Monge Properties, Optimal Greedy Policies, and Policy Improvement for the Dynamic Stochastic Transportation Problem

54 Pages Posted: 10 Nov 2017 Last revised: 6 Sep 2019

See all articles by Alexander Estes

Alexander Estes

University of Minnesota - Institute for Mathematics and its Applications

Michael O. Ball

University of Maryland - Decision and Information Technologies Department

Date Written: September 6, 2019

Abstract

We consider a dynamic, stochastic extension to the transportation problem. For the deterministic problem, there are known necessary and sufficient conditions under which a greedy algorithm achieves the optimal solution. We define a distribution-free type of optimality and provide analogous necessary and sufficient conditions under which a greedy policy achieves this type of optimality in the dynamic, stochastic setting. These results are used to prove that a greedy algorithm is optimal when planning a type of air traffic management initiative. We also provide weaker conditions under which it is possible to strengthen an existing policy. These results can be applied to the problem of matching passengers with drivers in an on-demand taxi service. They specify conditions under which a passenger and driver should not be left unassigned.

Keywords: transportation problem, Monge property, greedy policy, distribution-free optimization, stochastic optimization, combinatorial optimization

JEL Classification: C61

Suggested Citation

Estes, Alexander and Ball, Michael O., Monge Properties, Optimal Greedy Policies, and Policy Improvement for the Dynamic Stochastic Transportation Problem (September 6, 2019). Available at SSRN: https://ssrn.com/abstract=3067130 or http://dx.doi.org/10.2139/ssrn.3067130

Alexander Estes (Contact Author)

University of Minnesota - Institute for Mathematics and its Applications ( email )

425 Lind Hall
207 Church St SE
Minneapolis, MN 55455
United States

HOME PAGE: http://asestes1.github.io

Michael O. Ball

University of Maryland - Decision and Information Technologies Department ( email )

Robert H. Smith School of Business
4313 Van Munching Hall
College Park, MD 20815
United States
301-405-2227 (Phone)
301-405-8655 (Fax)

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
50
Abstract Views
305
PlumX Metrics