Congestion and Penalization in Optimal Transport

Marcelo Gallardo, Manuel Loaiza, Jorge Chávez

Published 2024-10-10Version 1

In this paper we introduce two novel models derived from the discrete optimal transport problem. The first model extends the traditional transport problem by adding a quadratic congestion factor directly into the cost function, while the second model replaces conventional constraints with weighted penalization terms. We present theoretical contributions, including the study and characterization of interior and corner solution for some specific cases, convergence to the optimal solutions, as well as smooth comparative statics analysis. Finally, we propose an $O((N+L)(NL)^2)$ algorithm for computing the optimal plan for the penalized model assuming interior solutions.