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A Weakest Link Marked Stopping Problem

Published online by Cambridge University Press:  14 July 2016

Steven A. Lippman ,
Sheldon M. Ross  and
Sridhar Seshadri
Steven A. Lippman*
Affiliation:
University of California, Los Angeles
Sheldon M. Ross*
Affiliation:
University of Southern California
Sridhar Seshadri*
Affiliation:
New York University
*
∗Postal address: Anderson Graduate School of Management, University of California, Los Angeles, CA 90095, USA.
∗∗Postal address: Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA. Email address: smross@usc.edu
∗∗∗Postal address: Department of Information, Operations, and Management Science, Leonard Stern School of Business, New York University, New York, NY 10012, USA.
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Abstract

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We consider a model in which we have k items to be sold. Potential buyers make offers in a sequential fashion. Once made, the offer is either rejected or marked for acceptance. Once k items have been marked, the items are then sold to the buyers whose offers were marked, but at a price equal to the minimum of the k marked offers. Assuming that the successive offers are independent and identically distributed according to a specified distribution and that there is a fixed cost incurred whenever an offer is rejected, we determine structural results about the optimal policy, present computational approaches for finding the optimal policy, and give some heuristic policies.

Keywords

Marked stopping problemweakest linkstructure of optimal policyonline heuristic

MSC classification

Secondary: 90C39: Dynamic programming 90C40: Markov and semi-Markov decision processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 843 - 851
Copyright
Copyright © Applied Probability Trust 2007 

References

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