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A note on “Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime”. (English) Zbl 1339.90025

Summary: In 2014, W.-C. Wang et al. [ibid. 232, No. 2, 315–321 (2014; Zbl 1305.90041)] extended the model of K.-R. Lou and W.-C. Wang [‘Optimal trade credit and order quantity when trade credit impacts on both demand rate and default risk‘”, J. Oper. Res. Soc. 64, No. 10, 1551–1556 (2012; doi:10.1057/jors.2012.134)] to incorporate the credit period dependent demand and default risk for deteriorating items with maximum lifetime. However, the rates of demand, default risk and deterioration in the model of Wang et al. [loc. cit.] are assumed to be specific functions of credit period which limits the contributions. In this note, we first generalize the theoretical results of Wang et al. [loc. cit.] under some certain conditions. Furthermore, we also present some structural results instead of a numerical analysis on variation of optimal replenishment and trade credit strategies with respect to key parameters.

MSC:

90B05 Inventory, storage, reservoirs

Citations:

Zbl 1305.90041
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References:

[1] Amir, R.; Dierker, H.; Grodal, B.; Hamilton, J.; francois Mertens, J.; Roberts, J., Supermodularity and complementarity in economics: An elementary survey, Southern Economic Journal, 71, 636-660 (2005)
[2] Cambini, A.; Martein, L., Generalized convexity and optimization: Theory and applications (2009), Springer: Springer Berlin · Zbl 1157.49001
[3] Lou, K. R.; Wang, W. C., Optimal trade credit and order quantity when trade credit impacts on both demand rate and default risk, Journal of the Operational Research Society, 64, 1551-1556 (2012)
[4] Teng, J. T.; Lou, K. R., Seller’s optimal credit period and replenishment time in a supply chain with up-stream and down-stream trade credits, Journal of Global Optimization, 53, 417-430 (2012) · Zbl 1260.90027
[5] Wang, W. C.; Teng, J. T.; Lou, K. R., Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime, European Journal of Operational Research, 232, 315-321 (2014) · Zbl 1305.90041
[6] Wu, J.; Ouyang, L. Y.; Cárdenas-Barrón, L. E.; Goyal, S. K., Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing, European Journal of Operational Research, 237, 898-908 (2014) · Zbl 1338.90037
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