A set of efficient heuristics and metaheuristics to solve a two-stage stochastic bi-level decision-making model for the distribution network problem

The performance of supply chain systems directly depends on the design of distribution networks. On the other hand, uncertainty is one of important and challenging subjects in distribution networks. Another real supposition is that the decisions in a distribution network are usually adopted in a hierarchical manner. By adopting these topics and contrary to previous works, this study firstly develops a two-stage stochastic bi-level decision-making model to simulate the behavior of a distribution network, more efficiently. Generally, the proposed problem is based on the static Stackelberg game between the Distribution Centers (DCs) in the upper-level and Customer Zones (CZs) in the lower-level of the model. Due to the uncertainty of the proposed problem, a financial risk model has been considered as well. The literature reveals that the most of different exact methods are not recommended to solve the bi-level models for large-scale problems. Another contribution of this study is to propose a set of quick heuristics along with two new hybrid metaheuristics based on the benefits of recent and traditional algorithms to solve the developed model in large-scale networks. In order to check the quality of algorithms' results, an explicit enumeration algorithm structured by ε-constraint method is considered in small sizes. A comparative study reveals that although the proposed heuristics reach the optimal solution in less time, the solution quality of hybrid metaheuristics is strongly better than others. Finally, the efficiency of the proposed model is validated by a set of sensitivity analyses through a real industrial example.