Heuristic approaches to solve the fixed-charge transportation problem with discount supposition

The fixed-charge transportation problem (FCTP) is one of important and classical transportation problems with many real-world applications in the area of logistics and supply chain management. Due to nature complexity of this problem, the literature has seen a large number of heuristics and meta-heuristics to solve the FCTP. This paper proposes a new heuristic along with well-known meta-heuristics to solve the FCTP with discount supposition on both fixed and variable charges. In addition, two models with all-units discount and incremental discount are firstly introduced in this study to apply the discount mechanism. As such, since the previous researchers mainly used spanning tree-based and priority-based representations, this study utilizes both of these methods and compared the results. Finally, a comprehensive discussion based on the computational results of heuristic and meta-heuristics with different encoding approaches has been investigated through different problem sizes.