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Multi-tier binary solution method for multi-product newsvendor problem with multiple constraints

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  • Zhang, Bin
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    Abstract

    This paper considers a multi-product newsvendor problem with multiple constraints. Multiple constraints in the problem make it more challenging to solve. Previous research has attempted to solve the problem by considering two-constraint case or/and using approximation techniques or active sets methods. The solution methods in literature for solving multi-constraint problem are limited or cumbersome. In this paper, by analyzing structural properties of the multi-constraint multi-product newsvendor problem, we develop a multi-tier binary solution method for yielding the optimal solution to the problem. The proposed method is applicable to the problem with any continuous demand distribution and more than two constraints, and its computational complexity is polynomial in the number of products. Numerical results are presented for showing the effectiveness of our method.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 218 (2012)
    Issue (Month): 2 ()
    Pages: 426-434

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    Handle: RePEc:eee:ejores:v:218:y:2012:i:2:p:426-434

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

    Related research

    Keywords: Inventory; Newsvendor; Multiple constraints; Mutiple products; Convex programming;

    References

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    1. Zhang, Bin & Du, Shaofu, 2010. "Multi-product newsboy problem with limited capacity and outsourcing," European Journal of Operational Research, Elsevier, vol. 202(1), pages 107-113, April.
    2. Zhang, Guoqing, 2010. "The multi-product newsboy problem with supplier quantity discounts and a budget constraint," European Journal of Operational Research, Elsevier, vol. 206(2), pages 350-360, October.
    3. Abdel-Malek, Layek L. & Areeratchakul, Nathapol, 2007. "A quadratic programming approach to the multi-product newsvendor problem with side constraints," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1607-1619, February.
    4. Chen, Liang-Hsuan & Chen, Ying-Che, 2010. "A multiple-item budget-constraint newsboy problem with a reservation policy," Omega, Elsevier, vol. 38(6), pages 431-439, December.
    5. Vairaktarakis, George L., 2000. "Robust multi-item newsboy models with a budget constraint," International Journal of Production Economics, Elsevier, vol. 66(3), pages 213-226, July.
    6. Zhang, Bin & Hua, Zhongsheng, 2008. "A unified method for a class of convex separable nonlinear knapsack problems," European Journal of Operational Research, Elsevier, vol. 191(1), pages 1-6, November.
    7. Choi, Sungyong & Ruszczynski, Andrzej, 2011. "A multi-product risk-averse newsvendor with exponential utility function," European Journal of Operational Research, Elsevier, vol. 214(1), pages 78-84, October.
    8. Abdel-Malek, Layek L. & Montanari, Roberto, 2005. "An analysis of the multi-product newsboy problem with a budget constraint," International Journal of Production Economics, Elsevier, vol. 97(3), pages 296-307, September.
    9. Niederhoff, Julie A., 2007. "Using separable programming to solve the multi-product multiple ex-ante constraint newsvendor problem and extensions," European Journal of Operational Research, Elsevier, vol. 176(2), pages 941-955, January.
    10. Chung, Chia-Shin & Flynn, James & Kirca, Omer, 2008. "A multi-item newsvendor problem with preseason production and capacitated reactive production," European Journal of Operational Research, Elsevier, vol. 188(3), pages 775-792, August.
    11. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    12. Shah, Janat & Avittathur, Balram, 2007. "The retailer multi-item inventory problem with demand cannibalization and substitution," International Journal of Production Economics, Elsevier, vol. 106(1), pages 104-114, March.
    13. Abdel-Malek, Layek & Montanari, Roberto & Morales, Libia Cristina, 2004. "Exact, approximate, and generic iterative models for the multi-product Newsboy problem with budget constraint," International Journal of Production Economics, Elsevier, vol. 91(2), pages 189-198, September.
    14. Zhang, Bin, 2011. "Optimal policy for a mixed production system with multiple OEM and OBM products," International Journal of Production Economics, Elsevier, vol. 130(1), pages 27-32, March.
    15. Lau, Hon-Shiang & Hing-Ling Lau, Amy, 1996. "The newsstand problem: A capacitated multiple-product single-period inventory problem," European Journal of Operational Research, Elsevier, vol. 94(1), pages 29-42, October.
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    Cited by:
    1. Zhang, Bin & Xu, Liang, 2013. "Multi-item production planning with carbon cap and trade mechanism," International Journal of Production Economics, Elsevier, vol. 144(1), pages 118-127.

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