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A binary solution method for the multi-product newsboy problem with budget constraint

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  • Zhang, Bin
  • Xu, Xiaoyan
  • Hua, Zhongsheng

Abstract

Multi-product newsboy problem (MPNP) with budget constraint is a classical inventory control/management problem. However, solution methods for MPNP under general demand distributions are limited in the current literature. In this paper, by analyzing properties of the optimal solution to the MPNP with a budget constraint, we develop a solution algorithm for the constrained MPNP. The proposed algorithm is binary in nature, and is applicable to general types of demand distribution functions, discrete as well as continuous. For continuous demand distribution function, our approach can obtain the optimal or near optimal solution to the constrained MPNP with polynomial computation complexity of the o(n) order. On the other hand, for discrete demand distribution functions, it can effectively provide good approximate solution. Numerical experiments are presented to show the performance of our method.

Suggested Citation

  • Zhang, Bin & Xu, Xiaoyan & Hua, Zhongsheng, 2009. "A binary solution method for the multi-product newsboy problem with budget constraint," International Journal of Production Economics, Elsevier, vol. 117(1), pages 136-141, January.
    • Handle: RePEc:eee:proeco:v:117:y:2009:i:1:p:136-141
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    References listed on IDEAS

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    7. 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.
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    10. 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.
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    Cited by:

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    6. De Schrijver, Steven K. & Aghezzaf, El-Houssaine & Vanmaele, Hendrik, 2013. "Aggregate constrained inventory systems with independent multi-product demand: Control practices and theoretical limitations," International Journal of Production Economics, Elsevier, vol. 143(2), pages 416-423.
    7. Zhang, Bin, 2012. "Multi-tier binary solution method for multi-product newsvendor problem with multiple constraints," European Journal of Operational Research, Elsevier, vol. 218(2), pages 426-434.
    8. Mohammad A.M. Abdel-Aal & Mujahid N. Syed & Shokri Z. Selim, 2017. "Multi-product selective newsvendor problem with service level constraints and market selection flexibility," International Journal of Production Research, Taylor & Francis Journals, vol. 55(1), pages 96-117, January.
    9. Serel, Doğan A., 2012. "Multi-item quick response system with budget constraint," International Journal of Production Economics, Elsevier, vol. 137(2), pages 235-249.
    10. Layek Abdel-Malek & Pinyuan Shan & Roberto Montanari, 2020. "A Constructive Methodology to Solving the Capacitated Newsvendor Problem: an Approximate Approach," SN Operations Research Forum, Springer, vol. 1(2), pages 1-16, June.
    11. 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.
    12. Chernonog, Tatyana & Goldberg, Noam, 2018. "On the multi-product newsvendor with bounded demand distributions," International Journal of Production Economics, Elsevier, vol. 203(C), pages 38-47.
    13. 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.
    14. Murray, Chase C. & Gosavi, Abhijit & Talukdar, Debabrata, 2012. "The multi-product price-setting newsvendor with resource capacity constraints," International Journal of Production Economics, Elsevier, vol. 138(1), pages 148-158.
    15. Tahir Ekin & Nicholas G. Polson & Refik Soyer, 2017. "Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(8), pages 613-627, December.
    16. Zhang, Guoqing & Shi, Jianmai & Chaudhry, Sohail S. & Li, Xindan, 2019. "Multi-period multi-product acquisition planning with uncertain demands and supplier quantity discounts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 132(C), pages 117-140.
    17. 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.
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