A Benders decomposition approach for a real case supply chain network design with capacity acquisition and transporter planning: wheat distribution network

This paper considers a real case problem of supply chain network design inspired from a wheat distribution network in Iran. It generates a network with capacity acquisition and fleet management. The problem first is formulated as a mixed integer linear programming model. Then, a logic-based Benders decomposition algorithm is appropriately developed as the solution methodology. In the presented algorithm, the problem is decomposed into two models of master and subproblem. The master problem is improved by means of the preprocessing and valid inequalities. Moreover, three Benders cuts, one optimality and two feasibility cuts, are developed for the algorithm. The general and relative performance of the model and algorithm is experimentally evaluated. The wheat distribution system of Iran is considered here as the case study of this research. The model is developed based on Iran's wheat distribution system. All the results show that the algorithm significantly outperforms the mathematical model of the case study. For example, the algorithm solves 95% of the tested instances to optimality, yet the model solves 29%.