Dynamic Lot-Sizing in Sequential Online Retail Auctions

Posted: 11 Jun 2010

See all articles by Xi Chen

Xi Chen

affiliation not provided to SSRN

Archis Ghate

University of Washington; Independent

Arvind Tripathi

affiliation not provided to SSRN

Date Written: June 8, 2010

Abstract

Retailers often conduct non-overlapping sequential online auctions as a revenue generation and inventory clearing tool. We build a stochastic dynamic programming model for the seller’s lot-size decision problem in these auctions. The model incorporates a random number of participating bidders in each auction, allows for any bid distribution, and is not restricted to any specific price-determination mechanism. Using stochastic monotonicity/stochastic concavity and supermodularity arguments, we present a complete structural characterization of optimal lot-sizing policies under a second order condition on the single-auction expected revenue function. We show that a monotone staircase with unit jumps policy is optimal and provide a simple inequality to determine the locations of these staircase jumps. Our examples demonstrate that the second order condition is met in common online auction mechanisms.

Keywords: online auctions, dynamic programming

JEL Classification: D44, C61

Suggested Citation

Chen, Xi and Ghate, Archis and Ghate, Archis and Tripathi, Arvind, Dynamic Lot-Sizing in Sequential Online Retail Auctions (June 8, 2010). Available at SSRN: https://ssrn.com/abstract=1623725

Xi Chen

affiliation not provided to SSRN ( email )

University of Washington ( email )

Seattle, WA
United States

Arvind Tripathi

affiliation not provided to SSRN ( email )

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