Abstract
In this paper, we focus on a production-distribution system consists of a producer and a distribution center. We formulate a bilevel multiobjective programming model for it. The upper model is to maximize the producer’s profit and the lower model is to maximize both the distribution center’s profit and customers’ satisfaction degree. Some decision parameters, including unit production cost, customers’ demand and unit sale price, are assumed as fuzzy random variables due to complex decision environment. Chance-constrained technique are used to tackle the uncertainty of this model. A modified genetic algorithm is be used to solve the problem. A numerical example illustrates the effectiveness and efficiency of the model and the algorithm.
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References
Aliev R, Fazlollahi B et al (2007) Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management. Inf Sci 177(20):4241–4255
Bard J (1984) Optimality conditions for the bilevel programming problem. Naval Res Logistics Q 31(1):13–26
Ben-Ayed O, Blair CE (1990) Computational difficulties of bilevel linear programming. Oper Res 38(3):556–560
Boudia M, Prins C (2009) A memetic algorithm with dynamic population management for an integrated production-distribution problem. Eur J Oper Res 195(3):703–715
Charnes A, Cooper WW (1959) Chance-constrained programming. Manage Sci 6(1):73–79
Dempe S, Gadhi N (2010) Second order optimality conditions for bilevel set optimization problems. J Global Optim 47(2):233–245
Gil M (2001) Fuzzy random variables. Inf Sci 133:1–2
Hu T, Guo X et al (2010) A neural network approach for solving linear bilevel programming problem. Knowl-Based Syst 23(3):239–242
Kwakernaak H (1978) Fuzzy random variables-I. Definitions and theorems. Inf Sci 15(1):1–29
Kwakernaak H (1979) Fuzzy random variables-II. Algorithms and examples for the discrete case. Inf Sci 17(3):253–278
López-Diaz M, Gil M (1997) Constructive definitions of fuzzy random variables. Stat Probab Lett 36(2):135–143
Luhandjula M (1996) Fuzziness and randomness in an optimization framework. Fuzzy Sets Syst 77(3):291–297
Lukač Z, Šorić K, Rosenzweig V (2008) Production planning problem with sequence dependent setups as a bilevel programming problem. Eur J Oper Res 187(3):1504–1512
Puri M, Ralescu D (1986) Fuzzy random variables. J Math Anal Appl 114(2):409–422
Vicente L, Savard G, Júdice J (1994) Descent approaches for quadratic bilevel programming. J Optim Theory Appl 81(2):379–399
Yan C, Banerjee A, Yang L (2011) An integrated production-distribution model for a deteriorating inventory item. Int J Prod Econ 133(1):228–232
Acknowledgments
This research was supported by the Programs of NSFC (Grant No. 70831005, 71273036, 71302134), Projects of International Cooperation and Exchanges NSFC (Grant No. 71011140076), the Research Foundation of Ministry of Education for the Doctoral Program of Higher Education of China (Grant No. 20130181110063), “985” Program of Sichuan University (Innovative Research Base for Economic Development and Management), Sichuan University Young Teachers Scientific Research Start Funds (Grant No. 2012SCU11016) and the Key Program of Sichuan System Science and Enterprise Development Research Center (Grant No.Xq13B04).
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Tao, Z., Qian, X. (2014). A Bilevel Programming Model for an Agriculture Production-Distribution System with Fuzzy Random Parameters. In: Xu, J., Cruz-Machado, V., Lev, B., Nickel, S. (eds) Proceedings of the Eighth International Conference on Management Science and Engineering Management. Advances in Intelligent Systems and Computing, vol 280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55182-6_6
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DOI: https://doi.org/10.1007/978-3-642-55182-6_6
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