Abstract
Clusterwise pricing is characterized by prices of each brand of a category being equal in stores belonging to the same cluster. Expected sales necessary to compute profits are estimated using coefficients of a multilayer perceptron which performs better than several parametric models. Store-specific coefficients of sales response models are estimated by a MCMC method. Both assignment of stores to clusters and prices of each cluster are determined by means of improving hit-and-run, a stochastic optimization method. The objective function to be optimized includes both profits and adherence to the usual price level at individual stores. Based on empirical data on sales, prices and marginal costs of a retail chain it is demonstrated that for a moderate level of risk aversion clusterwise pricing leads to higher expected utility than micromarketing pricing with different prices of each brand across individual stores. Clusterwise pricing attains a high percentage of the profits generated by micromarketing pricing and entails lower menu costs than micromarketing pricing.
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References
Allenby GM, Rossi PE (1999) Marketing models of consumer heterogeneity. J Econom 89:57–58
Boatwright P, McCulloch R, Rossi P (1999) Account level modeling for trade promotion. An application of a constrained parameter hierarchical model. J Am Statist Assoc 94:1063–1073
Chib S, Greenberg E (1995) Understanding the Metropolis-Hastings algorithm. Am Statist 49:327–335
Chib S, Greenberg E (1996) Markov chain Monte Carlo simulation methods in econometrics. Econom Theory 12:409–431
Chintagunta PK, Dub JP, Singh V (2003) Balancing profitability and customer welfare in a supermarket chain. Quant Mark Econ 1:111–147
Cybenko G (1989) Continuous value neural networks with two hidden layers are sufficient. Math Control Signal Systems 2:303–314
Elrod T, Winer RS (1982) An empirical evaluation of aggregation criteria for developing marketing segments. J Mark 65–74
Gelfand AE (1996) Model determination using sampling-based methods. In: Gilks WR, Richardson S, Spiegelhalter DJ (eds) Markov chain Monte Carlo in practice. Chapman & Hall, Boca Raton, pp 145–161
Gelfand AE, Dey DK (1994) Bayesian model choice: asymptotics and exact calculations. J R Statist Soc Series B 56:501–514
Gelfand AE, Smith AFM, Lee TM (1992) Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling. J Am Statist Assoc 87:523–531
Gelman A, Carlin, JB, Stern HS, Rubin DB (1995) Bayesian data analysis. Chapman & Hall, London
Green PJ (1995) Reversible-jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82:711–732
Hanssens DM, Parsons LJ, Schultz RL (2001) Market Response Models Econometric and time series analysis, 2nd edn. Kluwer, Boston
Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are Universal approximators. Neural Netw 3:359–366
Kass RE, Carlin BP, Gelman A, Neal RM (1998) Markov chain Monte Carlo in practice: a roundtable discussion. Am Statist 52(2):93–100
Koop G (2003) Bayesian econometrics. Wiley, Chichester
Lancaster T (2004) An introduction to modern Bayesian econometrics. Blackwell, Oxford
Lindley DV, Smith AFM (1972) Bayes estimates for the linear model. J R Statist Society B 34:1–14
Montgomery AL (1997) Creating micro-marketing pricing strategies using supermarket scanner data. Mark Sc 16:315–337
Montgomery AL, Rossi P (1999) Estimating price elasticities with theory-based priors. J Mark Res 36:413–423
Raftery AE (1996) Hypothesis testing and model selection. In: Gilks R, Richardson S, Spiegelhalter DJ (eds.) Markov chain Monte Carlo in practice. Chapman & Hall, Boca Raton, pp 163–187
Ripley BD (1993) Statistical aspects of neural networks. In: Barndorff-Nielsen OE, Jensen JL, Kendall WS (eds) Networks and chaos—statistical and probabilistic aspects. Chapman & Hall, London, pp 40—123
Romejin HE, Smith RL (1994) Simulated annealing for constrained global optimization. J Global Optim 4:101–126
Romejin HE, Zabinskiy ZB, Graesser DL, Neogi S (1996) Simulated annealing for mixed integer/continuous global optimization. Tinbergen Institute Discussion Paper, Rotterdam and Amsterdam
Shankar V, Bolton RN (2004) An empirical analysis of determinants of retailer pricing strategy. Mark Sci 23:28–49
Sisson SA (2005) Transdimensional markov chains: a decade of progress and future perspectives. J Am Statist Assoc 100:1077–1089
Train KE (2001) A comparison of hierarchical Bayes and maximum simulated likelihood for mixed logit. Working Paper, Department of Economics, University of California, Berkeley
Train KE (2003) Discrete choice methods with simulation. Cambridge University Press, Cambridge
Zabinsky ZB, Smith RL, McDonald JF, Romejin HE, Kaufman D (1993) Improving hit-and-run for global optimization. J Global Optim 3:171–192
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H. Hruschka thanks two anonymous reviewers for their interest and their detailed helpful comments.
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Hruschka, H. Clusterwise pricing in stores of a retail chain. OR Spectrum 29, 579–595 (2007). https://doi.org/10.1007/s00291-006-0075-y
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DOI: https://doi.org/10.1007/s00291-006-0075-y