scholarly journals Rectifiability of Optimal Transportation Plans

2012 ◽  
Vol 64 (4) ◽  
pp. 924-934 ◽  
Author(s):  
Robert J. McCann ◽  
Brendan Pass ◽  
Micah Warren
Keyword(s):  
Continuous Mapping ◽  
Transportation Cost ◽  
Optimal Transportation ◽  
Regularity Of Solutions ◽  
Change Of Variables ◽  
Almost Everywhere ◽  
Optimal Transportation Problem ◽  
Sign Conditions ◽  
The Cost ◽  
Optimal Measure

Abstract The regularity of solutions to optimal transportation problems has become a hot topic in current research. It is well known by now that the optimal measure may not be concentrated on the graph of a continuous mapping unless both the transportation cost and themasses transported satisfy very restrictive hypotheses (including sign conditions on the mixed fourth-order derivatives of the cost function). The purpose of this note is to show that in spite of this, the optimal measure is supported on a Lipschitz manifold, provided only that the cost is C2 with non-singular mixed second derivative. We use this result to provide a simple proof that solutions to Monge's optimal transportation problem satisfy a change of variables equation almost everywhere.

scholarly journals ON THE CONVERGENCE RATE OF POTENTIALS OF BRENIER MAPS

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.

OPTIMAL FEASIBLE SOLUTIONS TO A ROAD FREIGHT TRANSPORTATION PROBLEM

2020 ◽  
Vol 5 (1) ◽  
pp. 456
Author(s):  
Tolulope Latunde ◽  
Joseph Oluwaseun Richard ◽  
Opeyemi Odunayo Esan ◽  
Damilola Deborah Dare
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Transportation Cost ◽  
North West ◽  
Life Problems ◽  
Basic Feasible Solutions ◽  
Feasible Solutions ◽  
Road Freight Transportation ◽  
The Cost ◽  
Cost Of Transportation

For twenty decades, there is a visible ever forward advancement in the technology of mobility, vehicles and transportation system in general. However, there is no "cure-all" remedy ideal enough to solve all life problems but mathematics has proven that if the problem can be determined, it is most likely solvable. New methods and applications will keep coming to making sure that life problems will be solved faster and easier. This study is to adopt a mathematical transportation problem in the Coca-Cola company aiming to help the logistics department manager of the Asejire and Ikeja plant to decide on how to distribute demand by the customers and at the same time, minimize the cost of transportation. Here, different algorithms are used and compared to generate an optimal solution, namely; North West Corner Method (NWC), Least Cost Method (LCM) and Vogel’s Approximation Method (VAM). The transportation model type in this work is the Linear Programming as the problems are represented in tables and results are compared with the result obtained on Maple 18 software. The study shows various ways in which the initial basic feasible solutions to the problem can be obtained where the best method that saves the highest percentage of transportation cost with for this problem is the NWC. The NWC produces the optimal transportation cost which is 517,040 units.

The estimated healthcare cost of diabetic retinopathy in Indonesia and its projection for 2025

2019 ◽  
Vol 104 (4) ◽  
pp. 487-492 ◽  
Author(s):  
Muhammad Bayu Sasongko ◽  
Firman Setya Wardhana ◽  
Gandhi Anandika Febryanto ◽  
Angela Nurini Agni ◽  
Supanji Supanji ◽  
...  
Keyword(s):  
Diabetic Retinopathy ◽  
Laser Treatment ◽  
Healthcare Cost ◽  
Cost Of Illness ◽  
Public Health Intervention ◽  
Transportation Cost ◽  
Population Based ◽  
State Budget ◽  
Illness Model ◽  
The Cost

PurposeTo estimate the total healthcare cost associated with diabetic retinopathy (DR) in type 2 diabetes in Indonesia and its projection for 2025.MethodsA prevalence-based cost-of-illness model was constructed from previous population-based DR study. Projection for 2025 was derived from estimated diabetes population in 2025. Direct treatment costs of DR were estimated from the perspective of healthcare. Patient perspective costs were obtained from thorough interview including only transportation cost and lost of working days related to treatment. We developed four cost-of-illness models according to DR severity level, DR without necessary treatment, needing laser treatment, laser +intravitreal (IVT) injection and laser + IVT +vitrectomy. All costs were estimated in 2017 US$.ResultsThe healthcare costs of DR in Indonesia were estimated to be $2.4 billion in 2017 and $8.9 billion in 2025. The total cost in 2017 consisted of the cost for no DR and mild–moderate non-proliferative DR (NPDR) requiring eye screening ($25.9 million), severe NPDR or proliferative DR (PDR) requiring laser treatment ($0.25 billion), severe NPDR or PDR requiring both laser and IVT injection ($1.75 billion) and advance level of PDR requiring vitrectomy ($0.44 billion).ConclusionsThe estimated healthcare cost of DR in Indonesia in 2017 was considerably high, nearly 2% of the 2017 national state budget, and projected to increase significantly to more than threefold in 2025. The highest cost may incur for DR requiring both laser and IVT injection. Therefore, public health intervention to delay or prevent severe DR may substantially reduce the healthcare cost of DR in Indonesia.

scholarly journals DAMPAK PERUBAHAN HARGA BAHAN BAKAR MINYAK (BBM) TERHADAP NILAI TUKAR PETANI (NTP) DI PROVINSI SULAWESI UTARA

