The single-sink fixed-charge transportation problem (SSFCTP) consists in finding a minimum cost flow from a number of nodes to a single sink. Beside a cost proportional to the amount shipped, the flow cost encompass a fixed charge. The SSFCTP is an important subproblem of the well-known fixed-charge transportation problem. Nevertheless, just a few methods for solving this problem have been prop...

The Fixed Charge Transportation Problem (FCTP) is a generalization of the well-known Transportation Problem, where the cost for sending goods from origins to destinations is composed of a fixed cost and a continuous cost proportional to the amount of goods sent. In practical applications, the fixed costs may represent toll charges on highways, landing fees at airports, setup costs in production...

This paper presents a branching method for the solution of the fixed charge transportation problem. Starting with a linear formulation of the problem, we develop the method which converges to the optimal solution. The method is based on the computation of a lower bound and an upper bound embedded within a branching process. We present a detailed numerical example to illustrate the proposed meth...

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 ...

The fixed-charge transportation problem is a fixed-charge network flow problem on a bipartite graph. This problem appears as a subproblem in many hard transportation problems, and is also both a special case and a strong relaxation of the challenging bigbucket multi-item lot-sizing problem. In this paper, we provide a polyhedral analysis of the polynomially solvable special case in which the as...

—Competitive global markets oblige the firms to reduce their overall costs while maintaining the same customer service level and this can be achieved just through a precise and efficient management of their supply chain network. The Fixed Charge Transportation Problem (FCTP) which is a more comprehensive type of Transportation Problem (TP) has several applications from different aspects in this...

The bi-criteria fixed charge transportation problem is an extension of the classical transportation problem. The bi-criteria fixed charge transportation problem in a crisp environment is, often, not effective in dealing with imprecision or vagueness in the values of the problem parameters. To deal with such situations, it has been proposed that the parameters should be represented as fuzzy numb...

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...