Prophet Inequalities and Approximation Schemes for a New Class of Overbooking Problems in Container Shipping

55 Pages Posted: 27 Jun 2022 Last revised: 24 Feb 2024

See all articles by Jacob Feldman

Jacob Feldman

Washington University in St. Louis - John M. Olin Business School

Panos Kouvelis

Washington University in St. Louis

Yukai Huang

Washington University in Saint Louis, John M. Olin Business School

Date Written: May 31, 2022

Abstract

In the airline industry, the practice of overbooking has been a celebrated operational tool that has led to revenue gains exceeding hundreds of millions of dollars when implemented correctly. By contrast, in the container shipping industry, the story of overbooking is filled with tales of chronic mistrust between shippers and carriers. Specifically, loose and unenforceable contracting practices have led to a failed market where shippers constantly renege on their agreement to produce containers as promised, and as a result, carriers overbook too frequently in an effort to hedge against this no-show behavior. The cost of such behaviors has been estimated to be in the range of $30-40 billion annually, which highlights the glaring need for a remedy to this issue. In this paper, we propose and study a deposit-based booking system that draws inspiration from current practices that have been shown to be successful in mitigating no-show behavior and overbooking in the container shipping industry. Specifically, we consider a reservation system where inquiring shippers book cargo space using a customized deposit. The carrier, upon accepting the shipper’s booking request, matches the shipper’s deposit with a deposit of their own of equal size. If either party reneges on the agreement, the defaulting party loses their deposit to the more trustworthy party. However, if both parties uphold their side of the deal, the deposits are returned in full to both sides. Under this booking mechanism, we study the carrier’s sequential online booking problem, which gives rise to a new class of revenue management problems with overbooking and no-show behavior that share only superficial commonalities with existing frameworks.

First, we consider the adversarial setting, wherein the liner is guaranteed to face the worst-case deposit sequence for whatever policy it chooses to implement. Next, we consider a less pessimistic variant of our online booking problem often referred to as the stochastic setting, where the liner is privy to distributional information regarding the potential deposit tuples that can surface in each period. In both settings, we develop simple and easy-to-implement policies, which achieve near best-case competitive ratios as the number of available slots tends to infinity. These theoretical developments are complemented by an extensive set of numerical experiments, where we test the efficacy of our proposed policies and find that their practical performance is not only near-optimal with regard to the profits they garner, but also from utilization and overbooking perspectives.

Keywords: Container shipping, overbooking, competive ratio

JEL Classification: C61

Suggested Citation

Feldman, Jacob and Kouvelis, Panos and Huang, Yukai, Prophet Inequalities and Approximation Schemes for a New Class of Overbooking Problems in Container Shipping (May 31, 2022). Available at SSRN: https://ssrn.com/abstract=4124363 or http://dx.doi.org/10.2139/ssrn.4124363

Jacob Feldman (Contact Author)

Washington University in St. Louis - John M. Olin Business School ( email )

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States

Panos Kouvelis

Washington University in St. Louis ( email )

One Brookings Drive
Campus Box 1156
St. Louis, MO 63130-4899
United States

HOME PAGE: http://www.panoskouvelis.info

Yukai Huang

Washington University in Saint Louis, John M. Olin Business School ( email )

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