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Wine in Your Knapsack?*

Published online by Cambridge University Press:  08 June 2012

Jon M. Conrad
Affiliation:
Charles H. Dyson School of Applied Economics and Management, Cornell University, 455 Warren Hall, Ithaca, NY, 14853, email:jmc16@cornell.edu
Miguel I. Gómez
Affiliation:
Charles H. Dyson School of Applied Economics and Management, Cornell University, 246 Warren Hall, Cornell University, Ithaca, NY, 14853, email:mig7@cornell.edu
Alberto J. Lamadrid
Affiliation:
Charles H. Dyson School of Applied Economics and Management, Cornell University, 250 Warren Hall, Ithaca, NY, 14853, email: ajl259@cornell.edu

Abstract

We pose several Knapsack Problems (KPs) to select the optimal subset of wines subject to budget and quantity constraints. The first problem seeks the subset of wines, from a single cultivar (zinfandel) that maximizes the sum of ratings subject to a budget constraint. We modify this problem by adding an equality constraint on the number of bottles that must be chosen. The third problem seeks to maximize the sum of ratings from three different cultivars (cabernet sauvignon, pinot noir, and zinfandel) subject to a budget constraint and then a budget and minimum bottle constraints for each cultivar. The rating maximization problem may have multiple solutions. We also pose two expenditure minimization problems, subject to achieving the maximum sum of ratings. We extend the model by defining an integer choice problem, that allows multiple purchases of the same wine, and by accounting for possible non-linearities between wine ratings and utilities. Applications of this model include procurement decisions for tastings, special events or building a personal wine cellar. (JEL Classification: C61 D12)

Type
Articles
Copyright
Copyright © American Association of Wine Economists 2011

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References

Fourer, R., Gay, D.M. and Kernighan, B.W. (2002). AMPL: A Modeling Language for Mathematical Programming. Belmont, California: Duxbury Press.Google Scholar
Kellerer, H., Pferschy, U. and Pisinger, D. (2004). Knapsack Problems. Berlin: Springer.CrossRefGoogle Scholar
Martello, S. and Toth, P. (1990). Knapsack Problems: Algorithms and Computer Implementations. (Wiley-Interscience Series in Discrete Mathematics and Optimization). New York: John Wiley & Sons.Google Scholar
Parker, R. (2003). The Wine Advocate. Monkton, Maryland: The Wine Advocate, Inc. (online at www.erobertparker.com)Google Scholar
Srisuwannapa, C. and Charnsethikul, P. (2007). An exact algorithm for the unbounded Knapsack Problem with minimizing maximum processing time. Journal of Computer Science, 3, 138143.Google Scholar
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