The Capacitated Multiple Allocation Hub Location Problem under Demand Uncertainty and Excess Capacity with Possibilistic Programing Approach

Facility location is a factor of competitiveness and demand satisfaction. Using a hub on the network can facilitate communication across the network and reduce costs. In the current study, with regards to demand uncertainty, operational costs of the hub, and building extra capacity in the hub it has been aimed to develop a mathematical programing model for the middle hub location problem with a certain capacity,. Due to the presence of the uncertainty in the problem’s parameters, the possibilistic programing approach which is a subset of fuzzy programing has been used. The proposed model has been investigated via GAMS software and the CPLX solver. Finally, the proposed model has been validated by the dataset obtained from Iran Aviation Dataset (IAD) for a round-trip, and the proper locations for facilities in each level and allocation of the customers to the facilities, were determined by the obtained Pareto analysis answer.

The Split Feasibility Problem with Some Projection Methods in Banach Spaces

In this paper, we study the split feasibility problem in Banach spaces. At first, we prove that a solution of this problem is a solution of the equivalent equation defined by using a metric projection, a generalized projection, and sunny generalized nonexpansive retraction, respectively. Then, using the hybrid method with these projections, we prove strong convergence theorems in mathematical programing in order to find a solution of the split feasibility problem in Banach spaces.

Chemical U-Th-Pb geochronology: A precise explicit approximation of the age equation and associated errors

In a single decaying system, the age determined from the exponential decay law is directly related to its linear Maclaurin approximation. This relationship can be additively extended to several decaying systems resulting in the same daughter element, by using proportionality functions, thus allowing an explicit formulation of the age as a function of element concentrations. The values of the binary proportionality function for the 238U-235U-Pb system and the ternary proportionality function for the 232Th-238U-235U-Pb system were determined by iterations of the exponential decay formula up to 4 Ga, with a step of 10 Ma, for a set of 24 different U/Th ratios. From the iteration data, the expressions of the two functions and the associated coefficients were determined by polynomial regression and mathematical programing on conveniently separated time and compositional intervals.Additional time- and composition-dependent age corrections optimized by mathematical programming of the residuals lead to an accuracy of 0.005 Ma of the resulting age. The error propagation can be traced through all the operations defined by explicit formulas according to simple error propagation rules, finally allowing the calculation of the standard error of the result. The formulas and parameters derived can be used in a calculation spreadsheet.