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

  • Laslo, Zohar
  • Gurevich, Gregory
  • Keren, Baruch
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    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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    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
    Contact details of provider: Web page: http://www.elsevier.com/locate/ijpe

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    1. 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.
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    7. 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.
    8. 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.
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    10. 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.
    11. 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.
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