Restricted Optimal Transportation Flows

Optimal Transportation Flows

Zeitschrift für Analysis und ihre Anwendungen ◽

10.4171/zaa/681 ◽

1995 ◽

Vol 14 (2) ◽

pp. 391-401 ◽

Cited By ~ 2

Author(s):

R. Klötzler

Keyword(s):

Optimal Transportation ◽

Transportation Flows

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Minimal surfaces as webs of optimal transportation flows∗

Optimization ◽

10.1080/02331930108844525 ◽

2001 ◽

Vol 49 (1-2) ◽

pp. 151-159

Author(s):

R. Klötzler

Keyword(s):

Minimal Surfaces ◽

Optimal Transportation ◽

Transportation Flows

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Optimal Transportation and the Falsifiability of Incompletely Specified Economic Models. Part I: Parametric Restrictions on Latent Variables

SSRN Electronic Journal ◽

10.2139/ssrn.1123824 ◽

2008 ◽

Author(s):

Alfred Galichon ◽

Marc Henry

Keyword(s):

Latent Variables ◽

Economic Models ◽

Optimal Transportation

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A Model for Developing Existing Ports Considering Economic Impact and Network Connectivity

Sustainability ◽

10.3390/su13073705 ◽

2021 ◽

Vol 13 (7) ◽

pp. 3705

Author(s):

Veterina Nosadila Riaventin ◽

Sofyan Dwi Cahyo ◽

Ivan Kristianto Singgih

Keyword(s):

Network Connectivity ◽

Economic Consequences ◽

Real Problem ◽

Container Transportation ◽

Container Ports ◽

Investment Priority ◽

Time Required ◽

Transportation Flows ◽

Port Clusters

This study discusses the problem of determining which container port should be developed within an existing network and when this should be carried out. A case study of Indonesia’s port network is presented, where several new ports are to be improved to ensure smooth interisland transportation flows of goods. The effects of the investment on economic consequences and increased network connectivity are assessed. When improving the ports, we consider that the available budget limits the investment. The network connectivity is evaluated by considering the number of reachable ports from the developed ports or transportation time required from other ports within the same port cluster. Based on our knowledge, our study is the first one that discusses the investment problem in multiple container ports under single management, as well as its effects regarding the increase in container flows. The problem is introduced and three mathematical models are proposed and used to solve a real problem. The results show that different models have different improved aspects of container transportation flows—e.g., a balanced improvement of the whole port network (Model 2) and appropriate investment priority for port clusters (Model 3).

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ON THE CONVERGENCE RATE OF POTENTIALS OF BRENIER MAPS

Econometric Theory ◽

10.1017/s0266466621000037 ◽

2021 ◽

pp. 1-37

Author(s):

Florian F. Gunsilius

Keyword(s):

Convergence Rate ◽

Poincaré Inequality ◽

Optimal Transportation ◽

Matching Theory ◽

Economic Research ◽

Poincare Inequality ◽

Optimal Transportation Problem ◽

Minimax Rate ◽

The Cost ◽

Kantorovich Problem

The theory of optimal transportation has experienced a sharp increase in interest in many areas of economic research such as optimal matching theory and econometric identification. A particularly valuable tool, due to its convenient representation as the gradient of a convex function, has been the Brenier map: the matching obtained as the optimizer of the Monge–Kantorovich optimal transportation problem with the euclidean distance as the cost function. Despite its popularity, the statistical properties of the Brenier map have yet to be fully established, which impedes its practical use for estimation and inference. This article takes a first step in this direction by deriving a convergence rate for the simple plug-in estimator of the potential of the Brenier map via the semi-dual Monge–Kantorovich problem. Relying on classical results for the convergence of smoothed empirical processes, it is shown that this plug-in estimator converges in standard deviation to its population counterpart under the minimax rate of convergence of kernel density estimators if one of the probability measures satisfies the Poincaré inequality. Under a normalization of the potential, the result extends to convergence in the $L^2$ norm, while the Poincaré inequality is automatically satisfied. The main mathematical contribution of this article is an analysis of the second variation of the semi-dual Monge–Kantorovich problem, which is of independent interest.

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