Characterizing the Structure of Optimal Stopping Policies

Production and Operations Management, 25 (11) pp. 1820-1838, 2016

19 Pages Posted: 13 Nov 2015 Last revised: 14 Oct 2017

See all articles by Sechan Oh

Sechan Oh

IBM Research

Özalp Özer

Jindal School of Management - The University of Texas at Dallas

Date Written: October 13, 2015

Abstract

This paper studies a stochastic model of optimal stopping processes that arise frequently in operational problems (e.g., when a manager needs to determine an optimal epoch to stop a process). For such problems, we propose an effective method that characterizes the structure of the optimal stopping policy for the class of discrete-time optimal stopping problems. Using the method, we also provide a set of metatheorems that characterize when a threshold or control-band type stopping policy is optimal. We show that our proposed method can characterize the structure of the optimal policy for some stopping problems for which conventional methods fail to do so. Our method also simplifies the analysis of some existing results. In addition, the metatheorems help identify sufficient conditions that yield simple optimal policies when such policies are not generally optimal. We show the aforementioned benefits of our method by applying it to several optimal stopping problems frequently encountered, for example, in operations, marketing, finance and economics literature. We remark that structural results make an optimal-stopping policy easier to follow, describe, compute and hence implement. They also help understand how a stopping policy should respond to changes in the operational environment. In addition, structural results are critical for the development of efficient algorithms to solve optimal stopping problems numerically.

Keywords: optimal stopping, structure of optimal policy, threshold policy, control-band policy

Suggested Citation

Oh, Sechan and Özer, Özalp, Characterizing the Structure of Optimal Stopping Policies (October 13, 2015). Production and Operations Management, 25 (11) pp. 1820-1838, 2016. Available at SSRN: https://ssrn.com/abstract=1495366 or http://dx.doi.org/10.2139/ssrn.1495366

Sechan Oh

IBM Research ( email )

T. J. Watson Research Center
1 New Orchard Road
Armonk, NY 10504-1722
United States

Özalp Özer (Contact Author)

Jindal School of Management - The University of Texas at Dallas ( email )

Jindal School of Management
800 W. Campbell Road
Richardson, TX 75080
United States

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