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Technical note: Pricing under the nested attraction model with a multistage choice structure. (English) Zbl 1329.90011

Summary: We develop a solution approach to the centralized pricing problem of a nested attraction model with a multistage tree structure. We identify conditions under which the optimal solution can be uniquely determined, and we characterize the optimal solution as a fixed point of a single variable. In the special case of a multistage nested logit model, we show the impact of asymmetry in price sensitivity and adjustment index (also known as the dissimilarity index) and we derive a closed-form solution when the tree structure is symmetric. Many existing results in the literature regarding the single or two-stage nested attraction model are shown to be special cases of the results we have derived. We show that the equal markup property, which holds for the single-stage logit model with symmetric price sensitivity, in general does not hold for products that do not share the same immediate parent node in the nested choice structure even when price sensitivities are the same for all products.

MSC:

90B05 Inventory, storage, reservoirs
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[1] Akçay Y, Natarajan HP, Xu SH (2010) Joint dynamic pricing of multiple perishable products under consumer choice. Management Sci. 56(8):1345-1361. Abstract, · Zbl 1232.91234
[2] Arcidiacono P (2005) Affirmative action in higher education: How do admission and financial aid rules affect future earnings?Econometrica 73(5):1477-1524. CrossRef · Zbl 1152.91427
[3] Aydin G, Porteus EL (2008) Joint inventory and pricing decisions for an assortment. Oper. Res. 56(5):1247-1255. Abstract, · Zbl 1167.90478
[4] Aydin G, Ryan JK (2000) Product line selection and pricing under the multinomial logit choice model. Working paper, Stanford University, Stanford, CA.
[5] Davis J, Gallego G, Topaloglu H (2014) Assortment optimization under variants of the nested logit model. Oper. Res. 62(2):250-273. Abstract, · Zbl 1295.90076
[6] Dong L, Kouvelis P, Tian Z (2009) Dynamic pricing and inventory control of substitute products. Manufacturing Service Oper. Management 11(2):317-339. Abstract,
[7] Federgruen A, Yang N (2009) Competition under generalized attraction models: Applications to quality competition under yield uncertainty. Management Sci. 55(12):2028-2043. Abstract, · Zbl 1232.91059
[8] Gallego G, Wang R (2014) Multi-product price optimization and competition under the nested logit model with product-differentiated price sensitivities. Oper. Res. 62(2):450-461. Abstract, · Zbl 1298.91087
[9] Gallego G, Huh WT, Kang W, Phillips R (2006) Price competition with the attraction demand model: Existence of unique equilibrium and its stability. Manufacturing Service Oper. Management 8(4):359-375. Abstract,
[10] Goldberg PK (1995) Product differentiation and oligopoly in international markets: The case of the U.S. automobile industry. Econometrica 63(4):891-951. CrossRef · Zbl 0836.90036
[11] Hanson W, Martin K (1996) Optimizing multinomial logit profit functions. Management Sci. 42(7):992-1003. Abstract, · Zbl 0884.90096
[12] Hausman J, Leonard G, Zona J (1994) Competitive analysis with differenciated products. Ann. Econom. Statist./Annales d’Économie et de Statistique 34:159-180.
[13] Hopp WJ, Xu X (2005) Product line selection and pricing with modularity in design. Manufacturing Service Oper. Management 7(3):172-187. Abstract,
[14] Kannan P, Wright GP (1991) Modeling and testing structured markets: A nested logit approach. Marketing Sci. 10(1):58-82. Abstract,
[15] Karnani A (1985) Strategic implications of market share attraction models. Management Sci. 31(5):536-547. Abstract, · Zbl 0609.90006
[16] Kouvelis P, Xiao Y, Yang N (2013) PBM competition in pharmaceutical supply chain: Formulary design and drug pricing. Working paper, Washington University in St. Louis, St. Louis.
[17] Li H, Huh WT (2011) Pricing multiple products with the multinomial logit and nested logit models: Concavity and implications. Manufacturing Service Oper. Management 13(4):549-563. Abstract,
[18] Li G, Rusmevichientong P, Topaloglu H (2015) The d-level nested logit model: Assortment and price optimization problems. Oper. Res. 63(2):325-342. Abstract, · Zbl 1327.90315
[19] Maddah B, Bish EK (2007) Joint pricing, assortment, and inventory decisions for a retailer’s product line. Naval Res. Logist. 54(3):315-330. CrossRef · Zbl 1149.90305
[20] McFadden D (1978) Modelling the choice of residential location. Karlquist A, Lundqvist L, Snickars F, Weibull JW, eds. Spatial Interaction Theory and Planning Models (North-Holland, Amsterdam), 75-96.
[21] McFadden D (1986) The choice theory approach to market research. Marketing Sci. 5(4):275-297. Abstract,
[22] Monahan G (1987) Strategic implications of market share attraction models. Management Sci. 33(2):228-243. Abstract, · Zbl 0611.90018
[23] Naert P, Bultez A (1973) Logically consistent market share models. J. Marketing Res. 10(3):334-340. CrossRef
[24] Naert P, Weverbergh M (1981) On the prediction power of market share attraction models. J. Marketing Res. 18(2):146-153. CrossRef
[25] Nicolau J, Más F (2008) Sequential choice behavior: Going on vacation and type of destination. Tourism Management 29(5):1023-1034. CrossRef
[26] Rayfield W, Rusmevichientong P, Topaloglu H (2015) Approximation methods for pricing problems under the nested logit model with price bounds. INFORMS J. Comput. 27(2):335-357. Abstract, · Zbl 1329.91088
[27] Song J-S, Xue Z (2007) Demand management and inventory control for substitutable products. Working paper, Duke University, Durham, NC.
[28] Su X (2008) Bounded rationality in newsvendor models. Manufacturing Service Oper. Management 10(4):566-589. Abstract,
[29] Thurner P, Eymann A (2000) Policy-specific alienation and indifference in the calculus of voting: A simultaneous model of party choice and abstention. Public Choice 102(1/2):51-77. CrossRef
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