Modeling and Solving a Multi-Stage Supply Chain Network Design Problem with Step Solid Transportation

In this article we append a conveyance as third dimension to the transportation in the supply chain.In , the fixed cost is proportional to the amount shipped. This cost structure causes the value of the objective function to behave like a step function. Then, a mathematical programming model is presented for the problem. To solve such a hard problem, two Metaheuristics, simulated annealing algorithm (SA) and genetic algorithm (GA) are provided. In addition, some crossover and mutation operators are proposed in GA. Due to the important role of operators and parameters on the algorithm’s property, a wide regularize in both SA and GA is carried out with the help of a set of experimental design. Through extensive computational experiments, appropriate operator and parameter values of the proposed algorithms were chosen. The efficiency of employed parameters is measured by the Taguchi experimental design method that is a useful approach to tune the parameters and reduce the possible number of experiments in this research area. For this purpose, Sixty three problems with different configuration have been generated at random and then the effectiveness of the proposed algorithms was evaluated using the relative percentage deviation method. To evaluate the performance of proposed algorithms, various problem sizes are considered and the computational results are analyzed. Finally, the impact of the rise in the problem size on the performance of the algorithms is investigated. The results showed that the GA was more robust and consistently outperformed SA for all instances.