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Analysis of the newsboy problem with fuzzy demands and incremental discounts

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  • Chen, Shih-Pin
  • Ho, Yann-Horng

Abstract

This paper proposes an analysis method for the single-period (newsboy) inventory problem with fuzzy demands and incremental quantity discounts. In fuzzy environments, the availability of the quantity discount makes the analysis of the associated model more complex. The proposed analysis method is based on ranking fuzzy number and optimization theory. By applying the Yager ranking method, the fuzzy total cost functions with different unit purchasing costs are transformed into convex piecewise nonlinear functions. To effectively and efficiently find the optimal inventory policy, the proofs of two properties regarding the relative position between the price break and minimums of these nonlinear functions are proposed. The closed-form solutions to the optimal order quantities are also derived. Four cases of a numerical example are solved to demonstrate the validity of the proposed analysis method. It is clear that the proposed methodology is applicable to further cases with different types of quantity discounts and other more complicated cases. More importantly, managerial implications are also provided for decision-makers' references.

Suggested Citation

  • Chen, Shih-Pin & Ho, Yann-Horng, 2011. "Analysis of the newsboy problem with fuzzy demands and incremental discounts," International Journal of Production Economics, Elsevier, vol. 129(1), pages 169-177, January.
  • Handle: RePEc:eee:proeco:v:129:y:2011:i:1:p:169-177
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    References listed on IDEAS

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    2. Amid, Amin & Ghodsypour, S.H. & O'Brien, Christopher, 2009. "A weighted additive fuzzy multiobjective model for the supplier selection problem under price breaks in a supply Chain," International Journal of Production Economics, Elsevier, vol. 121(2), pages 323-332, October.
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    4. Shi, Jianmai & Zhang, Guoqing, 2010. "Multi-product budget-constrained acquisition and pricing with uncertain demand and supplier quantity discounts," International Journal of Production Economics, Elsevier, vol. 128(1), pages 322-331, November.
    5. Ishii, Hiroaki & Konno, Tutomu, 1998. "A stochastic inventory problem with fuzzy shortage cost," European Journal of Operational Research, Elsevier, vol. 106(1), pages 90-94, April.
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    9. Giannoccaro, Ilaria & Pontrandolfo, Pierpaolo & Scozzi, Barbara, 2003. "A fuzzy echelon approach for inventory management in supply chains," European Journal of Operational Research, Elsevier, vol. 149(1), pages 185-196, August.
    10. Mostard, Julien & de Koster, Rene & Teunter, Ruud, 2005. "The distribution-free newsboy problem with resalable returns," International Journal of Production Economics, Elsevier, vol. 97(3), pages 329-342, September.
    11. Mula, J. & Poler, R. & Garcia-Sabater, J.P. & Lario, F.C., 2006. "Models for production planning under uncertainty: A review," International Journal of Production Economics, Elsevier, vol. 103(1), pages 271-285, September.
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    Cited by:

    1. Guo, Peijun & Ma, Xiuyan, 2014. "Newsvendor models for innovative products with one-shot decision theory," European Journal of Operational Research, Elsevier, vol. 239(2), pages 523-536.
    2. Su, Rung Hung & Pearn, Wen Lea, 2011. "Product selection for newsboy-type products with normal demands and unequal costs," International Journal of Production Economics, Elsevier, vol. 132(2), pages 214-222, August.
    3. repec:eee:joreco:v:31:y:2016:i:c:p:239-245 is not listed on IDEAS
    4. repec:spr:ijsaem:v:8:y:2017:i:4:d:10.1007_s13198-016-0557-5 is not listed on IDEAS
    5. He, Zhou & Wang, Shouyang & Cheng, T.C.E., 2013. "Competition and evolution in multi-product supply chains: An agent-based retailer model," International Journal of Production Economics, Elsevier, vol. 146(1), pages 325-336.

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