Economic distribution of budget among producers for fulfilling orders under delivery chance constraints
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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,.
- 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.
- 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.
- 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.
- 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.
- A. Charnes & W. W. Cooper, 1959. "Chance-Constrained Programming," Management Science, INFORMS, vol. 6(1), pages 73-79, October.
- 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.
- 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.
- Marc J. Melitz, 2003.
"The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity,"
Econometric Society, vol. 71(6), pages 1695-1725, November.
- 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.
- Melitz, Marc J, 2002. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," CEPR Discussion Papers 3381, C.E.P.R. Discussion Papers.
- 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.
- 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.
- 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.
- 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.
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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.