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The exponomial choice model: a new alternative for assortment and price optimization. (English) Zbl 1336.91040

Summary: We investigate the use of a canonical version of a discrete choice model due to C. Daganzo [Multinomial probit. The theory and its application to demand forecasting. New York etc.: Academic Press (1979; Zbl 0476.62090)] in optimal pricing and assortment planning. In contrast to multinomial and nested logit (the prevailing choice models used for optimizing prices and assortments), this model assumes a negatively skewed distribution of consumer utilities, an assumption we motivate by conceptual arguments as well as published work. The choice probabilities in this model can be derived in closed form as an exponomial (a linear function of exponential terms). The pricing and assortment planning insights we obtain from the exponomial choice (EC) model differ from the literature in two important ways. First, the EC model allows variable markups in optimal prices that increase with expected utilities. Second, when prices are exogenous, the optimal assortment may exhibit leapfrogging in prices, i.e., a product can be skipped in favor of a lower-priced one depending on the utility positions of neighboring products. These two plausible pricing and assortment patterns are ruled out by multinomial logit (and by nested logit within each nest). We provide structural results on optimal pricing for monopoly and oligopoly cases, and on the optimal assortments for both exogenous and endogenous prices. We also demonstrate how the EC model can be easily estimated – by establishing that the log-likelihood function is concave in model parameters and detailing an estimation example using real data.

MSC:

91B24 Microeconomic theory (price theory and economic markets)
90B05 Inventory, storage, reservoirs
62P20 Applications of statistics to economics

Citations:

Zbl 0476.62090
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References:

