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

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  • Laslo, Zohar
  • Gurevich, Gregory
  • Keren, Baruch
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Production Economics.

    Volume (Year): 122 (2009)
    Issue (Month): 2 (December)
    Pages: 656-662

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    Handle: RePEc:eee:proeco:v:122:y:2009:i:2:p:656-662

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    Web page: http://www.elsevier.com/locate/ijpe

    Related research

    Keywords: Chance-constrained deliveries Capability-cost tradeoffs Stochastic production capabilities (random yields) Budget allocation Quantile methods;

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    1. A. Charnes & W. W. Cooper, 1959. "Chance-Constrained Programming," Management Science, INFORMS, vol. 6(1), pages 73-79, October.
    2. Mark J. Melitz, 2002. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," NBER Working Papers 8881, National Bureau of Economic Research, Inc.
    3. 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.
    4. 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,.
    5. 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.
    6. 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.
    7. 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.
    8. Yeaple, Stephen & Helpman, Elhanan & Melitz, Marc, 2004. "Export versus FDI with Heterogeneous Firms," Scholarly Articles 3229098, Harvard University Department of Economics.
    9. Krugman, Paul, 1980. "Scale Economies, Product Differentiation, and the Pattern of Trade," American Economic Review, American Economic Association, vol. 70(5), pages 950-59, December.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
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