Transportation problem is a linear programming which considers minimum cost for shipping a product from some origins to other destinations such as from factories to warehouse, or from a warehouse to supermarkets. To solve this problem simplex algorithmis utilized. In real projects costs and the value of supply and demands are fuzzy numbers and it is expected that optimal solutions for determining the value of commodities transported from a source to a destination be obtained as a fuzzy. So the first idea is to present the in the full fuzzy condition and then an algorithmwhich is of importance for solving such a problem. In this article, a new algorithm is suggested for solving fully fuzzy transportation problem. This algorithm transforms the fully fuzzy transportation problem into a triple-objective problem and then it utilizes a weighted method for solving multi-objective problems and solves the new problem using simplex transportation method. At the end, the suggested method is utilized for the real data.

In classical transport models, it is always assumed that parameters such as the distance from each supply node to each demand node or the cost of transferring goods from one node to another, as well as quantities such as supply and demand are definite and definite amounts. But in real matters, considering these assumptions is not logical. On the other hand, there may be a real problem in mathematical modeling with a variety of ambiguities in data simultaneously. In this paper, we consider a transport problem in which two types of fuzzy and grey data appear simultaneously. In the model under study, it is assumed that the coefficients of the grey objective function and the fuzzy supply and demand quantities are assumed. In this paper, we prove that by whitening grey numbers and defuzzification of the fuzzy numbers, the original problem can be turned into a crisp transport problem. Finally, with a numerical example, we describe the proposed method.

In the literature hardly any attention is paid to solving a fuzzy fixed charge transportation problem. In this paper, we consider the fully fixed-charge transportation problem and try to find both the lower and upper bounds on the fuzzy optimal value of such a problem in which all of the parameters are triangular fuzzy numbers. To illustrate the proposed method, a numerical example is presented.

Transportation costs today are considered as one of the most important costs affecting the cost of goods and the final price of consumption for the customer, especially in supply chain management. Therefore, it is necessary to focus on transportation costs due to lower prices, and consequently increase customer satisfaction and increase the position of the industry among competitors. Given that the available resources (capacity of supply centers) are generally considered as the minimum capacity available in the model, generally to solve such models, first the fuzzy supply limit is definitively converted and then using methods. The existing solution is a crisp problem that unfortunately does not fit well with the nature of the uncertainty in the decision. Therefore, in this paper, in order to adapt to the real conditions, the supply constraint in the flexible fuzzy transportation model is studied. For this purpose, a fuzzy mathematical programming approach to the transportation problem with flexible fuzzy constraints is proposed to obtain the most satisfactory solution. Finally, a numerical example for the proposed model and the proposed solution method is considered.

Transportation costs today are considered as one of the most important costs affecting the cost of goods and the final price of consumption for the customer, especially in supply chain management. Therefore, it is necessary to focus on transportation costs due to lower prices, and consequently increase customer satisfaction and increase the position of the industry among competitors. Given that the available resources (capacity of supply centers) are generally considered as the minimum capacity available in the model, generally to solve such models, first the fuzzy supply limit is definitively converted and then using methods. The existing solution is a crisp problem that unfortunately does not fit well with the nature of the uncertainty in the decision. Therefore, in this paper, in order to adapt to the real conditions, the supply constraint in the flexible fuzzy transportation model is studied. For this purpose, a fuzzy mathematical programming approach to the transportation problem with flexible fuzzy constraints is proposed to obtain the most satisfactory solution. Finally, a numerical example for the proposed model and the proposed solution method is considered.

Numerous algorithms have been proposed to solve the shortest path problem; many of them consider a single-mode network and crisp costs. Other attempts have addressed the problem of fuzzy costs in a single-mode network, the so-called fuzzy shortest-path problem (FSPP). The main contribution of the present work is to solve the optimum path problem in a multimodal transportation network, in which the costs of the arcs are fuzzy values. Metropolitan transportation systems are multimodal in that they usually contain multiple modes, such as bus, metro, and monorail. The proposed algorithm is based on the path algebra and dioid of k-shortest fuzzy paths. The approach considers the number of mode changes, the correct order of the modes used, and the modeling of two-way paths. An advantage of the method is that there is no restriction on the number and variety of the services to be considered. To track the algorithm step by step, it is applied to a pseudo-multimodal network.

Nowadays, the production scheduling systems are integrated by different transportation networks, e.g., airplanes, trains, and ships.Although the integrated air transportation and production scheduling problem is modelled with different factors, according to the literature reports, a fuzzy environment along with capacitated transportation systems has been scarcely considered. These facts motivate our attempts to contribute to a new formulation of this problem while considering the aforementioned suppositions. Another contribution of this study is to apply a number of nature-inspired metaheuristics.Accordingly, not only Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are used as famous metaheuristic algorithms existing in the literature, but also two recent ones, namely, Keshtel Algorithm (KA) and Virus Colony Search (VCS), are considered for the first time in the literature. In addition, the Taguchi experimental design method is utilized to tune the algorithms’ parameters. By generating different test problems, KA reveals a better performance when solving large-sized samples, in comparison to other metaheuristics.

The railway transportation planning under the fuzzy environment is investigated in this paper. As a main result, a new modeling method, called minimum risk chance-constrained model, is presented based on the credibility measure. For the convenience ofs olving the mathematical model, the crisp equivalents ofc hance functions are analyzed under the condition that the involved fuzzy parameters are trapezoidal fuzzy variables. An approximate model is also constructed for the problem based on an improved discretization method for fuzzy variables and the relevant convergence theorems. To obtain an approximate solution, a tabu search algorithm is designed for the presented model. Finally, some numerical experiments are performed to show the applications ofthe model and the algorithm.

The most convenient models of Solid Transportation (ST) problems have been justly considered a kind of uncertainty in their parameters such as fuzzy, grey, stochastic, etc. and usually, they suggest solving the main problems by solving some crisp equivalent model/models based on their proposed approach such as using ranking functions, embedding problems etc. Furthermore, there exist some shortcomings in formulating the main model for the realistic situations, since it omitted the flexibility conditions in their studies. Hence, to overcome these shortages, we formulate these conditions for the mentioned these problems with fuzzy flexible constraints, where there are no exact predictions for the values of the resources. In particluar, numerical investigation shows that each increasing for the values of the supply and demand is not effective for improving the objective function.  The value of the objective function is sensitive when supply and demand change, so we conduct a new study to diversify the value of the objective function, due to changes in resource and demand levels simultaneously.