In this paper, we study the optimal transportation on the hemisphere, with the cost function c(x, y) = 1 2 d(x, y), where d is the Riemannian distance of the round sphere. The potential function satisfies a Monge-Ampère type equation with natural boundary condition. We obtain the a priori oblique estimate without using any uniform convexity of domains, and in particular for two dimensional case...

A classical problem of transporting mass due to Monge and Kantorovich is solved. Given measures μ and ν on Rd, we find the measure-preserving map y(x) between them with minimal cost — where cost is measured against h(x − y) with h strictly convex, or a strictly concave function of |x − y|. This map is unique: it is characterized by the formula y(x) = x − (∇h)−1(∇ψ(x)) and geometrical restrictio...

We study Monge’s optimal transportation problem, where the cost is given by optimal control cost. We prove the existence and uniqueness of an optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures with respect to Lebesgue, and most importantly the absence of sharp abnormal minimizers. In particular, this result is applicable in the case of subriem...

the linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conicting in nature. this paper presents an application of fuzzy goal programming to the linear multiobjective transportation problem. in this paper, we use a special type of nonlinear (hyperbolic and exponential) membership functions to ...

This paper presents an approach for finding an optimal schedule of n-jobs and m-machines flowshop scheduling problem involving transportation time between jobs by using neural networks. An algorithm has been given for finding the optimal sequence in scheduling problem without transportation time [2]. Here, this algorithm is applied when transportation times are involved between machines to find...

In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is intuitively some kind of multistep transportation. Applications are given for construction of multifractal random changes of times and to the existence of random metr...

Solution of a fuzzy transportation problem determines the transportation schedule that minimizes the total fuzzy transportation cost while satisfying the availability and requirement limits. A number of methods have been devised to solve a fuzzy transportation problem, but the solution obtained by some methods is not optimal. Obviously, the method which gives the optimal solution should be pref...

An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transport...

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on each geodesic are continuous. It is known that...

A new algorithm namely, fuzzy zero point method is proposed for finding a fuzzy optimal solution for a fuzzy transportation problem where the transportation cost, supply and demand are trapezoidal fuzzy numbers. The optimal solution for the fuzzy transportation problem by the fuzzy zero point method is a trapezoidal fuzzy number. The solution procedure is illustrated with numerical example. Mat...