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\begin{document}
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%\DOI{10.1287/xxxx.0000.0000}%

% Author's names for the running heads
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% \RUNAUTHOR{Jones and Wilson}
% \RUNAUTHOR{Jones, Miller, and Wilson}
% \RUNAUTHOR{Jones et al.} % for four or more authors
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\RUNAUTHOR{ Aouad, Ji, and Shaposhnik }

% Title or shortened title suitable for running heads. Sample:
% \RUNTITLE{Predictive Maintenance in Manufacturing}
% Enter the (shortened) title:
\RUNTITLE{The Pandora's Box Problem with Sequential Inspections}

% Full title. Sample:
% \TITLE{Optimal Resource Allocation in Humanitarian Logistics: A Stochastic Programming Approach}
% Enter the full title:
\TITLE{The Pandora's Box Problem \\ with Sequential Inspections}

% Block of authors and their affiliations starts here:
% NOTE: Authors with same affiliation, if the order of authors allows,
%   should be entered in ONE field, separated by a comma.
%   \EMAIL field can be repeated if more than one author
\ARTICLEAUTHORS{%
%\AUTHOR{John Doe,\textsuperscript{a} Jane Smith,\textsuperscript{b}}
%\AFF{\textsuperscript{a}Department of Industrial Engineering, University of XYZ, \EMAIL{john.doe@xyz.edu; \textsuperscript{b}Department of Computer Science, University of ABC, \EMAIL{jane.smith@abc.edu}} 
\AUTHOR{Ali Aouad}
\AFF{Sloan School of Management, Massachusetts Institute of Technology, \EMAIL{maouad@mit.edu}} %, \URL{}}
\AUTHOR{Jingwei Ji}
\AFF{Management Science and Engineering, Stanford University, \EMAIL{jingwei.ji@stanford.edu}} %, \URL{}}
\AUTHOR{Yaron Shaposhnik}
\AFF{Simon Business School, University of Rochester, \EMAIL{yaron.shaposhnik@simon.rochester.edu} }
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} % end of the block

\ABSTRACT{%
The Pandora's box problem \citep{weitzman1979optimal}  is a core model in economic theory that captures an agent's (Pandora's) search for the best alternative (box).
We study an important generalization of the problem where the agent can either {\em fully open} boxes for a certain fee to reveal their exact values or {\em partially open} them at a reduced cost. This introduces a new tradeoff between information acquisition and cost efficiency.
We establish a hardness result and employ an array of techniques in stochastic optimization to provide a comprehensive analysis of this model. This includes (1) the identification of structural properties of the optimal policy that provide insights about optimal decisions; (2) the derivation of problem relaxations and provably near-optimal solutions; 
(3) the characterization of the optimal policy in special yet non-trivial cases; and (4) an extensive numerical study that compares the performance of various policies, and which provides additional insights about the optimal policy. Throughout, we show that intuitive threshold-based policies that extend the Pandora's box optimal solution can effectively guide search decisions. 
}%

% \FUNDING{This research was supported by [grant number, funding agency].}

%Supplemental Material:
%Data Ethics & Reproducibility Note:

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%\KEYWORDS{Stochastic programming, Decision support,Uncertainty, Disaster response, Optimization}

% Fill in data. If unknown, outcomment the field
\KEYWORDS{Pandora's box problem, dynamic programming, approximate algorithms} 
%\HISTORY{Received: Month DD, YYYY; Accepted: Month DD, YYYY; Published Online: Month DD, YYYY}

\maketitle

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\input{main_body/introduction}

\input{main_body/problem_formulation}

\input{main_body/characterization_optimal_policy}

\input{main_body/apx_algos}

\input{main_body/numerical}


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% Acknowledgments here
\ACKNOWLEDGMENT{We would like to express our sincere gratitude to the editorial team for their  insightful comments, which significantly improved the quality of the paper.}

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\theendnotes


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\bibliography{ref_pandora}
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\input{main_body/tables_n_figures}

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\begin{APPENDICES}

\input{appendix/appendix}

\input{appendix/numerical_appendix}

\end{APPENDICES}

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