A risk-averse newsvendor model with limited capacity and outsourcing under the CVaR criterion

Abstract

For seasonal products, the retailers usually launch various marketing efforts, like advertising and promotion, to promote them in a selling season. While facing large demand from the customers, one should take the capacity constraint and outsourcing into consideration. Considering the shorten life cycles of most products, in this paper we adopt the traditional newsvendor model to investigate the optimal marketing effort along with optimal order quantity. We address the risk aversion issue and characterize the influence of the sellers’ risk propensity with CVaR criterion, and we develop an effective algorithm to obtain the optimal strategy. The impact of sellers’ risk propensity on the performance of the system is illustrated via numerical examples. The innovation of this paper is threefold. First, the optimal joint strategy of the marketing effort and order quantity is investigated and an efficient algorithm to find the optimal strategy is developed. Second, the capacity constraint option and an outsourcing strategy are studied jointly for excess products. Finally, the risk propensity of the seller and its influence are investigated by using the CVaR criterion, through which we obtain some new managerial insights.

Keywords

Newsvendor model / marketing effort / order quantity / CVaR / capacity constraint / outsourcing

References

[1] Agrawal V, Seshadri S. Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem. Manufacturing & Service Operations Management, 2000, 2(4): 410-423.

[2] Ahmed S, Çakmak U, Shapiro A. Coherent risk measures in inventory problems. European Journal of Operational Research, 2007, 182(1): 226-238.

[3] Burke GJ, Carrillo JE, Vakharia AJ. Single versus multiple supplier sourcing strategies. European Journal of Operational Research, 2007, 182(1): 95-112.

[4] Chen F, Federgruen A. Mean-variance analysis of basic inventory models, 2000

[5] Chen J 2014. Optimal strategy of the capital-constrained retailer based on CVaR. IEEE Workshop on Electronics, Computer and Applications, 2014 383-386.

[6] Chen X, Sim M, Simchi-Levi D, Sun P. Risk aversion in inventory management. Operations Research, 2007, 55(5): 828-842.

[7] Chen YF, Xu M, Zhang ZG. Technical note — a risk-averse newsvendor model under the CVaR criterion. Operations Research, 2009, 57(4): 1040-1044.

[8] Choi S, Ruszczyński A. A risk-averse newsvendor with law invariant coherent measures of risk. Operations Research Letters, 2008, 36(1): 77-82.

[9] Eeckhoudt L, Gollier C, Schlesinger H. The risk-averse (and prudent) newsboy. Management Science, 1995, 41(5): 786-794.

[10] Erlebacher SJ. Optimal and heuristic solutions for the multi-item Newsvendor problem with capacity constraint. Production and Operations Management, 2000, 9(3): 303-318.

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

[12] Hadley G, Whitin TM. Analysis of Inventory Systems, 1963.

[13] Han Y, Zhao B, Song H M. Two-ordering newsvendor based on CVaR decision criteria with information updating. Journal of Applied Sciences, 2013, 13(23): 5611-5615.

[14] Jorion P. Value at Risk, 2006, 3rd ed. New York: McGraw-Hill

[15] Kraiselburd S, Narayanan VG, Raman A. Contracting in a supply chain with stochastic demand and substitute products. Production and Operations Management, 2004, 13(1): 46-62.

[16] Lau HS, Lau HLA. The multi-product multi-constraint newsboy problem: applications, formulation and solution. Journal of Operations Management, 1995, 13(2): 153-162.

[17] 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(2): 361-374.

[18] Qiu R, Shang J, Huang X. Robust inventory decision under distribution uncertainty: a CVaR-based optimization approach. International Journal of Production Economics, 2014, 153: 13-23.

[19] Rockafellar RT, Uryasev S. Optimization of conditional value-at-risk. Journal of Risk, 2000, 2: 21-42.

[20] Rockafellar RT, Uryasev S. Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 2002, 26(7): 1443-1471.

[21] Taaffe K, Geunes J, Romeijn HE. Target market selection and marketing effort under uncertainty: the selective newsvendor. European Journal of Operational Research, 2008, 189(3): 987-1003.

[22] Wu M, Zhu S X, Teunter R H. Newsvendor problem with random shortage cost under a risk criterion. International Journal of Production Economics, 2013, 145(2): 790-798.

[23] Wu M, Zhu S X, Teunter R H. A risk-averse competitive newsvendor problem under the CVaR criterion. International Journal of Production Economics, 2014

[24] Xanthopoulos A, Vlachos D, Iakovou E. Optimal newsvendor policies for dual-sourcing supply chains: a disruption risk management framework. Computers & Operations Research, 2012, 39(2): 350-357.

[25] Xu M. A price-setting newsvendor model under CVaR decision criterion with emergency procurement. Journal of Systems Science and Systems Engineering, 2010, 19(1): 85-104.

[26] Zhang B, Du S. Multi-product newsboy problem with limited capacity and outsourcing. European Journal of Operational Research, 2010, 202(1): 107-113.