IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v122y2009i2p656-662.html

Economic distribution of budget among producers for fulfilling orders under delivery chance constraints

Author

Listed:
  • Laslo, Zohar
  • Gurevich, Gregory
  • Keren, Baruch

Abstract

At a common due date, k orders with known quantities of the same product should be delivered. The product can be manufactured by n producers with stochastic production capabilities (random yields). The expected capability and its standard deviation increase linearly with the allocated budget, according to the pre-given plant's capability-cost trade-off functions. Our problem is to minimize the total budget and to determine its distribution among the producers, in order to ensure the complete fulfillment of all orders in accordance with their pre-given confidence levels (probabilities). Necessary and sufficient conditions for the existence of an optimal solution of the considered problem, as well as the proof that if the problem has a feasible solution then the optimal solution is unique, are provided. We propose a method for evaluating the optimal solution and demonstrate it through a numerical example.

Suggested Citation

  • Laslo, Zohar & Gurevich, Gregory & Keren, Baruch, 2009. "Economic distribution of budget among producers for fulfilling orders under delivery chance constraints," International Journal of Production Economics, Elsevier, vol. 122(2), pages 656-662, December.
    • Handle: RePEc:eee:proeco:v:122:y:2009:i:2:p:656-662
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925-5273(09)00220-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Parlar, Mahmut & Wang, Dan, 1993. "Diversification under yield randomness in inventory models," European Journal of Operational Research, Elsevier, vol. 66(1), pages 52-64, April.
    2. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    3. A. Charnes & W. W. Cooper, 1959. "Chance-Constrained Programming," Management Science, INFORMS, vol. 6(1), pages 73-79, October.
    4. Yunzeng Wang & Yigal Gerchak, 1996. "Periodic Review Production Models with Variable Capacity, Random Yield, and Uncertain Demand," Management Science, INFORMS, vol. 42(1), pages 130-137, January.
    5. Laslo, Zohar & Golenko-Ginzburg, Dimitri & Keren, Baruch, 2008. "Optimal booking of machines in a virtual job-shop with stochastic processing times to minimize total machine rental and job tardiness costs," International Journal of Production Economics, Elsevier, vol. 111(2), pages 812-821, February.
    6. Krugman, Paul, 1980. "Scale Economies, Product Differentiation, and the Pattern of Trade," American Economic Review, American Economic Association, vol. 70(5), pages 950-959, December.
    7. Elhanan Helpman & Marc J. Melitz & Stephen R. Yeaple, 2004. "Export Versus FDI with Heterogeneous Firms," American Economic Review, American Economic Association, vol. 94(1), pages 300-316, March.
    8. Candace Arai Yano & Hau L. Lee, 1995. "Lot Sizing with Random Yields: A Review," Operations Research, INFORMS, vol. 43(2), pages 311-334, April.
    9. Kelle, Peter & Transchel, Sandra & Minner, Stefan, 2009. "Buyer-supplier cooperation and negotiation support with random yield consideration," International Journal of Production Economics, Elsevier, vol. 118(1), pages 152-159, March.
    10. L-C Lin & K-L Hou, 2005. "An inventory system with investment to reduce yield variability and set-up cost," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(1), pages 67-74, January.
    11. Andrew J. Hogan & James G. Morris & Howard E. Thompson, 1981. "Decision Problems Under Risk and Chance Constrained Programming: Dilemmas in the Transition," Management Science, INFORMS, vol. 27(6), pages 698-716, June.
    12. Sarkar, Ashutosh & Mohapatra, Pratap K.J., 2009. "Determining the optimal size of supply base with the consideration of risks of supply disruptions," International Journal of Production Economics, Elsevier, vol. 119(1), pages 122-135, May.
    13. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
    14. Laslo, Zohar & Gurevich, Gregory, 2007. "Minimal budget for activities chain with chance constrained lead-time," International Journal of Production Economics, Elsevier, vol. 107(1), pages 164-172, May.
    15. Bruce Kogut & Nalin Kulatilaka, 1994. "Operating Flexibility, Global Manufacturing, and the Option Value of a Multinational Network," Management Science, INFORMS, vol. 40(1), pages 123-139, January.
    16. Leamer, E.E., 1995. "The Heckscher-Ohlin Model in Theory and Practice," Princeton Studies in International Economics 77, International Economics Section, Departement of Economics Princeton University,.
    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. Li, Linda & Firouz, Mohammad & Ahmed, Abdulaziz & Delen, Dursun, 2023. "On the Egalitarian–Utilitarian spectrum in stochastic capacitated resource allocation problems," International Journal of Production Economics, Elsevier, vol. 262(C).

