Companies use different existing products or services to create probabilistic goods. When consumers purchase goods, they calculate their net utility based on the price of the product and thus determine their purchase behaviour. We propose a model related to opaque sales, through which we can determine the optimal price of multiple products and calculate the average profit of the firm and the average net utility of the consumer. Based on the above model, we also present a condition that allows the company to profit from all products when the consumer evaluation presents a particular distribution. This model can be used to help enterprises develop the optimal pricing strategy of products to achieve the desired profit.
Xiao-Ya Xu, Nan Zhao, Jin-Shan Zhang, Jian-Wei Yin
. Pricing Options for Multiple Quality Types of Products[J]. Journal of the Operations Research Society of China, 2026
, 14(1)
: 104
-128
.
DOI: 10.1007/s40305-024-00558-9
[1] Elmachtoub, A.N., Hamilton, M.L.: The power of opaque products in pricing. Manag. Sci. 67(8), 4686-4702(2021)
[2] Fay, S., Xie, J.: Timing of product allocation: using probabilistic selling to enhance inventory management. Manag. Sci. 61(2), 474-484(2015)
[3] Feng, B., Mao, Z., Li, H.: Choices for competing service providers with heterogeneous customers: traditional versus opaque sales modes. Omega 98, 102133(2021)
[4] Guo, X., Bian, J., Wu, P., Shi, V., Chen, H.: Probabilistic product design with regret-anticipated consumers. Int. J. Prod. Econ. 263, 108917(2023)
[5] Huang, T., Yin, Z.: Dynamic probabilistic selling when customers have boundedly rational expectations. Manuf. Serv. Oper. Manag. 23(6), 1597-1615(2021)
[6] Huang, T., Yu, Y.: Sell probabilistic goods? a behavioral explanation for opaque selling. Mark. Sci. 33(5), 743-759(2014)
[7] Huang, Y.S., Wu, T.Y., Fang, C.C., Tseng, T.L.: Decisions on probabilistic selling for consumers with different risk attitudes. Decis. Anal. 18(2), 121-138(2021)
[8] Jiang, Y.: Price discrimination with opaque products. J. Revenue Pricing Manag. 6, 118-134(2007)
[9] Pan, X.A., Honhon, D.: Assortment planning for vertically differentiated products. Prod. Oper. Manag. 21(2), 253-275(2012)
[10] Ren, H., Huang, T.: Opaque selling and inventory management in vertically differentiated markets. Manuf. Serv. Oper. Manag. 24(5), 2543-2557(2022)
[11] Rice, D.H., Fay, S.A., Xie, J.: Probabilistic selling vs. markdown selling: price discrimination and management of demand uncertainty in retailing. Int J Res Market 31(2), 147-155(2014)
[12] Sasanuma, K., Hibiki, A., Sexton, T.: An opaque selling scheme to reduce shortage and wastage in perishable inventory systems. Oper. Res. Perspect. 9, 100220(2022)
[13] Shapiro, D., Shi, X.: Market segmentation: the role of opaque travel agencies. J. Econ. Manag. Strategy 17(4), 803-837(2008)
[14] Yang, Y., Jiang, L., Schwartz, Z.: Who’s hiding? Room rate discounts in opaque distribution channels. Int. J. Hosp. Manag. 80, 113-122(2019)
[15] Zhan, D., Ward, A.R.: Staffing, routing, and payment to trade off speed and quality in large service systems. Oper. Res. 67(6), 1738-1751(2019)
[16] Zhang, J., Deng, L., Liu, H., Cheng, T.: Which strategy is better for managing multi-product demand uncertainty: Inventory substitution or probabilistic selling? Eur. J. Oper. Res. 302(1), 79-95(2022)
[17] Zhang, Y., Hua, G., Wang, S., Zhang, J., Fernandez, V.: Managing demand uncertainty: probabilistic selling versus inventory substitution. Int. J. Prod. Econ. 196, 56-67(2018)
