This paper introduces a new approach to optimize the cost per unit of product for the Transportation Problem to achieve better outcomes. We present Basic Feasible Solution (BFS) approach compromised of five main steps: (1) Create a Matrix A = mod |Supply(si)-Demand(dj)| (2) Add the ...
The intuition behind an optimal transportation problem is rather clear. One aims at finding the best transportation plan γ⋆(x,y)γ⋆(x,y) to match 2 distributions psps and ptpt. The cost of the optimal plan gives the Wasserstein-distance: WD(ps,pt)=infγ∈Π∑C(x,y)γ(x,y)WD...
1.1 Monge Problem Diagram Monge Problem Equation minT{∑ic(xI,T(xi)):T♯α=β} T(Xi) 1.2 Kantorovich Relaxation Equation: Optimal TransportationSolution Formula: P is a map, which all row sum is alpha, all column sum is beta. C_{ij} is the transportation cost of transferring P_{ij}...
Optimal solution of a Monge-Kantorovitch transportation problem - Abdellaoui - 1998 () Citation Context ...at models and that of m-flat models. Let g0 and g1 be two gradient maps. The g-flat model connecting the two maps is p[(1− θ)g0 + θg1](x) and the m-flat model is...
A gradient descent solution to the Monge-Kantorovich problem[J]. Applied Mathematical Sciences, 2009, 3(22): 1071-1080. [7] Cuturi, Marco. "Sinkhorn distances: Lightspeed computation of optimal transport." Advances in neural information processing systems(NIPS). 2013. [8] Genevay, A., Cuturi...
A Method for Optimal Solution of Intuitionistic Fuzzy Transportation Problems via CentroidIn this work, we introduce the method for solving intuitionistic fuzzy transportation problem (IFTP) in which supplies and availability are crisp numbers and cost is intuitionistic fuzzy number (IFN). We are ...
The equivalent formulations are then used to give numerical approximations to the optimal partial transport problem , which comes from a variational problem. This method also provides at the same time active submeasures and the associated optimal transportation. 展开 ...
Finding an exact optimal solution of the Nonlinear Discrete Transportation Problem (NDTP) represents a challenging task in transportation science. Development of an adequate model formulation and selection of an appropriate optimization method are thus significant for attaining valuable solution of the ND...
Short Communication Distribution of 4'Epi-doxorubicin in human tissues We establish the exact complexity of these problems and develop optimal, in the run time sense, solution algorithms. A new and simple solution algorithm ... C Italia,L Paglia,A Trabattoni,... - 《Transportation Research Reco...
We study Monge's optimal transportation problem, where the cost is given by an 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...