Planning of a decentralized distribution network using bilevel optimization

• We consider distribution and manufacturing processes in decentralized supply chain.
• A bilevel optimization model for the hierarchical distribution problem is proposed.
• A fast and efficient hybrid evolutionary algorithm is proposed.
• An ad hoc chromosome encoding which stands for an upper bound of the depot delivery.
• Experiments demonstrate the valuable contribution of the new algorithm.

This paper proposes a bilevel optimization problem to model the planning of a distribution network that allows us to take into account how decisions made at the distribution stage of the supply chain can affect and be affected by decisions made at the manufacturing stage. Usually, the distribution network design problem decides on the opening of depots and the distribution from the depots to customers only and pays no attention to the manufacturing process itself. By way of example, the paper discusses the implications of formulating a bilevel model to integrate distribution and manufacturing, maintaining the hierarchy existing in the decision process. The resulting model is a bilevel mixed integer optimization problem. Hence, only small instances can be optimally solved in an acceptable computing time. In order to be able to solve the optimization model for realistic large systems, a metaheuristic approach based on evolutionary algorithms is developed. The algorithm combines the use of an evolutionary algorithm to control the supply of depots with optimization techniques to determine the delivery from depots to customers and the supply from manufacturing plants to depots. A computational experiment is carried out to assess the efficiency and robustness of the algorithm.