The distribution-free newsvendor problem with balking and penalties for balking and stockout

Abstract

This paper investigates the ordering policy for the newsvendor problem with customer balking and penalties for balking and stockout. Our analysis is based on the assumption that only the mean and the variance of the demand distribution are known. In contrast to the existing research, we provide a new tradeoff tool as a replacement of the traditional one to weigh the holding cost and the goodwill cost segment: the balking penalty cost and the stockout penalty cost. Specifically, in addition to the stockout penalty, we also introduce the balking penalty, provide a new proof of the optimality of robust ordering policy to guarantee that the lower bound of expected profit obtained by us is tight, and get an robust optimal order quantity which is an exact solution but not an approximate one as before. Numerical experiments are conducted to illustrate the effect of penalties for balking and stockout.

Keywords

Newsvendor problem / distribution-free / customer balking / balking penalty / stockout penalty

References

[1] Alfares HK, Elmorra HH. The distribution-free newsboy problem: Extension to the shortage penalty case. International Journal of Production Economics, 2005, 93–94: 465-477.

[2] Barron F. Payoff matrices pay off at Hallmark. Interfaces, 1985, 15(1): 20-25.

[3] Brojeswar P, Shib SS, Kripasindhu C. A distribution-free newsvendor problem with nonlinear holding cost. International Journal of Systems Science, 2013

[4] Gallego G. A min-max distribution free procedure for the (Q, R) inventory model. Operations Research Letters, 1992, 11: 55-60.

[5] Gallego G, Moon I. The distribution free newsboy problem: review and extensions. Journal of the Operational Research Society, 1993, 44(8): 825-834.

[6] Gallego G. New bounds and heuristics for (Q, r) policies. Management Science, 1998, 44(2): 219-233.

[7] Godfrey GA, Powell WB. An adaptive, distribution-free approximation for the newsvendor problem with censored demands, with applications to inventory and distribution problems. Management Science, 2001, 47(8): 1101-1112.

[8] Khouja M. The single period (newsvendor) problem: literature review and suggestions for future research. Omega, 1999, 27(5): 537-553.

[9] Kysang K, Taesu C. A minimax distribution-free procedure for a newsvendor problem with free shipping. European Journal of Operational Research, 2014, 232: 234-240.

[10] Liao Y, Banerjee A, Yan C. A distribution-free newsvendor model with balking and lost sales penalty. Int. J. Production Economics, 2011, 133: 224-227.

[11] Moon I, Choi S. Distribution free newsboy problem with balking. Journal of the Operational Research Society, 1995, 46(4): 537-542.

[12] Mostard J, Koster R, Teunter R. The distribution-free newsboy problem with resalable returns. International Journal of Production Economics, 2005, 97(3): 329-342.

[13] Natarajan K, Zhou L. A mean-variance bound for a three-piece linear function. Probab. Engrg. Informational Sci., 2007, 21(4): 611-621.

[14] Pasternack B. The newsboy problem with balking, 1990, Philadelphia: Presented at ORSA/TIMS Conference

[15] Qin Y, Wang R, Vakharia AJ, Chen Y, Seref MMH. The newsvendor problem: review and directions for future research. European Journal of Operational Research, 2011, 213: 361-374.

[16] Scarf H. Arrow K, Karlin S, Scarf H. A min-max solution of an inventory problem. Studies in The Mathematical Theory of Inventory and Production, 1958, California: Stanford University Press 201-209.

[17] Silver EA, Peterson R. Decision Systems for Inventory Management and Production Planning, 1985, 2nd ed. New York: John Wiley

[18] Yue J, Chen B, Wang M. Expected value of distribution information for the newsvendor problem. Operations Research, 2006, 54(6): 1128-1136.