The Pandora's Box Problem with Sequential Inspections

73 Pages Posted: 13 Mar 2021 Last revised: 17 Jun 2021

See all articles by Ali Aouad

Ali Aouad

London Business School

Jingwei Ji

University of Southern California

Yaron Shaposhnik

University of Rochester - Simon Business School

Date Written: November 6, 2020

Abstract

We study a generalized Pandora's box problem Weitzman (1979) in which boxes could be either (fully) opened for a certain fee to reveal their exact prizes, or partially opened at a reduced cost prior to being fully opened. This feature introduces a tradeoff where on one hand, partial opening provides a more accurate estimation of the box's prize without commitment to full opening, but on the other hand, overusing the option of partial opening may lead to excessive costs.

We employ an array of techniques that were used to analyze related problems to provide a comprehensive analysis which includes (1) the identification of structural properties of the optimal policy that provide insights into what drives optimal opening decisions; (2) the derivation of provably near-optimal solutions to the stochastic and online problems; and (3) an extensive numerical study designed to examine the practical effectiveness of our policies. We find that while in general, characterizing the optimal policy is difficult, certain intuitive threshold-based policies that extend Pandora's box solution are extremely effective in solving our generalized problem.

Keywords: pandora's box problem, dynamic programming, approximate algorithms

Suggested Citation

Aouad, Ali and Ji, Jingwei and Shaposhnik, Yaron, The Pandora's Box Problem with Sequential Inspections (November 6, 2020). Available at SSRN: https://ssrn.com/abstract=3726167 or http://dx.doi.org/10.2139/ssrn.3726167

Ali Aouad

London Business School ( email )

Sussex Place
Regent's Park
London, London NW1 4SA
United Kingdom

Jingwei Ji (Contact Author)

University of Southern California ( email )

3650 McClintock Ave
Los Angeles, CA 90089
United States

Yaron Shaposhnik

University of Rochester - Simon Business School ( email )

Rochester, NY 14627
United States

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