    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. Esposito, Federico, 2022. "Demand risk and diversification through international trade," Journal of International Economics, Elsevier, vol. 135(C).
    2. Gao, Yue & Whalley, John & Ren, Yonglei, 2014. "Decomposing China's export growth into extensive margin, export quality and quantity effects," China Economic Review, Elsevier, vol. 29(C), pages 19-26.
    3. Harach, Monika & Rodriguez-Crespo, Ernesto, 2014. "Foreign direct investment and trade: A bi-directional gravity approach," Kiel Advanced Studies Working Papers 467, Kiel Institute for the World Economy.
    4. Bauer, Christian J. & Langenmayr, Dominika, 2013. "Sorting into outsourcing: Are profits taxed at a gorilla's arm's length?," Journal of International Economics, Elsevier, vol. 90(2), pages 326-336.
    5. Gel, Esma S. & Salman, F. Sibel, 2022. "Dynamic ordering decisions with approximate learning of supply yield uncertainty," International Journal of Production Economics, Elsevier, vol. 243(C).
    6. Kristian Behrens & Giordano Mion & Yasusada Murata & Jens Südekum, 2014. "Trade, Wages, And Productivity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(4), pages 1305-1348, November.
    7. Philipp J. H. Schröder & Allan Sørensen, 2014. "A Welfare Ranking of Multilateral Reductions in Real and Tariff Trade Barriers when Firms are Heterogenous," Review of International Economics, Wiley Blackwell, vol. 22(3), pages 423-443, August.
    8. Mrázová, Monika & Neary, J. Peter, 2020. "IO for exports(s)," International Journal of Industrial Organization, Elsevier, vol. 70(C).
    9. Gabriel Felbermayr & Benjamin Jung, 2011. "Sorting It Out: Technical Barriers to Trade and Industry Productivity," Open Economies Review, Springer, vol. 22(1), pages 93-117, February.
    10. Mondal, Supriyo, 2023. "International Trade and Global Value Chain: An Overview," MPRA Paper 116018, University Library of Munich, Germany.
    11. Rutger Teulings, 2017. "Brexit and The Impact of Gradual Economic Integration on Export," Tinbergen Institute Discussion Papers 17-075/VI, Tinbergen Institute.
    12. Yasuhiro Sato & Kazuhiro Yamamoto, 2007. "Trade impacts on skill formation: welfare improvements accompanied by rises in inequality," Discussion Papers in Economics and Business 07-12, Osaka University, Graduate School of Economics.
    13. Jørgensen, Jan G. & Schröder, Philipp J.H., 2008. "Fixed export cost heterogeneity, trade and welfare," European Economic Review, Elsevier, vol. 52(7), pages 1256-1274, October.
    14. Jarko Fidrmuc & Reiner Martin, 2011. "FDI, Trade and Growth in CESEE Countries," Focus on European Economic Integration, Oesterreichische Nationalbank (Austrian Central Bank), issue 1, pages 70-89.
    15. Asli Sencer Erdem & Mehmet Murat Fadilog̃lu & Süleyman Özekici, 2006. "An EOQ model with multiple suppliers and random capacity," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(1), pages 101-114, February.
    16. Baruah, Pundarikaksha, 2006. "Supply Chains Facing Atypical Demand: Optimal Operational Policies And Benefits Under Information Sharing," MPRA Paper 16101, University Library of Munich, Germany.
    17. Costas Arkolakis, 2010. "Market Penetration Costs and the New Consumers Margin in International Trade," Journal of Political Economy, University of Chicago Press, vol. 118(6), pages 1151-1199.
    18. Andrew B. Bernard & J. Bradford Jensen & Stephen J. Redding & Peter K. Schott, 2018. "Global Firms," Journal of Economic Literature, American Economic Association, vol. 56(2), pages 565-619, June.
      • Andrew B. Bernard & J. Bradford Jensen & Stephen J. Redding & Peter K. Schott, 2016. "Global Firms," NBER Working Papers 22727, National Bureau of Economic Research, Inc.
      • Redding, Stephen & Bernard, Andrew & Jensen, J Bradford & Schott, Peter, 2016. "Global Firms," CEPR Discussion Papers 11555, C.E.P.R. Discussion Papers.
      • Andrew B. Bernard & J. Bradford Jensen & Stephen J. Redding & Peter K. Schott, 2016. "Global firms," CEP Discussion Papers dp1420, Centre for Economic Performance, LSE.
    19. Andersen, Torben M. & Sørensen, Allan, 2023. "The interdependencies between the private and public sectors in open economies," European Economic Review, Elsevier, vol. 160(C).
    20. Stephen Devadoss & Jeff Luckstead, 2018. "Implications of the Comprehensive Economic and Trade Agreement for Processed Food Markets," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 66(3), pages 415-440, September.

    More about this item

    Keywords

    ;

    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:eee:proeco:v:122:y:2009:i:2:p:656-662. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijpe .

    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.