)

  • Elyès Jouini

    (Crest)

  • Rabah Tahraoui

    (Crest)

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.

Suggested Citation

  • Marie Chazal & Elyès Jouini & Rabah Tahraoui, 2003. "Production Planning and Inventories Optimization : A Backward Approach in the Convex Storage Cost Case," Working Papers 2003-45, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2003-45
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    References listed on IDEAS

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    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. Dov Pekelman, 1974. "Simultaneous Price-Production Decisions," Operations Research, INFORMS, vol. 22(4), pages 788-794, August.
    6. 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.

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    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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