2017 ◽  
Vol 13 (2A) ◽  
pp. 91
Author(s):  
Muhammad R. Ipango ◽  
Eyverson ., Ruauw ◽  
Nootje M. Benu
Keyword(s):  
Exchange Rate ◽  
Agricultural Production ◽  
Secondary Data ◽  
Transportation Cost ◽  
Fuel Oil ◽  
Fuel Price ◽  
Descriptive Research ◽  
North Sulawesi ◽  
The Cost ◽  
The Impact

This study aims to determine the impact of changes in increasing fuel price on Farmers Exchange Rate (NTP) in North Sulawesi Province. This study uses secondary data, mainly from the Central Bureau of Statistics (BPS) of North Sulawesi. Data collection was conducted for four months, from December 2016 until April 2017. The data used in this research is data from 2013 until 2016. The research method used in this research is descriptive research. The results showed that with the increase of Fuel Oil price is one of the factors that influence the Farmer's Farmer's Exchange Rate (NTP) as a whole by increasing the cost of household consumption, agricultural production cost, transportation cost, and transportation cost

scholarly journals ESTIMATED TRANSPORTATION COST OF LOW-TONNAGE LNG

2020 ◽  
Vol 17 (5) ◽  
pp. 130-163
Author(s):  
O. V. Tarovik ◽  
O. M. Mudrova
Keyword(s):  
Coastal Waters ◽  
Unit Cost ◽  
Transportation Cost ◽  
Model Calculations ◽  
Inland Waterways ◽  
Universal Approach ◽  
Environmental Requirements ◽  
Regression Relations ◽  
The Cost ◽  
Cost Of Transportation

Demand for low-tonnage transportation of LNG requires improved logistics. Assessing the value of all parts of the supply chain is an important component of solving the problem of optimizing transportation costs for both consumers and LNG suppliers. In connection with tightening of environmental requirements regarding bunker fuel, the task of optimizing the supply of LNG for water transport by the cost of transportation becomes particularly relevant.The objective of the study is to develop a universal approach to estimating the cost of transporting low-tonnage LNG for bunkering vessels in the Russian Federation.The research methodology is focused on the analytical method based on a system-structural approach.As part of the departmental project of the Russian Ministry of Industry and Trade «Development of  gaspowered fleet for navigation in coastal waters and inland waterways», the authors developed technical and economic models for calculating the unit cost of LNG transportation by road and water. To calculate the unit cost of LNG transportation by rail, the data of TMkarta information and reference system were used. Based on model calculations and data of TMkarta system, regression relations were obtained that allow one to determine the cost of transportation for various options of transport and technological schemes based on a limited set of parameters. An approach has also been proposed for estimating the cost of LNG transshipment. The regression ratios were tested for selected routes. As a result,conclusions were drawn about the most effective LNG transportation options.

Limit theorems for suprema, threshold-stopped random variables and last exits of i.i.d. random variables with costs and discounting, with applications to optimal stopping

1992 ◽  
Vol 24 (02) ◽  
pp. 241-266
Author(s):  
Douglas P. Kennedy ◽  
Robert P. Kertz
Keyword(s):  
Optimal Stopping ◽  
Limit Theorems ◽  
Continuous Mapping ◽  
Random Variables ◽  
Exit Times ◽  
Convergence Results ◽  
Process Convergence ◽  
Optimal Stopping Problems ◽  
The Cost ◽  
Linear Cost

For linear-cost-adjusted and geometric-discounted infinite sequences of i.i.d. random variables, point process convergence results are proved as the cost or discounting effect diminishes. These process convergence results are combined with continuous-mapping principles to obtain results on joint convergence of suprema and threshold-stopped random variables, and last-exit times and locations. Applications are made to several classical optimal stopping problems in these settings.

scholarly journals Nutrient Cost-Effectiveness of Fortified Blended Food Aid Products

2019 ◽  
Vol 40 (3) ◽  
pp. 326-339 ◽  
Author(s):  
Gregory K. Regier ◽  
Brian L. Lindshield ◽  
Nina K. Lilja
Keyword(s):  
Cost Effectiveness ◽  
Transportation Cost ◽  
Cost Effective ◽  
The United States ◽  
Food Aid ◽  
African Countries ◽  
Nutrient Value ◽  
Nutritional Data ◽  
The Cost ◽  
Blended Food

Background: Sorghum-Soy Blend (SSB) and Sorghum-Cowpea Blend (SCB) fortified blended food aid porridge products were developed as alternatives to Corn-Soy Blend Plus (CSB+) and Super Cereal Plus (SC+), the most widely used fortified blended food aid products. However, the cost and nutrient cost-effectiveness of these products procured from different geographical areas have not been determined. Objective: The objective of this study is to determine the nutrient cost-effectiveness of SSB and SCB compared to existing fortified blended foods. Methods: Nutritional data as well as ingredient, processing, and transportation cost for SSB, SCB, and existing fortified blended foods were compiled. Using the omega value, the ratio of the fortified blended food’s Nutrient Value Score to the total cost of the fortified blended food divided by an identical ratio of a different fortified blended food or the same fortified blended food produced in a different country and the nutrient cost-effectiveness of each of the fortified blended foods procured in the United States and several African countries were determined. Results: Both CSB+ and SC+ are less expensive than SSB and SCB, but they also have lower Nutrient Value Scores of 7.7 and 8.6, respectively. However, the omega values of CSB+ and SC+ are all above 1 when compared to SSB and SCB, suggesting that the existing fortified blended foods are more nutrient cost-effective. Conclusions: Comparing the nutrient cost-effectiveness of various food aid products could provide valuable information to food aid agencies prior to making procurement decisions.

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