Customized Bundle Pricing for Information Goods: A Nonlinear Mixed-Integer Programming Approach

This paper proposes using nonlinear mixed-integer programming to solve the customized bundle-pricing problem in which consumers are allowed to choose up to N goods out of a larger pool of J goods. Prior work has suggested that this mechanism has attractive features for the pricing of information and...

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Published in:	Management science Vol. 54; no. 3; pp. 608 - 622
Main Authors:	Wu, Shin-yi, Hitt, Lorin M, Chen, Pei-yu, Anandalingam, G
Format:	Journal Article
Language:	English
Published:	Linthicum, MD INFORMS 01.03.2008 Institute for Operations Research and the Management Sciences
Series:	Management Science
Subjects:	Applied sciences Bundling Consumer behavior Consumer goods Consumer surplus Consumers Cost of sales Customers Customization customized bundle Economic profit Electronic commerce Exact sciences and technology Information Information goods Integer programming Intellectual property Marginal costs Marketing Mathematical programming Menu costs Merchants Non-linear models Nonlinear programming Operational research and scientific management Operational research. Management science Optimal pricing Price policy Pricing Pricing policies Product bundling Product management Profits Programming Reservation prices Studies Valuation Welfare United States Script nonlinear programming Customization customized bundle Commerce Mixed integer programming Non linear programming Modeling Exact solution Integer programming Bundling Uncertain system Digital goods Welfare Preference Information value information goods Pricing Firm structure Profit Incomplete information Marginal cost electronic commerce
ISSN:	0025-1909, 1526-5501
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Abstract	This paper proposes using nonlinear mixed-integer programming to solve the customized bundle-pricing problem in which consumers are allowed to choose up to N goods out of a larger pool of J goods. Prior work has suggested that this mechanism has attractive features for the pricing of information and other low-marginal cost goods. Although closed-form solutions exist for this problem for certain cases of consumer preferences, many interesting scenarios cannot be easily handled without a numerical solution procedure. In this paper, we investigate the efficiency gains created by customized bundling over the alternatives of pure bundling or individual sale under different assumptions about customer preferences and firm cost structure, as well as the potential loss of efficiency caused by pricing with incomplete information about consumer reservation values. Our analysis suggests that customized bundling enhances sellers' profits and enhances welfare when consumers do not place positive values on all goods, and that this consumer characteristic is much more important than the shape of the valuation distribution in determining the optimal pricing scheme. We also find that customized bundling outperforms both pure bundling and individual sale in the presence of incomplete information, and that customized bundling still outperforms other simpler pricing schemes even when exact consumer valuations are not known ex ante.
AbstractList	This paper proposes using nonlinear mixed-integer programming to solve the customized bundle-pricing problem in which consumers are allowed to choose up to N goods out of a larger pool of J goods. Prior work has suggested that this mechanism has attractive features for the pricing of information and other low-marginal cost goods. Although closed-form solutions exist for this problem for certain cases of consumer preferences, many interesting scenarios cannot be easily handled without a numerical solution procedure. In this paper, we investigate the efficiency gains created by customized bundling over the alternatives of pure bundling or individual sale under different assumptions about customer preferences and firm cost structure, as well as the potential loss of efficiency caused by pricing with incomplete information about consumer reservation values. Our analysis suggests that customized bundling enhances sellers' profits and enhances welfare when consumers do not place positive values on all goods, and that this consumer characteristic is much more important than the shape of the valuation distribution in determining the optimal pricing scheme. We also find that customized bundling outperforms both pure bundling and individual sale in the presence of incomplete information, and that customized bundling still outperforms other simpler pricing schemes even when exact consumer valuations are not known ex ante. [PUBLICATION ABSTRACT] This paper proposes using nonlinear mixed-integer programming to solve the customized bundle-pricing problem in which consumers are allowed to choose up to N goods out of a larger pool of J goods. Prior work has suggested that this mechanism has attractive features for the pricing of information and other low-marginal cost goods. Although closed-form solutions exist for this problem for certain cases of consumer preferences, many interesting scenarios cannot be easily handled without a numerical solution procedure. In this paper, we investigate the efficiency gains created by customized bundling over the alternatives of pure bundling or individual sale under different assumptions about customer preferences and firm cost structure, as well as the potential loss of efficiency caused by pricing with incomplete information about consumer reservation values. Our analysis suggests that customized bundling enhances sellers' profits and enhances welfare when consumers do not place positive values on all goods, and that this consumer characteristic is much more