IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2003-45.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2003-45.pdf
    File Function: Crest working paper version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    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.
    3. Dov Pekelman, 1974. "Simultaneous Price-Production Decisions," Operations Research, INFORMS, vol. 22(4), pages 788-794, August.
    4. Elyès Jouini & Marie Chazal & Rabah Tharaoui, 2003. "Production planning and inventories optimization with a general storage cost function," Post-Print halshs-00167148, HAL.
    5. repec:dau:papers:123456789/360 is not listed on IDEAS
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Xueping & Wang, Jiao & Sawhney, Rapinder, 2012. "Reinforcement learning for joint pricing, lead-time and scheduling decisions in make-to-order systems," European Journal of Operational Research, Elsevier, vol. 221(1), pages 99-109.
    2. Lihao Lu & Jianxiong Zhang & Wansheng Tang, 2016. "Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(6), pages 1480-1494, April.
    3. K Kogan & U Spiegel, 2006. "Optimal policies for inventory usage, production and pricing of fashion goods over a selling season," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(3), pages 304-315, March.
    4. Lamas, Alejandro & Chevalier, Philippe, 2018. "Joint dynamic pricing and lot-sizing under competition," European Journal of Operational Research, Elsevier, vol. 266(3), pages 864-876.
    5. Shiming Deng & Candace A. Yano, 2006. "Joint Production and Pricing Decisions with Setup Costs and Capacity Constraints," Management Science, INFORMS, vol. 52(5), pages 741-756, May.
    6. Abhijit Upasani & Reha Uzsoy, 2008. "Incorporating manufacturing lead times in joint production-marketing models: A review and some future directions," Annals of Operations Research, Springer, vol. 161(1), pages 171-188, July.
    7. Gila E. Fruchter & Hussein Naseraldin, 2021. "Coordinating Carbon Emissions via Production Quantities: A Differential Game Approach," Games, MDPI, vol. 12(1), pages 1-16, February.
    8. Erickson, Gary M., 2012. "Transfer pricing in a dynamic marketing-operations interface," European Journal of Operational Research, Elsevier, vol. 216(2), pages 326-333.
    9. Hyun-soo Ahn & Mehmet Gümüş & Philip Kaminsky, 2007. "Pricing and Manufacturing Decisions When Demand Is a Function of Prices in Multiple Periods," Operations Research, INFORMS, vol. 55(6), pages 1039-1057, December.
    10. van den Berg, A.H.J. & Herings, P.J.J. & Peters, H.J.M., 2014. "The economic order decision with continuous dynamic pricing and batch supply," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).
    11. Erickson, Gary M., 2011. "A differential game model of the marketing-operations interface," European Journal of Operational Research, Elsevier, vol. 211(2), pages 394-402, June.
    12. Fernando Alvarez & Francesco Lippi & Roberto Robatto, 2019. "Cost of Inflation in Inventory Theoretical Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 32, pages 206-226, April.
    13. Wilhelm, Wilbert E. & Xu, Kaihong, 2002. "Prescribing product upgrades, prices and production levels over time in a stochastic environment," European Journal of Operational Research, Elsevier, vol. 138(3), pages 601-621, May.
    14. Jones, Philip C. & Moses, Leon N. & Zydiak, James L., 1998. "Inventory investment, product cycles, and the imperfectly competitive firm," International Journal of Production Economics, Elsevier, vol. 54(3), pages 267-276, May.
    15. Sébastien Mitraille & Michel Moreaux, 2013. "Inventories and Endogenous Stackelberg Leadership in Two‐Period Cournot Oligopoly," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 22(4), pages 852-874, December.
    16. Kadipasaoglu, Sukran N. & Xiang, Wenuang & Hurley, Simon F. & Khumawala, Basheer M., 2000. "A study on the effect of the extent and location of protective capacity in flow systems," International Journal of Production Economics, Elsevier, vol. 63(3), pages 217-228, January.
    17. Serhan Ziya & Hayriye Ayhan & Robert D. Foley, 2004. "Relationships Among Three Assumptions in Revenue Management," Operations Research, INFORMS, vol. 52(5), pages 804-809, October.
    18. Abel Cadenillas & Peter Lakner & Michael Pinedo, 2010. "Optimal Control of a Mean-Reverting Inventory," Operations Research, INFORMS, vol. 58(6), pages 1697-1710, December.
    19. Loeffen, R.L., 2009. "An optimal dividends problem with transaction costs for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 41-48, August.
    20. Girlich, Hans-Joachim, 2003. "Transaction costs in finance and inventory research," International Journal of Production Economics, Elsevier, vol. 81(1), pages 341-350, January.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:2003-45. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.