An Application of real-coded Genetic Algorithm (RCGA) for integer linear programming in Production-Transportation Problems with flexible transportation cost

In this paper, an application of real-coded Genetic Algorithm (RCGA) for integer linear programming in a production-transportation problem has been discussed. In this discussion, firstly, the model has been developed under the assumption that a company produces a single commodity in different factories, situated at different places. The raw material cost, production cost as well as marketing costs per unit are different for different factories. The transportation cost from a particular factory to a particular market is not fixed, but flexible It depends upon the transported units and the capacity of transport vehicle. Generally, when the number of transported units is above a certain limit, then the transportation cost for full load of vehicle will be charged, otherwise transportation cost is charged per unit. The mathematical formulation of the problem indicates that the model is an integer linear programming problem. In order to solve the problem, a real coded genetic algorithm (RCGA) for discrete values of decision variables with rank based selection, whole crossover and mutation has been developed. The proposed model has been solved using RCGA and illustrated with four different types of numerical examples.