The Modified Hybrid Firefly Approach to the Two-Stage Fixed-Charge Transportation Problem
DOI:
https://doi.org/10.54536/ajiri.v5i4.8629Keywords:
Firefly Algorithm, Mixed-Integer Linear Programming, Optimum Solution, Two-Stage Fixed-Charge Transportation ProblemAbstract
The two-stage fixed-charge transportation problem (TS-FCTP) is a transportation problem in supply chain management. This problem considers determining the most cost-effective way to transport goods through an intermediate state, taking into account both the variable transportation costs and the fixed costs associated with opening or using different routes. Various methods have been used to obtain solutions in various ways, either heuristically or exact solutions. The aim of this research paper is to propose a more accurate algorithm for this purpose. TS-FCTP is an optimization problem of the mixed-integer linear programming (MILP) model. Accordingly, the proposed algorithm is presented as a hybrid based on MILP and the modified firefly model. Furthermore, the solution is obtained in Python to improve the computational efficiency. The robustness of the proposed algorithm is tested on twenty problems with node sizes ranging from seven to fourteen. The convergence behavior of the algorithm shows that the model reaches optimal solutions in reasonable computational time. This performance suggests that combining metaheuristics inspired by nature with mathematical programming can provide efficient solutions. Also, as an extension of this research, the goal is to develop a more accurate algorithm for large-scale TS-FCTP problems.
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