Field Experiments on Seasonal Products and Markdown Pricing - Draft coming soon
Marcelo Gallardo and Carlos Noton.
Abstract | Coming soon
Preprints available
Congestion and Penalization in Optimal Transport Marcelo Gallardo, Manuel Loaiza, and Jorge Chávez.
Abstract | Pre-print
We propose a new model that transforms the classical discrete optimal transport framework by incorporating heterogeneous congestion costs and replacing traditional equality constraints with weighted penalization terms. The resulting formulation is a strictly convex optimization problem that better captures demand–supply imbalances in economic matching contexts and the congestion phenomenon. We first introduce the model and establish existence and uniqueness of the optimal transport plan under general conditions. For interior solutions, we present two analytical methods—based on the Neumann series expansion and the Sherman–Morrison formula—and develop a practical $O((N+L)N^2L^2)$ algorithm for computing the optimum. We then address the case of infinitely many types, corresponding to optimal transport on measure spaces, absolutely continuous with respect to Lebesgue, and prove existence and uniqueness under reasonable assumptions via infinite-dimensional optimization methods. Finally, we illustrate the applicability of our framework with examples from Peru’s health and education sectors, showing how it yields allocation patterns that differ from classical approaches and provide more accurate predictions. Pre-print in arXiv differs from the last version.
Heterogenous Quadratic Regularization in Optimal Transport Marcelo Gallardo, Manuel Loaiza and Jorge Chávez.
Abstract | Pre-print
In this paper, we build upon the optimal transport quadratic regularization model to develop a framework that incorporates congestion costs, particularly in matching within the healthcare and education sectors. Specifically, we introduce a model with heterogeneous quadratic costs. We analyze the model's properties under specific cases, extending the existing literature. Furthermore, we explore key structural characteristics of the model and provide numerical examples illustrating why this formulation more accurately captures real-world phenomena, particularly in the Peruvian context. The main result consists of identifying a specific type of corner solution when matching the same number of clusters, i.e., N=L.
Irregular wave dynamics driven by a random force within the Burgers equation
Marcelo Gallardo and Marcelo Flamarion.
Abstract | Pre-print available under request
In this article, we study the classical Burgers equation as a model for random fields. First, we consider initial data defined as a sum of harmonics with random phases and compute the blow-up time. Several simulations are performed, revealing that, while the critical blow-up time is approximately distributed according to a Gaussian law, the statistical tests reject the normality hypothesis. For the viscous case, we analyze waves driven by a random force. Using the Cole-Hopf transformation, the averaged wave field is computed numerically. Through a change of variables, we demonstrate that randomness primarily affects the phase of the wave field. Assuming the phase follows a uniform distribution, we show that the averaged field spreads and diminishes over time.