[1] Alptekinoğlu A, Corbett CJ (2010) Leadtime–Variety tradeoff in product differentiation. Manufacturing Service Oper. Management 12(4):569-582. Link
[2] Alptekinoğlu A, Grasas A (2014) When to carry eccentric products? Optimal retail assortment under consumer returns. Production Oper. Management 23(5):877-892. CrossRef
[3] Anderson SP, de Palma A, Thisse JF (1992) Discrete Choice Theory of Product Differentiation (MIT Press, Cambridge, MA).
[4] Aydın G, Hausman WH (2009) The role of slotting fees in the coordination of assortment decisions. Production Oper. Management 18(6):635-652. CrossRef
[5] Aydın G, Porteus EL (2008) Joint inventory and pricing decisions for an assortment. Oper. Res. 56(5):1247-1255. Link · Zbl 1167.90478
[6] Ben-Akiva M, Lerman SR (1985) Discrete Choice Analysis: Theory and Application to Travel Demand (MIT Press, Cambridge, MA).
[7] Besanko D, Gupta S, Jain D (1998) Logit demand estimation under competitive pricing behavior: An equilibrium framework. Management Sci. 44(11):1533-1547. Link · Zbl 0989.90525
[8] Bhat CR (1995) A heteroscedastic extreme value model of intercity mode choice. Transportation Res. Part B 29(6):471-483. CrossRef
[9] Blattberg RC, Wisniewski KJ (1989) Price-induced patterns of competition. Marketing Sci. 8(4):291-309. Link
[10] Bohm P, Linden J, Sonnegard J (1997) Eliciting reservation prices: Becker-DeGroot-Marschak mechanisms vs. markets. Econom. J. 107(443):1079-1089.
[11] Breidert C (2005) Estimation of willingness-to-pay: Theory, measurement, and application. Doctoral thesis, WU Vienna University of Economics and Business, Vienna.
[12] Briesch RA, Dillon WR, Fox EJ (2013) Category positioning and store choice: The role of destination categories. Marketing Sci. 32(3):488-509. Link
[13] Cachon GP, Kök AG (2007) Category management and coordination in retail assortment planning in the presence of basket shopping consumers. Management Sci. 53(6):934-951. Link · Zbl 1232.91417
[14] Cachon GP, Terwiesch C, Xu Y (2005) Retail assortment planning in the presence of consumer search. Manufacturing Service Oper. Management 7(4):330-346. Link
[15] Cachon GP, Terwiesch C, Xu Y (2008) On the effects of consumer search and firm entry in a multiproduct competitive market. Marketing Sci. 27(3):461-473. Link
[16] Chaneton JM, Vulcano G (2011) Computing bid prices for revenue management under customer choice behavior. Manufacturing Service Oper. Management 13(4):452-470. Link
[17] Currim I (1982) Predictive testing of consumer choice models not subject to independence of irrelevant alternatives. J. Marketing Res. 19(2):208-222. CrossRef
[18] Daganzo C (1979) Multinomial Probit: The Theory and Its Application to Demand Forecasting (Academic Press, New York). · Zbl 0476.62090
[19] Davis JM, Gallego G, Topaloğlu H (2014) Assortment optimization under variants of the nested logit model. Oper. Res. 62(2):250-273. Link · Zbl 1295.90076
[20] Duffin RJ, Whidden P (1961) An exponomial extrapolator. J. Math. Anal. Appl. 3(3):526-536. CrossRef · Zbl 0123.12103
[21] Fosgerau M, Bierlaire M (2009) Discrete choice models with multiplicative error terms. Transportation Res. Part B 43(5):494-505. CrossRef
[22] 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. Link · Zbl 1298.91087
[23] Garbade KD, Silber WL (1976) Price dispersion in the government securities market. J. Political Econom. 84(4):721-740. CrossRef
[24] Guadagni PM, Little JDC (1983) A logit model of brand choice calibrated on scanner data. Marketing Sci. 2(3):203-238. Link
[25] Jagabathula S (2014) Assortment optimization under general choice. Working paper, New York University, New York.
[26] Kök AG, Fisher ML, Vaidyanathan R (2009) Assortment planning: Review of literature and industry practice. Agrawal N, Smith SA, eds. Retail Supply Chain Management (Springer, New York), 99-153.
[27] Koppelman FS, Bhat C (2006) A self instructing course in mode choice modeling: Multinomial and nested logit models. Technical Report, U.S. Department of Transportation, Federal Transit Administration.
[28] Koppelman FS, Sethi V (2005) Incorporating variance and covariance heterogeneity in the generalized nested logit model: An application to modeling long distance travel choice behavior. Transportation Res. Part B 39(9):825-853. CrossRef
[29] Li B (2011) The multinomial logit model revisited: A semi-parametric approach in discrete choice analysis. Transportation Res. Part B 45(3):461-473. CrossRef
[30] Li G, Rusmevichientong P, Topaloğlu H (2014) The d-level nested logit model: Assortment and price optimization problems. Oper. Res. 63(2):325-342. Link · Zbl 1327.90315
[31] 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. Link
[32] Louviere JJ, Woodworth G (1983) Design and analysis of simulated consumer choice or allocation experiments: An approach based on aggregate data. J. Marketing Res. 20(4):350-367. CrossRef
[33] Manski C, McFadden D (1981) Structural Analysis of Discrete Data (MIT Press, Cambridge, MA). · Zbl 0504.00023
[34] McFadden D (2001) Economic choices. Amer. Econom. Rev. 91(3):351-378. CrossRef
[35] Miller KM, Hofstetter R, Krohmer H, Zhang ZJ (2011) How should consumers’ willingness to pay be measured? An empirical comparison of state-of-the-art approaches. J. Marketing Res. 48(1):172-184. CrossRef
[36] Mishra VK, Natarajan K, Padmanabhan D, Teo C-P, Li X (2014) On theoretical and empirical aspects of marginal distribution choice models. Management Sci. 60(6):1511-1531. Link
[37] Natarajan K, Song M, Teo C-P (2009) Persistency model and its applications in choice modeling. Management Sci. 55(3):453-469. Link · Zbl 1232.91139
[38] Norwood FB, Luter RL, Massey RE (2005) Asymmetric willingness-to-pay distributions for livestock manure. J. Agricultural Resource Econom. 30(3):431-448.
[39] Philips Z, Whynes DK, Avis M (2006) Testing the construct validity of willingness to pay valuations using objective information about risk and health benefit. Health Econom. 15(2):195-204. CrossRef
[40] Rusmevichientong P, Topaloğlu H (2012) Robust assortment optimization in revenue management under the multinomial logit choice model. Oper. Res. 60(4):865-882. Link · Zbl 1262.90205
[41] Rusmevichientong P, Shen Z-JM, Shmoys DB (2010) Dynamic assortment optimization with a multinomial logit choice model and capacity constraint. Oper. Res. 58(6):1666-1680. Link · Zbl 1228.90170
[42] Scarpa R, Thiene M, Train K (2008) Utility in willingness to pay space: A tool to address confounding random scale effects in destination choice to the Alps. Amer. J. Agricultural Econom. 90(4):994-1010. CrossRef
[43] Shogren JF, Cho S, Koo C, List J, Park C, Polo P, Wilhelmi R (2001) Auction mechanisms and the measurement of WTP and WTA. Resource Energy Econom. 23(2):97-109. CrossRef
[44] Sinha A, Sahgal A, Mathur SK (2013) Category optimizer: A dynamic-assortment, new-product-introduction, mix-optimization, and demand-planning system. Marketing Sci. 32(2):221-228. Link
[45] Steckel JH, Vanhonacker WR (1988) A heterogeneous conditional logit model of choice. J. Bus. Econom. Statist. 6(3):391-398. CrossRef
[46] Talluri K, van Ryzin G (2004) Revenue management under a general discrete choice model of consumer behavior. Management Sci. 50(1):15-33. Link · Zbl 1168.91427
[47] Train KE (2009) Discrete Choice Methods with Simulation, 2nd ed. (Cambridge University Press, New York). CrossRef · Zbl 1269.62073
[48] van Ryzin G, Mahajan S (1999) On the relationship between inventory costs and variety benefits in retail assortments. Management Sci. 45(11):1496-1509. Link · Zbl 0953.90002
[49] Yellott JI (1977) The relationship between Luce’s choice axiom, Thurstone’s theory of comparative judgment, and the double exponential distribution. J. Math. Psych. 15(2):109-144. CrossRef · Zbl 0362.92024
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