In this paper, we develop the fuzzy fixed charge transportation problem when the costs are the fuzzy numbers. The first step it transform into the classical fuzzy transportation problem. The next, we obtain the best approximation fuzzy on the optimal value of the fuzzy fixed-charge transportation problem. This method obtains a lower and upper bounds both on the fuzzy optimal value of the fuzzy ...

In this paper, a step fixed charge transportation problem is developed where the products are sent from the sources to the destinations in existence of both unit and step fixed-charges. The proposed model determines the amount of products in the existing routes with the aim of minimizing the total cost (sum of unit and step fixed-charges) to satisfy the demand of each customer. As the problem i...

In the present paper the step fixed charge transportation problem under uncertainty, particularly when variable and fixed cost are given in fuzzy forms, is formulated. In order to solve the problem, two metaheuristic, simulated annealing algorithm (SA) and variable neighbourhood search (VNS), are developed for this NP-hard problem. Due to the significant role of parameters and operators on the ...

We consider a class of fixed-charge transportation problems over graphs. We show that this problem is strongly NP-hard, but solvable in pseudo-polynomial time over trees using dynamic programming. We also show that the LP formulation associated to the dynamic program can be obtained from extended formulations of single-node flow polytopes. Given these results, we present a unary expansion-based...

In this paper, we consider the step fixed-charge transportation problem (FCTP) in which a step fixed cost, sometimes called a setup cost, is incurred if another related variable assumes a nonzero value. In order to solve the problem, two metaheuristic, a spanning tree-based genetic algorithm (GA) and a spanning tree-based memetic algorithm (MA), are developed for this NP-hard problem. For compa...

in this paper, we consider the fuzzy fixed-charge transportation problem (ffctp). both of fixed and transportation cost are fuzzy numbers. contrary to previous works, electromagnetism-like algorithms (em) is firstly proposed in this research area to solve the problem. three types of em; original em, revised em, and hybrid em are firstly employed for the given problem. the latter is being firstl...

In this paper, we consider the fuzzy fixed-charge transportation problem (FFCTP). Both of fixed and transportation cost are fuzzy numbers. Contrary to previous works, Electromagnetism-like Algorithms (EM) is firstly proposed in this research area to solve the problem. Three types of EM; original EM, revised EM, and hybrid EM are firstly employed for the given problem. The latter is being firstl...