Reaping the Benefits of Bundling under High Production Costs

40 Pages Posted: 8 Dec 2015 Last revised: 10 Sep 2016

See all articles by Will Ma

Will Ma

Massachusetts Institute of Technology (MIT)

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Date Written: September 8, 2016


It has long been known in the economics literature that selling different goods in a single bundle can significantly increase revenue, even when the valuations for the goods are independent. However, bundling is no longer profitable if the goods have high production costs. To overcome this issue, we introduce Pure Bundling with Disposal for Cost (PBDC), where after buying the bundle, we allow the customer to return any subset of items for their production cost. We demonstrate using classical examples that PBDC captures the concentration effects of bundling while allowing for the flexibility of individual sales, extracting all of the consumer welfare in situations where previous simple mechanisms could not.

Furthermore, we prove a theoretical guarantee on the performance of PBDC that holds for arbitrary independent distributions, using techniques from the mechanism design literature. We transform the problem with costs to a problem with negative valuations, extend the mechanism design techniques to negative valuations, and use the Core-Tail decomposition of Babaioff et al. from [BILW14] to show that either PBDC or individual sales will obtain at least 1/5.2 of the optimal profit. This also improves the bound of 1/6 from [BILW14]. We advance the upper bound as well, constructing two IID items with zero cost where mixed bundling earns 1.19 more revenue than either pure bundling or individual sales.

Our numerical experiments show that PBDC outperforms all other simple pricing schemes, including the Bundle-Size Pricing (BSP) introduced by Chu et al. in [CLS11], under the same families of distributions used in [CLS11]. We also provide the first theoretical explanation for some of the great experimental successes in [CLS11]. All in all, our work shows establishes PBDC as a robust, computationally-minimal heuristic that is easy to market to the customer.

Keywords: revenue management, monopolist pricing, bundling, marketing, Bayesian mechanism design

Suggested Citation

Ma, Will and Simchi-Levi, David, Reaping the Benefits of Bundling under High Production Costs (September 8, 2016). Available at SSRN: or

Will Ma

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

David Simchi-Levi (Contact Author)

Massachusetts Institute of Technology (MIT) - School of Engineering ( email )

United States

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