A genetic algorithm for solving the fixed‐charge transportation model: Two‐stage problem

Transportation of goods in a supply chain from plants to customers through distribution centers (DCs) is modeled as a two‐stage distribution problem in the literature. In this paper we propose genetic algorithms to solve a two‐stage transportation problem with two different scenarios. The first scenario considers the per‐unit transportation cost and the fixed cost associated with a route, coupled with unlimited capacity at every DC. The second scenario considers the opening cost of a distribution center, per‐unit transportation cost from a given plant to a given DC and the per‐unit transportation cost from the DC to a customer. Subsequently, an attempt is made to represent the two‐stage fixed‐charge transportation problem (Scenario‐1) as a single‐stage fixed‐charge transportation problem and solve the resulting problem using our genetic algorithm. Many benchmark problem instances are solved using the proposed genetic algorithms and performances of these algorithms are compared with the respective best existing algorithms for the two scenarios. The results from computational experiments show that the proposed algorithms yield better solutions than the respective best existing algorithms for the two scenarios under consideration.