At the time of natural disasters occurrence, prompt responding and providing required items to affected areas is the most urgent priority. Moreover, given a stochastic nature of the crisis severity and the number of the affected areas, effective planning is a crucial task. In this study, two major steps in the disaster management cycle, namely preparation and response phases, are formulated using a Multi-Objective Mathematical Model under uncertainty. In the preparation phase, the optimum location of relief distributions, medical centers and inventories of relief goods to storage items received from suppliers are determined. Also, in the second step or response phase, the amount of relief goods transported from supply points to relief distribution centers and from these centers to affected areas as well as the number of injured people transferred to medical centers and hospitals through ambulances and aerial transportationare determined. Moreover, regarding the problem nature, its key parameters (e. g., demand and the number of injured people) are considered to be uncertain. Furthermore, given that the failureof facilities in both supplier and distributor sections can adverselyaffect their service provision, this issueisconsidered in the Model. To efficiently solve the Model, the non-dominated sorting genetic algorithm II (NSGA-II) and the Multi-Objective grey wolf optimizer (MOGWO) areused. Comparison of the results obtained from the proposed meta-heuristics with the exact solution method indicates that these algorithms can provide acceptable solutions in a reasonable amount of computational time.

Structure of runoff. rainfall Mathematical Model comprises of separation base flow discharge and determining infiltration, effective rainfall and direct runoff. These processes are calculated by various methods. Instantaneous unit hydro graph which Nash Model in its index sample has considered as a conceptual Model, applied widely in runoff. Rainfall Models. Here, the author produces a conceptual Mathematical Model with some proposed methods for determining separation processes of baseflow infiltration, effective rainfall runoff and direct runoff. Non. Linear Mathematical optimization is used for calculation of the Model's parameters. Performance results of the Model prove the superiority of the proposed method over the other common ones. For doing the research, both methods of artificial neural networks and Mathematical optimization of instataneous unit hydrograph are used, because the artificial neural network only, requires a lot of information and the results may not always be obtainable, but an artificial neural network. Mathematical optimization combination makes possible a quick convergence and assured results.

Optimization of the product portfolio has been recognized as a critical problem in industry, manage-ment, economy and so on. It aims at the selection of an optimal mix of the products to o er in the target market. As a probability function, reliability is an essential objective of the problem which linear Models often fail to evaluate it. Here, we develop a multiobjective integer nonlinear constraint Model for the problem. Our Model provides opportunities to consider the knowledge transferring cost and the environmental e ects, as nowadays important concerns of the world, in addition to the classical factors operational cost and reliability. Also, the Model is designed in a way to simultane-ously optimize the input materials and the products. Although being to some extent complicated, the Model can be e ciently solved by the metaheuristic algorithms. Finally, we make some numerical experiments on a simulated test problem.

In this paper, modified laplace homotopy perturbation method(LHPM) is implemented to give approximate and analytical solutions of nonlinear ordinary differential equation systems Model for HIV infection . Mathematical Models have proven valuable in understanding the dynamics of HIV infection. By comparing these Models to data obtained from patients undergoing antiretroviral drug therapy, it has been possible to determine many quantitative features of the interaction between HIV, the virus that causes AIDS, and the cells that are infected by the virus. We apply modified LHPM by setting a perturbation parameter and an embedding parameter as the damping parameter. Fourth-order Runge-Kutta method (RK4) is used to evaluate the effectiveness of the proposed algorithm. When we do not know the exact solution of a given problem, generally we use the RK4 method for comparison since it is widely used and accepted. Comparison of the results with RK4 method is confirmed that modified LHPM performs with very high accuracy. Results show that modified LHPM is a very promising method for obtaining approximate solutions to the Model for HIV. The results validate the accuracy and efficiency of the proposed method for the approximate solution of the HIV infection Model.

Supplier selection is one of the main discussions in the Supply Chain. The issue of assigning purchase orders to suppliers that act differently in terms of quality, cast, services, etc. criteria is one of the significant concerns of purchase managers in the supply chain. To adopt an optimal decision in this regard is related to a Multi-Objective problem that the objectives are contradicting each other and have different importance and priority depending on the location. In practice, the existence of kind of ambiguity in explaining the information related to the problem constraints and complicated. In this regard, the emergence of Fuzzy set theory as a tool to describe such conditions besides presenting question Model realistically can help to solve such problems well. Despite the importance of the Model with the mentioned structure, unfortunately, few original works have been done in this field. As a result, in this paper, in addition to presenting a new Multi-Objective Fuzzy Model being Modelled based on assigning purchase order to suppliers in a supply chain a solution method is introduced based on using Fuzzy linear programming. To clarify solution process Modelling and description, a case study is included related to selecting flour supplier for providing industrial bread of Khoshkar factory. The proposed Model includes four objective functions: Aggregate costs of minimizing type, Services of maximizing type (such as packing, being faithful to promise, factory heath, discount, correct transportation, good relationships, honestly, etc.), Flour useful survival of maximizing type (regarding monthly flour buying by the factory), The purchased flour quality of maximizing type (concerning product type).  Especially in the solution process, a method is determined based on setting weight for each of the objectives concerning the major factory stockholders.

The sewer layout in flat areas significantly influences the construction and operational costs as well as reliability of the network performance. To find an optimum design of sewer networks for flat areas, this study presents a Multi-Objective optimization problem with the objective functions of 1- the cost and 2- the reliability. The reliability criterion is defined as the effect of a clogging in a sewer on its upstream population. To solve the problem, the NSGA-II Algorithm is coupled to two self-adaptive design algorithms for generating the layout and sizing of sewers. A case study is solved using the proposed Model to demonstrate its application and advantages.

Algebraic hyperstructures have many applications in various sciences. The main purpose of this paper is to provide a new application of weak hyperstructures in Chemistry. The Motivation for the study of hyperstructures comes from chemical reactions. By hyperstructures theory, we provide Mathematical Models for chemical reactions. We study chemical hyperstructures of standard reduction potentials for consecutive oxidation states of elements of Cm; Er; Pm; Mg; Tm; Au and Cf.