Artificial immune system and sheep flock algorithms for two-stage fixed-charge transportation problem

Abstract

In this paper, we cope with a two-stage distribution planning problem of supply chain regarding fixed charges. The focus of the paper is on developing efficient solution methodologies of the selected NP-hard problem. Based on computational limitations, common exact and approximation solution approaches are unable to solve real-world instances of such NP-hard problems in a reasonable time. These approaches involve cumbersome computational steps in real-size cases. In order to solve the mixed integer linear programming model, we develop an artificial immune system and a sheep flock algorithm to achieve better solutions in comparison to earlier approaches. The evaluations are set up based on two phases; first, comparing performances of two proposed algorithms with two previous studies with the same data (two previously proposed genetic algorithm and ant colony optimization methods) and second, evaluating two proposed algorithms in larger instances. Computational studies reveal that the proposed algorithms present acceptable performance by achieving solutions that are more robust in a proper time.