important than the shape of the valuation distribution in determining the optimal pricing scheme. We also find that customized bundling outperforms both pure bundling and individual sale in the presence of incomplete information, and that customized bundling still outperforms other simpler pricing schemes even when exact consumer valuations are not known ex ante. This paper proposes using nonlinear mixed-integer programming to solve the customized bundle-pricing problem in which consumers are allowed to choose up to N goods out of a larger pool of J goods. Prior work has suggested that this mechanism has attractive features for the pricing of information and other low-marginal cost goods. Although closed-form solutions exist for this problem for certain cases of consumer preferences, many interesting scenarios cannot be easily handled without a numerical solution procedure. In this paper, we investigate the efficiency gains created by customized bundling over the alternatives of pure bundling or individual sale under different assumptions about customer preferences and firm cost structure, as well as the potential loss of efficiency caused by pricing with incomplete information about consumer reservation values. Our analysis suggests that customized bundling enhances sellers' profits and enhances welfare when consumers do not place positive values on all goods, and that this consumer characteristic is much more important than the shape of the valuation distribution in determining the optimal pricing scheme. We also find that customized bundling outperforms both pure bundling and individual sale in the presence of incomplete information, and that customized bundling still outperforms other simpler pricing schemes even when exact consumer valuations are not known ex ante. This paper proposes using nonlinear mixed-integer programming to solve the customized bundle-pricing problem in which consumers are allowed to choose up to N goods out of a larger pool of J goods. Prior work has suggested that this mechanism has attractive features for the pricing of information and other low-marginal cost goods. Although closed-form solutions exist for this problem for certain cases of consumer preferences, many interesting scenarios cannot be easily handled without a numerical solution procedure. In this paper, we investigate the efficiency gains created by customized bundling over the alternatives of pure bundling or individual sale under different assumptions about customer preferences and firm cost structure, as well as the potential loss of efficiency caused by pricing with incomplete information about consumer reservation values. Our analysis suggests that customized bundling enhances sellers' profits and enhances welfare when consumers do not place positive values on all goods, and that this consumer characteristic is much more important than the shape of the valuation distribution in determining the optimal pricing scheme. We also find that customized bundling outperforms both pure bundling and individual sale in the presence of incomplete information, and that customized bundling still outperforms other simpler pricing schemes even when exact consumer valuations are not known ex ante. Key words: information goods; electronic commerce; customized bundle; pricing; nonlinear programming; integer programming This paper proposes using nonlinear mixed-integer programming to solve the customized bundle-pricing problem in which consumers are allowed to choose up to N goods out of a larger pool of J goods. Prior work has suggested that this mechanism has attractive features for the pricing of information and other low-marginal cost goods. Although closed-form solutions exist for this problem for certain cases of consumer preferences, many interesting scenarios cannot be easily handled without a numerical solution procedure. In this paper, we investigate the efficiency gains created by customized bundling over the alternatives of pure bundling or individual sale under different assumptions about customer preferences and firm cost structure, as well as the potential loss of efficiency caused by pricing with incomplete information about consumer reservation values. Our analysis suggests that customized bundling enhances sellers' profits and enhances welfare when consumers do not place positive values on all goods, and that this consumer characteristic is much more important than the shape of the valuation distribution in determining the optimal pricing scheme. We also find that customized bundling outperforms both pure bundling and individual sale in the presence of incomplete information, and that customized bundling still outperforms other simpler pricing schemes even when exact consumer valuations are not known ex ante. Reprinted by permission of the Institute for Operations Research and Management Science (INFORMS)
Audience	Trade Academic
Author	Anandalingam, G Wu, Shin-yi Chen, Pei-yu Hitt, Lorin M
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SubjectTerms	Applied sciences Bundling Consumer behavior Consumer goods Consumer surplus Consumers Cost of sales Customers Customization customized bundle Economic profit Electronic commerce Exact sciences and technology Information Information goods Integer programming Intellectual property Marginal costs Marketing Mathematical programming Menu costs Merchants Non-linear models Nonlinear programming Operational research and scientific management Operational research. Management science Optimal pricing Price policy Pricing Pricing policies Product bundling Product management Profits Programming Reservation prices Studies Valuation Welfare
Title	Customized Bundle Pricing for Information Goods: A Nonlinear Mixed-Integer Programming Approach
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